Add Batch 12040c63-bdd6-475f-b285-8471f31f9b8e data

.gitattributes

@@ -3876,3 +3876,67 @@ saved_model/**/* filter=lfs diff=lfs merge=lfs -text
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2024/LASA_ Instance Reconstruction from Real Scans using A Large-scale Aligned Shape Annotation Dataset/e66a9d83-37a7-45da-8099-3af5a6b6fd8b_content_list.json

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+        "text": "LASA: Instance Reconstruction from Real Scans using A Large-scale Aligned Shape Annotation Dataset",
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+        "text": "Haolin Liu $^{1,2*}$ , Chongjie Ye $^{1,2*}$ , Yinyu Nie $^{3}$ , Yingfan He $^{1,2}$ , Xiaoguang Han $^{2,1\\dagger}$",
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+        "text": "\\*equal contribution \\*corresponding author",
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+    },
+    {
+        "type": "text",
+        "text": "$^{1}$ FNii, CUHKSZ  $^{2}$ SSE, CUHKSZ  $^{3}$ Technical University of Munich",
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+        "text": "gap-lab-cuhk-sz.github.io/LASA",
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+        "text": "920 Scenes + 10,412 Unique CADs",
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+            "Figure 1. We introduce LASA, a Large-scale Aligned Shape Annotation Dataset containing 10,412 unique object CAD models aligned with 920 real-world scene scans. Supported by LASA, we achieve state-of-the-art in real-world object reconstruction and 3D object detection."
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+        "text": "Reconstruction Results",
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+        "type": "text",
+        "text": "Abstract",
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+        "text": "Instance shape reconstruction from a 3D scene involves recovering the full geometries of multiple objects at the semantic instance level. Many methods leverage data-driven learning due to the intricacies of scene complexity and significant indoor occlusions. Training these methods often requires a large-scale, high-quality dataset with aligned and paired shape annotations with real-world scans. Existing datasets are either synthetic or misaligned, restricting the performance of data-driven methods on real data. To this end, we introduce LASA, a Large-scale Aligned Shape Annotation Dataset comprising 10,412 high-quality CAD annotations aligned with 920 real-world scene scans from ArkitScenes, created manually by professional artists. On this top, we propose a novel Diffusion-based Cross-Modal Shape Reconstruction (DisCo) method. It is empowered by a hybrid feature aggregation design to fuse multi-modal inputs and recover high-fidelity object geometries (see Fig. 1). Besides, we present an Occupancy-Guided 3D Object Detection (OccGOD) method and demonstrate that our shape",
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+        "type": "text",
+        "text": "annotations provide scene occupancy clues that can further improve 3D object detection. Supported by LASA, extensive experiments show that our methods achieve state-of-the-art performance in both instance-level scene reconstruction and 3D object detection tasks.",
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+    {
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+        "text": "1. Introduction",
+        "text_level": 1,
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+        "text": "The widespread use of hand-held RGB-D sensors has facilitated the effortless acquisition of indoor scene scans. However, these scans often suffer from noises and incompleteness due to limitations in sensor accuracy, the complexity of indoor environments, and occlusion among objects. This further limits its applications in scenarios such as VR/AR and 3D industry where a complete and high-quality reconstruction is desired. This shortage absorbs great attention in 3D vision and graphics community, particularly in the realm of indoor instance-level scene reconstruction. In this task, the objective is to reconstruct the shapes of observed objects based on 3D scans or images captured by sensors. Many advances [8, 36, 56, 58, 61] have been seen by leveraging the power of deep learning methods for this task. They",
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+        "text": "CVF",
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+    {
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+        "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
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+    {
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+        "text": "20454",
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+    {
+        "type": "text",
+        "text": "are data-driven and demand a substantial number of paired scene scans and objects' CAD ground truths.",
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+    {
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+        "text": "Existing data-driven methods rely on two types of datasets. [1, 7-9, 19, 27, 39, 50, 52, 55-58] utilized synthetic datasets [5, 10, 15] by synthesizing images and scans that mimic real-world distributions. Synthetic data provides CAD models perfectly aligned with input observations (images or scans) though. Models trained on it are vulnerable to domain gaps from the real world [53] that could impair the generalizability. Scan2CAD[2] attempts to bridge this gap by annotating objects' CAD in real-world scene scans. However, their CADs are retrieved from a synthetic database [5] and their poses are manually adjusted to roughly align the object scans. However, retrieved shapes are often unlike the real observed objects, introducing shape misalignment issues. Many works [13, 18, 28, 32, 47, 48] using it as instance shape supervision are potentially biased with inferior alignment. In summary, The absence of a well-aligned real-world dataset barriers the further advancement of the community.",
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+    {
+        "type": "text",
+        "text": "To surmount this challenge, we present a new dataset LASA, a Large-scale Aligned Shape Annotation dataset that contains 10,412 high-quality instance CAD annotations meticulously crafted by skilled artists. Each CAD shape is designed and placed to precisely align with objects' scans from 920 real-world scene scans in ArkitScene [3]. We deliberately annotate objects in ArkitScene instead of ScanNet[11] because it provides scans obtained from both accurate Laser sensors and hand-held RGB-D sensors. The accurate Laser scan benefits high-quality and aligned manual annotations. Meanwhile, the less accurate scans from hand-held devices support research on reconstruction and completion using consumer-level devices.",
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+        "text": "A large-scale scan dataset with high-quality instance CAD annotations empowers many downstream applications. We first investigate how LASA benefits indoor instance-level scene reconstruction. Given an indoor scene, images and scene scans can be obtained through scanning. Typically, the initial step involves 3D object detection, after which the partial point clouds and multi-view images of each detected instance are acquired, serving as visual cues for subsequent shape reconstruction. Point cloud provides natural 3D information though, they are often noisy and incomplete. On the other hand, images present rich appearance clues but lack 3D constraints. Inspired by the complementary nature of these two modalities in describing object surfaces, we advocate utilizing both modalities as inputs to fuse their advantages. Recently, diffusion models have shown appealing performance in shape generation [7, 19, 44, 61, 64]. We advance it further for instance reconstruction and propose Diffusion-based Cross-modal Shape Reconstruction, namely DisCo. DisCo is a triplane diffusion model tailored to accommodate multi-modal in",
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+    {
+        "type": "text",
+        "text": "puts, towards robust real-world object reconstruction, where a hybrid feature aggregation layer is proposed to aggregate and align two input modalities effectively. Supported by the LASA dataset, extensive experiments show that our method achieves state-of-the-art reconstruction performance with real-world inputs.",
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+        "text": "Moreover, the LASA dataset has full annotations covering every instance within each of the 920 real-world scenes. This extensive coverage enables LASA to provide scene-level occupancy labels. We further explore how they can affect indoor scene 3D object detection. 3D Object detection [37, 42, 49] usually comprises a backbone and a detection head. We propose to integrate an occupancy prediction head for occupancy-guided 3D object detection, namely OccGOD. Our experiments demonstrate that incorporating occupancy prediction leads to substantial improvements in detection performance. In summary, our key contributions are four-fold:",
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+            "- We introduce a large-scale dataset, LASA. It contains 10,412 manually crafted, high-quality instance CAD annotations geometrically aligned with 920 real-world scene scans.",
+            "- We propose DisCo, a novel diffusion-based method that leverages hybrid representation, effectively interacting with both input partial point cloud and multi-view images, achieving state-of-the-art reconstruction.",
+            "- With LASA's scene-level annotation, we introduce occupancy-guided 3D object detection (OccGOD) with decent improvements.",
+            "- We strongly believe the large-scale dataset of well-aligned shape annotations can break the bottleneck of current research on 3D indoor scene understanding and reconstruction."
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+        "text": "2. Related Works",
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+        "text": "2.1. Indoor Instance Shape Dataset",
+        "text_level": 1,
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+    {
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+        "text": "Recently, many advances have been seen in learning-based 3D object and scene reconstruction from images and videos. However, numerous challenges persist due to the limitations of existing datasets.",
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+        "text": "These learning-based approaches are usually trained either on existing synthetic datasets or real-world datasets. While synthetic datasets are demonstrated valuable for training models, they lack realism. Large synthetic object collections like ShapeNet[5] and ABO[10] provide diverse 3D models but lack environment context. Synthetic scene datasets such as 3D-Front[14], Replica[45], and Structured3D[63] possess complete synthetic environments with CAD annotations for objects. However, models trained on these datasets often struggle to generalize with real inputs due to substantial domain gaps[53].",
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+        "type": "text",
+        "text": "Some works [2, 29, 34, 46, 53, 54] annotate CAD",
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+    {
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+        "text": "20455",
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+    {
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+        "img_path": "images/1494b02ad58fea5756601f0600a2e7bc6691b15a5a1c1927e6d5c051e16a2078.jpg",
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+        "table_body": "<table><tr><td>Dataset</td><td>Aligned</td><td>#Scenes</td><td>#CADs</td><td>Sensor Type</td><td>Annotation Method</td></tr><tr><td>Scan2CAD [2]</td><td>-</td><td>1,506</td><td>3,049</td><td>RGB-D</td><td>Retrieval</td></tr><tr><td>CAD-Estate [29]</td><td>-</td><td>19,512</td><td>12,024</td><td>RGB</td><td>Retrieval</td></tr><tr><td>IKEA [16]</td><td>✓</td><td>null</td><td>90</td><td>RGB</td><td>Retrieval</td></tr><tr><td>Pix3D [46]</td><td>✓</td><td>null</td><td>219</td><td>RGB</td><td>Retrieval</td></tr><tr><td>ScanSalon [53]</td><td>✓</td><td>413</td><td>800</td><td>RGB-D</td><td>Artist</td></tr><tr><td>Aria&#x27;s Digital Twin [34]</td><td>✓</td><td>2</td><td>370</td><td>RGB-D</td><td>Artist</td></tr><tr><td>LASA (Ours)</td><td>✓</td><td>920</td><td>10,412</td><td>RGB-D</td><td>Artist</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Table 1. Comparisons with existing 3D indoor datasets with instance shape annotations",
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+    {
+        "type": "text",
+        "text": "models on real-world data to bridge the domain gaps. Scan2CAD [2] and CAD-estate [29] have provided scanned object-CAD pairs by retrieving them from ShapeNet [5] and are further manually aligned to the real-world scenes. However, these retrieved CAD models lack alignment with real objects, potentially biasing data-driven reconstruction methods towards inferior reconstruction. This motivates us to build a real-world dataset with well-aligned CAD annotations. Aria's Digital Twin [34] and ScanSalon [53] provide such CADs though, the limited quantities restrict their application for data-hungry tasks. Datasets such as Pix3d [46] and PASCAL3D+ [54] supply single-view images with aligned shapes but are limited in scene modalities lacking point cloud and multi-view images.",
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+    {
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+        "text": "2.2. 3D Shape Reconstruction",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Object-level Reconstruction Existing approaches leverage images or partial point clouds as input. Images based reconstruction methods accept either single-view [6, 17, 19, 20, 25, 27, 30, 31, 33, 35, 50, 55, 57, 62, 64] or sparse multiview images [4, 9, 39, 56, 59] as inputs for shape reconstruction. They extract 2D image features and utilize them for shape reconstruction. Some [27, 43] leverage 2D pixel-aligned local features for reconstruction, demonstrating appealing performance for high-quality reconstruction. Other works [1, 8, 12, 26, 40, 52, 58, 61] conduct shape reconstruction from noisy, incomplete partial point clouds. Both paradigms have their advantages, with image-based methods perceiving rich 2D appearance features, while point-based methods process native 3D signals. [21] proposed to combine both inputs to fuse their advantages. Our proposed approach also accepts both inputs, focusing on effectively aggregating and aligning local features from both input sources. Since diffusion model [7, 19, 44, 51, 61, 64] have demonstrated strong capabilities in both shape generation and reconstruction, we opt for a diffusion model for robust and high-quality reconstruction.",
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+    {
+        "type": "text",
+        "text": "Instance-level Scene Reconstruction Recent instance scene reconstruction methods [13, 18, 21-23, 28, 32, 47, 48] follow a detect-then-reconstruct pipeline from a single scan. First, these methods use a 3D object detector to localize objects in either scene scans or videos. Subsequently, the detected 3D objects are fed into a 3D shape reconstruction",
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+    {
+        "type": "image",
+        "img_path": "images/a9e8e291f691372d1661d76b3bf441b41a5f83b739e2d63fbde559d6887cebf2.jpg",
+        "image_caption": [
+            "Figure 2. Visual comparison between aligned and unaligned CAD annotations"
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+    {
+        "type": "text",
+        "text": "module individually to obtain object shapes. Finally, the reconstructed 3D object shapes are placed back at their original locations to obtain a reconstruction of the full scene. These methods commonly utilize the Scan2CAD [2] dataset for training, where the inferior alignment limits their reconstruction quality. In contrast, the CAD models in our LASA dataset are manually crafted by artists to guarantee alignment, which we hope can lay a foundation for future research in this area.",
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+        "text": "3. LASA Dataset",
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+        "text": "LASA is a large-scale dataset that contains 10,412 unique CAD models covering 920 scenes across 17 categories. Rather than relying on a pre-existing CAD database to annotate scenes, LASA engages professional artists to manually create aligned CAD models with 3D scans. Our annotations provide precise and consistent (as shown in Fig. 2) training data for data-driven reconstruction algorithms.",
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+    {
+        "type": "text",
+        "text": "3.1. Data Annotation",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "LASA is built upon the 3D laser scans from ArkitScenes since it is accurate with high resolution, which is critical for",
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+    {
+        "type": "page_number",
+        "text": "20456",
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+    },
+    {
+        "type": "text",
+        "text": "high-fidelity CAD annotations.",
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+    },
+    {
+        "type": "text",
+        "text": "Data Preprocessing. Each laser scan from ArkitScenes is exceptionally dense with  $1\\mathrm{GB}+$  data storage. To improve annotation efficiency, we downsample the scans to a 4mm density. Since ArkitScenes does not publicly provide alignment transformations between the laser scans and the RGB-D scans, we utilize a coarse-to-fine registration method to calculate the transformation matrix (see our supplemental for details). With the transformation matrix, we align the laser data with the RGB-D sequence coordinates from ArkitScenes. We then use ArkitScenes' 3D bounding box annotations to partition the aligned laser point clouds for each single object. These segmented point clouds are transformed into the canonical space. Furthermore, for each object, we select 2-5 frames from RGB-D scans that maximize the 2D projection area of its 3D bounding box. These selected frames serve as references for annotation.",
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+    },
+    {
+        "type": "text",
+        "text": "Shape Annotation. The CAD annotation process involves a team of 35 artists working over 4 months. With preprocessed point clouds and reference images, each artist spent approximately 69 minutes designing a single model. Each model is annotated with Autodesk Maya or Cinema 4D.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Shape Verification. We involve a shape verification procedure for annotation quality control. This procedure has both algorithmic validation and manual reviews to thoroughly evaluate CAD model's accuracy against ground truth scans and images. Our multi-step verification process includes",
+        "bbox": [
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+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- Senior Review: After initial annotations, 6 senior designers reviewed every CAD model to verify quality, accuracy, and reliability by manually cross-checking against the 3D scans. Any models that failed to meet the standards were flagged for rework.",
+            "- Geometry Alignment: We matched the CAD models to aligned laser scans and calculated the unidirectional Chamfer distance between them. This quantified the raw geometric alignment error for the CAD surface compared to the ground truth scan.",
+            "- View Alignment: We also verified alignment in the pixel level, where we rendered 112,639 images across all scenes by positioning the CAD models in the view frustum of RGB-D sensors. Crowd workers performed a manual inspection to check if the rendered views overlay on the real images. They checked for inconsistencies along object edges and intricate details which would indicate misalignment. This pixel-level evaluation ensured precise alignment. Any rendering mismatches were fixed by re-annotating the CAD model."
+        ],
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2. Dataset Statistics",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Tab. 1 shows the statistics of LASA compared to the existing datasets. LASA contains a comparable number of unique CAD models to CAD-Estate [29], which was previously the largest scene CAD dataset. However, LASA pro",
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+    },
+    {
+        "type": "text",
+        "text": "vides better CAD annotation quality against their retrieved CAD models. Additionally, LASA demonstrates greater shape diversity than Scan2CAD [2], with over 3 times as many unique CAD models.",
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+    },
+    {
+        "type": "text",
+        "text": "Among all aligned datasets, LASA stands out with a total of 10,412 CADs. This is 13 times more than ScanSalon [53] and 28 times more than Aria's Digital Twin dataset[34]. Unlike IKEA [16] and Pix3D [46] which are annotated on single-view RGB images, LASA captures full RGB-D sequences. This enables a wider range of downstream applications compared to static image datasets.",
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+    },
+    {
+        "type": "text",
+        "text": "Furthermore, we compare LASA with Scan2CAD in terms of alignment quality by measuring the Chamfer distance between CAD annotation and the scene scans, which are 0.161 vs 0.269. LASA provides much better aligned data.",
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+    },
+    {
+        "type": "text",
+        "text": "4. Instance-level Scene reconstruction",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We propose a Diffusion-based Cross-modal Shape Reconstruction method (DisCo). DisCo is a diffusion-based model to pursue high-fidelity 3D shape reconstruction from partial point clouds and multi-view images. Various representation including latent sets [61], volumetric grids [7, 64], and triplanes [19, 39, 51] are popular choice for diffusion model. We opt for the triplane since its efficiency enables higher output resolution compared to volumetric grids; while reserving 3D structure compared to latent sets. We employ latent triplane diffusion, where a triplane variational auto-encoder (VAE) first encodes shape into triplane latent space (in Sec. 4.1). Subsequently, a triplane diffusion model operates on this latent space for 3D shape reconstruction conditioned on both partial points and multi-view images (in Sec. 4.2). The overall pipeline of DisCo is shown in the upper part of Fig. 3.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "It has been demonstrated that using multiple input modalities (images and scans) presents complementary benefits for semantic scene completion [21]. In DisCo, we also fuse image and point features and introduce Hybrid Feature Aggregation Layer (in Sec. 4.3). In this layer, we utilize a hybrid representation combining a triplane and a volumetric grid. This combination facilitates efficient local feature aggregation and feature alignment from both partial point clouds and multi-view images.",
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+    {
+        "type": "text",
+        "text": "4.1. Triplane Variational Auto-Encoder",
+        "text_level": 1,
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+        "type": "text",
+        "text": "To conduct a latent triplane diffusion, the first step is to learn an encoder capable of encoding shapes in a triplane latent space. The Triplane VAE [19] comprises an encoder  $\\psi_{enc}$  and a decoder  $\\psi_{dec}$ . The encoder processes inputs and encodes them into latent space, while the decoder recovers shape from the latent representation. Surface point cloud  $\\mathbf{P} \\in \\mathbb{R}^{K \\times 3}$  sampled from a ground truth shape, serves as inputs to  $\\psi_{enc}$ .  $K = 20,000$  in our experiment. These points are projected onto a triplane and subsequently processed by",
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+    {
+        "type": "page_number",
+        "text": "20457",
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+    {
+        "type": "image",
+        "img_path": "images/0b51d3c5063ba281352084f533b9cf9ce768d10f3b7df4ed39c53f869f3a8be0.jpg",
+        "image_caption": [
+            "Figure 3. Pipeline of our DisCo. Firstly, a triplane VAE model is trained to encode shape into triplane latent space (top-left). Subsequently, a triplane diffusion model is trained in this latent space for conditional shape reconstruction (top-right). A novel Hybrid Feature Aggregation Layer is proposed to effectively aggregate and align local features in both partial points cloud and multi-view images (bottom)."
+        ],
+        "image_footnote": [],
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+    },
+    {
+        "type": "text",
+        "text": "a PointNet to form a triplane feature map. Followed by a UNet [41], the encoder  $\\psi_{enc}$  outputs a normal distribution  $\\mathcal{N}(\\mu, \\sigma^2)$ , where  $\\mu, \\sigma \\in \\mathbb{R}^{H \\times W \\times 3 \\times C}$ . A latent triplane  $T_0 \\in \\mathbb{R}^{H \\times W \\times 3 \\times C}$  can be sampled from this distribution. The above process can be summarized as:",
+        "bbox": [
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nT _ {0} \\sim \\mathcal {N} (\\mu , \\sigma^ {2}) \\quad \\mu , \\sigma = \\psi_ {\\text {e n c}} (\\mathbf {P}) \\tag {1}\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "The occupancy field is chosen as the shape representation. The decoder  $\\psi_{dec}$  takes a point  $p$  in space and the triplane latent  $T_0$  as inputs, yielding the occupancy of this point. Specifically, A UNet model first refines  $T_0$  and outputs a triplane feature map. Then, point  $p$  is projected onto this triplane feature map, where features are sampled using bilinear interpolation. These sampled features are fed into MLPs which outputs the occupancy prediction  $\\tilde{o}$ . The training of the VAE model is supervised by reconstruction loss and KL divergence loss as  $\\mathcal{L}_{vae} = \\| \\tilde{o} - o_{gt} \\|_2^2 + \\lambda_{kl} \\mathcal{L}_{kl}$ . In our experiment,  $\\lambda_{kl} = 0.025$ . As in [51], the network layers in both  $\\psi_{enc}$  and  $\\psi_{dec}$  adopt 3d aware convolution for triplane processing.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The reconstruction is conducted in canonical object space. During training, augmentation such as random shifting, rotating and scaling are applied, so that it will be more robust to inaccurate objects' pose during inference.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "4.2. Triplane Diffusion for reconstruction",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Our approach employs latent triplane diffusion to reconstruct shapes based on partial point clouds and multi-view images as conditions. Specifically, a 2D UNet model serves as a denoise function  $D(\\cdot)$ . This model comprises cascades of residual convolutional block and Hybrid Feature Aggregation Layer with 3d aware convolution. we introduce a novel Hybrid Feature Aggregation Layer, designed to fos",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "ter effective interaction between local features derived from partial point clouds and multi-view images. We use continuous diffusion steps as in [24]. The forward diffusion process during training is defined as  $T_{\\sigma} = T_{0} + n$ , where  $n \\sim \\mathcal{N}(0, \\sigma^{2}\\mathbf{I})$ ,  $\\sigma$  indicates the diffusion steps, and also the deviation of the noise added. The denoise UNet takes a noisy triplane latent  $T_{\\sigma}$  as input, and outputs a denoised triplane latent  $T_{\\text{denoise}}$ . We follow the diffusion formulation in EDM [24], the objective function during training is:",
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+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbb {E} _ {\\sigma , n, T _ {0}} \\lambda_ {\\sigma} \\| D (T _ {0} + n, \\sigma , c) - T _ {0} \\| _ {2} ^ {2} \\quad n \\sim \\mathcal {N} (0, \\sigma^ {2} \\mathbf {I}) \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Here  $c$  denotes the conditional inputs. In our case, they are partial point clouds and multi-view images.  $\\lambda_{\\sigma}$  denotes a loss normalization factor. Inference can be conducted through sampling from noise triplane as in EDM [24].",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "During training our diffusion model, we implement a strategy to first pretrain on synthetic datasets, then fine-tune on LASA dataset. We leverage ShapeNet [5], ABO [10], and 3D-Future [15] dataset to synthesize partial point cloud and render images by embedding CAD models in HM3D scene[38, 60]. This strategy enhances both the robustness and the performance of our method, enabling more effective real-world object reconstruction.",
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.3. Hybrid Feature Aggregation Layer",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The objective of the Hybrid Feature Aggregation Layer is to aggregate and align local features from two input modalities to the triplane space. Points-triplane interaction is implemented by projecting points onto the triplane. However, such interaction becomes challenging when fusing images and triplanes. An alternative way is to expand the triplane into a volumetric grid and project the grids to images. This motivates us to propose this Hybrid Feature Aggregation",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "20458",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/b2962bb6dfcf0089acb16245acb467a1e1eba6736fd59b9b9ed51654a14b5b72.jpg",
+        "table_caption": [
+            "Table 2. Quantitative comparison on shape reconstruction. Evaluation metrics are mIoU / Chamfer L2 / F-score respectively. Higher mIoU and F-score are better while lower Chamfer L2 is better. Chamfer L2 is scaled by 1,000. LAS doesn't have mIoU value since it uses a surface occupancy representation."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>Chair</td><td>Sofa</td><td>Table</td><td>Cabinet</td><td>Bed</td><td>Shelf</td></tr><tr><td>IFNet</td><td>28.9 / 19.8 / 25.2</td><td>66.1 / 3.61 / 31.1</td><td>28.3 / 21.4 / 27.4</td><td>73.8 / 3.20 / 36.6</td><td>64.0 / 2.95 / 28.8</td><td>17.2 / 5.24 / 29.6</td></tr><tr><td>LAS-pts</td><td>- / 13.2 / 22.6</td><td>- / 4.47 / 22.9</td><td>- / 19.5 / 23.9</td><td>- / 4.81 / 22.1</td><td>- / 4.77 / 25.8</td><td>- / 4.70 / 26.8</td></tr><tr><td>LAS-pts+imgs</td><td>- / 10.7 / 24.1</td><td>- / 3.76 / 24.1</td><td>- / 15.7 / 24.6</td><td>- / 4.56 / 24.4</td><td>- / 4.58 / 26.5</td><td>- / 4.35 / 27.2</td></tr><tr><td>3DShape2VecSec</td><td>32.5 / 6.43 / 25.6</td><td>66.7 / 3.39 / 27.6</td><td>30.9 / 12.9 / 25.3</td><td>68.1 / 4.09 / 23.7</td><td>62.3 / 3.69 / 30.5</td><td>22.3 / 3.79 / 32.0</td></tr><tr><td>Ours-pts</td><td>33.4 / 5.68 / 26.6</td><td>68.8 / 3.21 / 29.0</td><td>38.0 / 10.5 / 32.2</td><td>72.3 / 3.63 / 36.5</td><td>54.0 / 2.97 / 34.1</td><td>23.2 / 3.68 / 36.5</td></tr><tr><td>Ours-pts+imgs</td><td>38.6 / 3.57 / 31.0</td><td>70.7 / 2.88 / 31.6</td><td>41.5 / 6.52 / 36.1</td><td>75.1 / 3.10 / 37.0</td><td>62.5 / 2.62 / 35.4</td><td>24.5 / 3.45 / 37.5</td></tr></table>",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Layer, introducing a hybrid representation that facilitates both points-triplane and images-triplane interactions.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "As in the bottom part of Fig. 3, inputs of this layer are partial point cloud  $\\tilde{P}$ , k posed images  $I_{i}, i \\in 1,2\\dots k$ , and triplane feature  $\\tilde{T}_l$  from the l-th convolutional layer. It begins with the aggregation of local features from partial points, achieved by projecting them onto the triplane and incorporating a PointNet layer. Image features map is first extracted using pretrained Vision Transformer. Then, the triplane expands into a volumetric grids  $G_{l} \\in \\mathbb{R}^{H \\times W \\times L \\times C}$ . The volumetric grids are then projected to k images using their camera poses, and image local features are sampled using bi-linear interpolation.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "To fuse features from multiple images, we employ a transformer. Specifically, the voxel feature serves as the query, while the sampled image feature serves as the key and value. The transformer outputs a volumetric grid attended with local image features from multi-view images. Finally, the volumetric grid is flattened back to a triplane by pooling, producing an output triplane feature map. This process ensures the effective aggregation and alignment of local features from diverse input modalities.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5. Occupancy-guided 3D Object Detection",
+        "text_level": 1,
+        "bbox": [
+            76,
+            618,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "3D object detection takes scene scans as input and parses the scene objects into 3D bounding boxes. In real-world scenarios, object scans are often incomplete and sparse due to occlusion, inaccurate sensors, and limited views during capture, making objects hard to recognize. To address it, we propose an Occupancy-Guided 3D Object Detection (OccGOD) approach that utilizes shape completeness prior for better scene understanding. We generate scene-level occupancy ground truth from LASA's fully-covered annotations. Specifically, scenes are partitioned into numerous  $384 \\times 384 \\times 96$  voxel grids, with a resolution of  $4 \\mathrm{~cm}$ . All CAD models are then placed back into the scene, on which the surface points are densely sampled at  $2 \\mathrm{~cm}$  intervals. Subsequently, we iterate through each point, marking their corresponding voxel to be occupied.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Our methodology follows a simple 'plug-and-play' manner. It is compatible with any detection method based on a 3D",
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "structured representation like volumetric grids [42, 49]. For ease of use, we built our OccGOD upon Cagroup3D [49]. In addition to the original backbone and bounding box prediction head, we introduce an occupancy head and augment the bounding box prediction head with another two output parameters for orientation regression. The occupancy heads takes backbone features as inputs, and output the occupancy of each voxel. More details of network design are in the supplemental. To further explore occupancy representations, we concatenate the features from the occupancy head with the backbone's features during ROI pooling for second-stage bounding box prediction. The occupancy head is supervised with a binary cross-entropy loss function with scene-level occupancy labels from LASA.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Our proposed OccGOD predicts a complete foreground structure to guide the bounding box detection. By leveraging the complete scene context, it achieves significant gains in detecting occluded and sparse objects compared to baseline methods.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "6. Experiment",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "6.1. Experiment Setup",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "For indoor object reconstruction, we employ mean Intersection over Union (mIoU), L2 chamfer distance, and  $1\\%$  F-score. We first normalize both results and ground-truth CAD into the interval from -0.5 to 0.5, and compute the above metrics between them. The experiment is conducted over 6 categories merged from 17 categories in LASA dataset.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "For 3D object detection, we assess mean average precision (mAP) and mean average recall (mAR) with an IoU threshold at 0.5. Evaluations for both object reconstruction and 3D object detection are performed on LASA's test set.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "6.2. Evaluation on Indoor Object Reconstruction",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "In this session, we compare our methods with existing baselines. We choose IFNet [8] and two state-of-the-art diffusion-based methods, LAS Diffusion [64] and 3DShape2VecSet [61], for comparison. We first pretrain all methods on synthetic dataset [5, 10, 15], then finetune them",
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+    },
+    {
+        "type": "page_number",
+        "text": "20459",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/55fedb28b91e3e2955b818b8399779d65cb623cd29c9364bf20d76ab3bd56183.jpg",
+        "image_caption": [
+            "Figure 4. Qualitative comparison between our method and IFNet, 3DShape2Vecset, and LAS."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "on LASA. IFNet and 3DShape2VecSet receive point clouds as inputs. For LAS Diffusion, we extend it into two versions: with point clouds as input (LAS-pts), and with both point clouds and images as input (LAS-pts+imgs). We compare them with our DisCo with two variants: 1) with partial point clouds only (Ours-pts); 2) with both modalities (Ours-pts+imgs). The quantitative and qualitative comparisons are shown in Tab. 2 and Fig. 4. Our method achieves state-of-the-art performance both quantitatively and qualitatively.",
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+    {
+        "type": "text",
+        "text": "6.3. Ablation Study",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Real-world Performance Boost using LASA We investigate the impact of our LASA dataset on real-world object reconstruction through three training setups: training from scratch on LASA (w/o pretrain), training on synthetic datasets only (w/o finetune), and pretraining on synthetic",
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+    {
+        "type": "text",
+        "text": "datasets followed by finetuning on LASA (full). The quantitative comparison is in Tab. 4. The table shows that finetuning on LASA significantly improves real-world reconstruction, with pretraining on synthetic data followed by finetuning on real strategy achieving the best performance.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Effectiveness of Hybrid Feature Aggregation Layer We verify the effectiveness of the Hybrid Feature Aggregation (HFA) layer in aggregating and aligning local features from both partial points and multi-view images. We compare it against not using the expanded grids to project onto the images. Specifically, the latter directly projects the triplane's pixels to the images. The quantitative comparison is shown in Tab. 5. The decent improvement of the HFA layer verifies its powerfulness in fusing multi-modal features.",
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+    {
+        "type": "text",
+        "text": "Robustness to inaccurate detection We further investigate how inaccurate detection results could affect the re",
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+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "20460",
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+    {
+        "type": "table",
+        "img_path": "images/061539d5c2725aad88f382663e3a43479da59098c0cc1d91d1361ab2b5e80c49.jpg",
+        "table_caption": [
+            "Table 3. Quantitative comparison between the state-of-the-art (CAGroup3D) and our OccGOD. Oriented bounding boxes are predicted. Evaluation metrics are mAP / mAR. Higher mAP / mAR indicates better performance."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>@IoU &gt; 0.50</td><td>Chair</td><td>Table</td><td>Cabinet</td><td>Refrigerator</td><td>Shelf</td><td>Bed</td><td>Sink</td><td>Washer</td><td>Bathtub</td></tr><tr><td>CaGroup3D</td><td>92.05 / 93.09</td><td>46.68 / 66.37</td><td>33.93 / 54.64</td><td>90.56 / 91.22</td><td>35.12 / 57.54</td><td>67.31 / 73.89</td><td>64.03 / 74.15</td><td>87.77 / 89.39</td><td>27.99 / 45.97</td></tr><tr><td>Our OccGOD</td><td>92.57 / 93.25</td><td>49.17 / 66.76</td><td>35.05 / 55.90</td><td>90.45 / 91.89</td><td>38.15 / 58.19</td><td>70.78 / 78.33</td><td>70.30 / 78.74</td><td>86.27 / 88.64</td><td>26.56 / 46.77</td></tr><tr><td>@IoU &gt; 0.50</td><td>Toilet</td><td>Oven</td><td>Dishwasher</td><td>Fireplace</td><td>Stool</td><td>TV Monitor</td><td>Sofa</td><td>Stove</td><td>Overall</td></tr><tr><td>CAGroup3D</td><td>50.94 / 68.99</td><td>78.93 / 81.28</td><td>92.19 / 92.86</td><td>28.21 / 45.19</td><td>70.69 / 80.78</td><td>1.16 / 6.63</td><td>46.32 / 65.51</td><td>33.32 / 41.73</td><td>55.72 / 66.43</td></tr><tr><td>Our OccGOD</td><td>59.41 / 74.68</td><td>79.54 / 82.19</td><td>90.96 / 92.75</td><td>30.22 / 46.15</td><td>71.61 / 80.78</td><td>0.73 / 5.19</td><td>47.65 / 64.98</td><td>35.64 / 41.73</td><td>57.36 / 67.47</td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/2834d4ba2707806691ca38501c535bbfd9a105933f71328126862423aa377913.jpg",
+        "table_caption": [
+            "Table 4. Quantitative comparison on different training setups. The evaluation metrics are mIoU / chamfer L2 / F-score respectively."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Strategy</td><td>Chair</td><td>Sofa</td><td>Table</td></tr><tr><td>w/o pretrain</td><td>35.6 / 4.35 / 27.4</td><td>66.7 / 3.80 / 26.0</td><td>36.7 / 8.20 / 30.4</td></tr><tr><td>w/o finetune</td><td>25.0 / 10.8 / 23.5</td><td>66.7 / 5.11 / 26.8</td><td>30.9 / 12.5 / 26.1</td></tr><tr><td>full</td><td>38.6 / 3.57/ 31.0</td><td>70.7/ 2.88/ 31.6</td><td>41.5 / 6.52 / 36.1</td></tr><tr><td></td><td>Cabinet</td><td>Bed</td><td>Shelf</td></tr><tr><td>w/o pretrain</td><td>72.6 / 3.49 / 34.2</td><td>66.0 / 2.21 / 30.6</td><td>14.8 / 4.76 / 30.5</td></tr><tr><td>w/o finetune</td><td>67.2 / 5.22 / 29.1</td><td>55.3 / 3.38 / 29.0</td><td>23.9 / 4.18 / 30.8</td></tr><tr><td>full</td><td>75.1 / 3.10 / 37.0</td><td>62.5 / 2.62 / 35.4</td><td>24.5 / 3.45 / 37.5</td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/518eca94d2182b3fb4bff36112dc87420d739112ab0c8ac4f6f1f5ba427ccc91.jpg",
+        "table_caption": [
+            "Table 5. Quantitative comparison between HFA layer and direct triplane projection. The evaluation metrics are mIoU / chamfer L2 / F-score respectively."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>Chair</td><td>Sofa</td></tr><tr><td>Triplane project</td><td>38.1 / 3.95 / 30.6</td><td>70.0 / 3.03 / 30.8</td></tr><tr><td>HFA layer</td><td>38.6 / 3.57 / 31.0</td><td>70.7 / 2.88 / 31.6</td></tr></table>",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/6f4539924f719f50ab6e3463152e8c7b4d6de9dd12ea0d2183ecba0eaf43c056.jpg",
+        "table_caption": [
+            "Table 6. Quantitative comparison between reconstruction using GT 3D bounding boxes and noisy bounding boxes. Evaluation metrics are mIoU / chamfer L2 / F-score respectively."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Detection type</td><td>Chair</td><td>Sofa</td><td>Table</td></tr><tr><td>noisy_bbox</td><td>38.7 / 3.77 / 31.3</td><td>70.2 / 2.90 / 31.8</td><td>40.6 / 7.42 / 34.4</td></tr><tr><td>GT_bbox</td><td>38.6 / 3.57 / 31.0</td><td>70.7/ 2.88/ 31.6</td><td>41.5 / 6.52 / 36.1</td></tr><tr><td></td><td>Cabinet</td><td>Bed</td><td>Shelf</td></tr><tr><td>noisy_bbox</td><td>73.1 / 3.70 / 34.4</td><td>65.5 / 2.64 / 36.2</td><td>24.1 / 3.85 / 36.0</td></tr><tr><td>GT_bbox</td><td>75.1 / 3.10 / 37.0</td><td>62.5 / 2.62 / 35.4</td><td>24.5 / 3.45 / 37.5</td></tr></table>",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "construction. An experiment is conducted by randomly rotating between -10 and 10 degrees, scaling between 0.8 and 1.1, and shifting the center between  $-10\\%$  and  $10\\%$  for each object. The quantitative results are shown in Tab. 6. We observe that, with considerable disturbances on object poses, our method achieves robust accuracy.",
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+    },
+    {
+        "type": "text",
+        "text": "Effectiveness of scene-level occupancy to OccGOD Tab. 3 compares the baseline (Cagroup3D) and our proposed OccGOD. Cagroup3D achieves an mAP of 55.72 and an mAR of 66.43 with an IOU threshold of 0.5. Our OccGOD enhances the baseline, improving mAP by 1.64 and mAR by 1.04. Notable increases occurred for larger",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "furniture like tables (+2.42 in AP), toilets (+8.47 in AP and +5.69 in AR), shelves (+3.03 in AP), beds (+3.47 in AP and 4.44 in AR), and sinks (+6.27 in AP and 4.59 in AR).",
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+    },
+    {
+        "type": "text",
+        "text": "7. Conclusion",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We have introduced a new dataset LASA, a Large-scale Aligned Shape Annotation Dataset. In this work, we have illustrated the substantial benefits LASA brings to the community, particularly in the realms of indoor instance-level scene reconstruction and 3D object detection. Empowered by LASA, we propose a novel Diffusion-based CrossModal Shape Reconstruction approach, namely DisCo, and an Occupancy-guided 3D Object Detection method, namely OccGOD. In DisCo, we design a novel Hybrid Feature Aggregation Layer to effectively fuse and align local features from two input modalities - partial point clouds and multiview images. In OccGOD, we leverage the scene-level occupancy labels provided by LASA, to enhance 3D object detection by learning object completeness priors. Extensive experiments demonstrated that, with the support of LASA, both methods achieve state-of-the-art performance in real-world scenarios.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We firmly believe that the large-scale and well-aligned features of LASA present better annotation quality and quantity, laying a foundation for many 3D downstream applications, including 3D understanding and reconstruction.",
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+    {
+        "type": "text",
+        "text": "8. Acknowledgements",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "The work was supported in part by Guangdong Provincial Outstanding Youth Project No. 2023B1515020055, the Basic Research Project No. HZQB-KCZYZ-2021067 of Hetao Shenzhen-HK S&T Cooperation Zone, NSFC-62172348, the National Key R&D Program of China with grant No. 2018YFB1800800, by Shenzhen Outstanding Talents Training Fund 202002, by Guangdong Research Projects No. 2017ZT07X152 and No. 2019CX01X104, by Key Area R&D Program of Guangdong Province (Grant No. 2018B030338001), by the Guangdong Provincial Key Laboratory of Future Networks of Intelligence (Grant No. 2022B1212010001), and by Shenzhen Key Laboratory of Big Data and Artificial Intelligence (Grant No. ZDSYS201707251409055). It is also partly supported by NSFC-61931024 and Shenzhen General Project No. JCYJ20220530143604010.",
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+        "type": "page_number",
+        "text": "20461",
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+    {
+        "type": "text",
+        "text": "References",
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+            106
+        ],
+        "page_idx": 8
+    },
+    {
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+        "sub_type": "ref_text",
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2024/LASA_ Instance Reconstruction from Real Scans using A Large-scale Aligned Shape Annotation Dataset/e66a9d83-37a7-45da-8099-3af5a6b6fd8b_origin.pdf

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2024/LASA_ Instance Reconstruction from Real Scans using A Large-scale Aligned Shape Annotation Dataset/full.md

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+# LASA: Instance Reconstruction from Real Scans using A Large-scale Aligned Shape Annotation Dataset
+
+Haolin Liu $^{1,2*}$ , Chongjie Ye $^{1,2*}$ , Yinyu Nie $^{3}$ , Yingfan He $^{1,2}$ , Xiaoguang Han $^{2,1\dagger}$
+
+\*equal contribution \*corresponding author
+
+$^{1}$ FNii, CUHKSZ  $^{2}$ SSE, CUHKSZ  $^{3}$ Technical University of Munich
+
+gap-lab-cuhk-sz.github.io/LASA
+
+920 Scenes + 10,412 Unique CADs
+
+![](images/250f7aba2f0d0ed674bac9d0d817575f4c2c315eb2c28d6bb78d3d454e6867b7.jpg)
+
+![](images/d2db398d93e153f11ff0a35b8312cdbe2f25278979f027dd91e6f39accf7b466.jpg)  
+Figure 1. We introduce LASA, a Large-scale Aligned Shape Annotation Dataset containing 10,412 unique object CAD models aligned with 920 real-world scene scans. Supported by LASA, we achieve state-of-the-art in real-world object reconstruction and 3D object detection.
+
+![](images/e21ddd04138c3c785c1c5b5fdca31b0e0665726e661a24e944ea65317457f7e0.jpg)
+
+![](images/ffc6a5a8d2e899ace848d26b2e134cb11cf1d3d92cb9a896053a9e6437abacfa.jpg)
+
+![](images/2e76eb70f3920aa8b231a84824906074c69598e1bd7749a69e443a526c4161ba.jpg)
+
+![](images/96dabc861db0528e2d36664c51b2c24b6927d4178e72a52169ff8bb3e25f22e0.jpg)
+
+![](images/3ebe7ab88b8ddf99b334e59a60375e35afd494e0ea99a2c0685dbf8f7b4e2c1d.jpg)
+
+![](images/f124df7c5e8989ebf26c41de3b0694980d77c6df5cf746c699c0d5293e407705.jpg)
+
+![](images/5f53da1c19e3f1167d744266c5711a57b0ae598e6a6854823265e3c87e08908c.jpg)
+
+![](images/8eb88f5dd7c7870c5c60ed4b6c6a877265ef2787e72d788b71998e7086670644.jpg)
+
+Large-scale Aligned CAD Annotations
+
+![](images/f4f314354ca6b825ac15f587ae20156c86c8b3844faedf64e6c6aeb09df164a7.jpg)
+
+![](images/63b8636a0b3f66e55b0a7d7e1a17a452212975dc20ec173641c99db1228e7ae5.jpg)
+
+![](images/968cdb0a1c96d242eeec51a027813212ffe68957e2d75a0a56ef252ba10da2d6.jpg)  
+Monocular RGB-D video
+
+![](images/b1fa87864012d14ec262b6d4a2e33b8c3d9043193a3f874b7e92b464d303ff53.jpg)
+
+![](images/052bc906431840c2762d7f94457aa1aed39906726dc16b186df3d9cf68b81f94.jpg)
+
+![](images/d28a971c530ebb099f0d0f03385485d35b6d0989b0b35bc0b5e499b74ee9d797.jpg)
+
+![](images/0ddd3e77910a700d0f50e7307bdd9865806a2d601d82447a9f699a99ba674d77.jpg)
+
+![](images/292844475f887dafc5f80d7ee29acb8b9496cfa4e0967f67ce9e69f4a4e2f5c9.jpg)
+
+![](images/c38814998b2bf490b7f9c3b15c0c32d08919b752ee535456ab8e1b9046b7fdcb.jpg)
+
+![](images/ac9ab39c2f2507753a599fd65c3cef306f00a0a1ad9a6b9d75f808d669123b5d.jpg)
+
+![](images/86eca4bfb0549f5ba7db7f2add5682ef78d28f8cc2a712fa60ab639d1d80d3dd.jpg)
+
+![](images/733dcbe6abad5b4c0f85072a097c9273b4ea1b2ef29978444e5a7cd7cd283b05.jpg)
+
+Reconstruction Results
+
+# Abstract
+
+Instance shape reconstruction from a 3D scene involves recovering the full geometries of multiple objects at the semantic instance level. Many methods leverage data-driven learning due to the intricacies of scene complexity and significant indoor occlusions. Training these methods often requires a large-scale, high-quality dataset with aligned and paired shape annotations with real-world scans. Existing datasets are either synthetic or misaligned, restricting the performance of data-driven methods on real data. To this end, we introduce LASA, a Large-scale Aligned Shape Annotation Dataset comprising 10,412 high-quality CAD annotations aligned with 920 real-world scene scans from ArkitScenes, created manually by professional artists. On this top, we propose a novel Diffusion-based Cross-Modal Shape Reconstruction (DisCo) method. It is empowered by a hybrid feature aggregation design to fuse multi-modal inputs and recover high-fidelity object geometries (see Fig. 1). Besides, we present an Occupancy-Guided 3D Object Detection (OccGOD) method and demonstrate that our shape
+
+annotations provide scene occupancy clues that can further improve 3D object detection. Supported by LASA, extensive experiments show that our methods achieve state-of-the-art performance in both instance-level scene reconstruction and 3D object detection tasks.
+
+# 1. Introduction
+
+The widespread use of hand-held RGB-D sensors has facilitated the effortless acquisition of indoor scene scans. However, these scans often suffer from noises and incompleteness due to limitations in sensor accuracy, the complexity of indoor environments, and occlusion among objects. This further limits its applications in scenarios such as VR/AR and 3D industry where a complete and high-quality reconstruction is desired. This shortage absorbs great attention in 3D vision and graphics community, particularly in the realm of indoor instance-level scene reconstruction. In this task, the objective is to reconstruct the shapes of observed objects based on 3D scans or images captured by sensors. Many advances [8, 36, 56, 58, 61] have been seen by leveraging the power of deep learning methods for this task. They
+
+are data-driven and demand a substantial number of paired scene scans and objects' CAD ground truths.
+
+Existing data-driven methods rely on two types of datasets. [1, 7-9, 19, 27, 39, 50, 52, 55-58] utilized synthetic datasets [5, 10, 15] by synthesizing images and scans that mimic real-world distributions. Synthetic data provides CAD models perfectly aligned with input observations (images or scans) though. Models trained on it are vulnerable to domain gaps from the real world [53] that could impair the generalizability. Scan2CAD[2] attempts to bridge this gap by annotating objects' CAD in real-world scene scans. However, their CADs are retrieved from a synthetic database [5] and their poses are manually adjusted to roughly align the object scans. However, retrieved shapes are often unlike the real observed objects, introducing shape misalignment issues. Many works [13, 18, 28, 32, 47, 48] using it as instance shape supervision are potentially biased with inferior alignment. In summary, The absence of a well-aligned real-world dataset barriers the further advancement of the community.
+
+To surmount this challenge, we present a new dataset LASA, a Large-scale Aligned Shape Annotation dataset that contains 10,412 high-quality instance CAD annotations meticulously crafted by skilled artists. Each CAD shape is designed and placed to precisely align with objects' scans from 920 real-world scene scans in ArkitScene [3]. We deliberately annotate objects in ArkitScene instead of ScanNet[11] because it provides scans obtained from both accurate Laser sensors and hand-held RGB-D sensors. The accurate Laser scan benefits high-quality and aligned manual annotations. Meanwhile, the less accurate scans from hand-held devices support research on reconstruction and completion using consumer-level devices.
+
+A large-scale scan dataset with high-quality instance CAD annotations empowers many downstream applications. We first investigate how LASA benefits indoor instance-level scene reconstruction. Given an indoor scene, images and scene scans can be obtained through scanning. Typically, the initial step involves 3D object detection, after which the partial point clouds and multi-view images of each detected instance are acquired, serving as visual cues for subsequent shape reconstruction. Point cloud provides natural 3D information though, they are often noisy and incomplete. On the other hand, images present rich appearance clues but lack 3D constraints. Inspired by the complementary nature of these two modalities in describing object surfaces, we advocate utilizing both modalities as inputs to fuse their advantages. Recently, diffusion models have shown appealing performance in shape generation [7, 19, 44, 61, 64]. We advance it further for instance reconstruction and propose Diffusion-based Cross-modal Shape Reconstruction, namely DisCo. DisCo is a triplane diffusion model tailored to accommodate multi-modal in
+
+puts, towards robust real-world object reconstruction, where a hybrid feature aggregation layer is proposed to aggregate and align two input modalities effectively. Supported by the LASA dataset, extensive experiments show that our method achieves state-of-the-art reconstruction performance with real-world inputs.
+
+Moreover, the LASA dataset has full annotations covering every instance within each of the 920 real-world scenes. This extensive coverage enables LASA to provide scene-level occupancy labels. We further explore how they can affect indoor scene 3D object detection. 3D Object detection [37, 42, 49] usually comprises a backbone and a detection head. We propose to integrate an occupancy prediction head for occupancy-guided 3D object detection, namely OccGOD. Our experiments demonstrate that incorporating occupancy prediction leads to substantial improvements in detection performance. In summary, our key contributions are four-fold:
+
+- We introduce a large-scale dataset, LASA. It contains 10,412 manually crafted, high-quality instance CAD annotations geometrically aligned with 920 real-world scene scans.  
+- We propose DisCo, a novel diffusion-based method that leverages hybrid representation, effectively interacting with both input partial point cloud and multi-view images, achieving state-of-the-art reconstruction.  
+- With LASA's scene-level annotation, we introduce occupancy-guided 3D object detection (OccGOD) with decent improvements.  
+- We strongly believe the large-scale dataset of well-aligned shape annotations can break the bottleneck of current research on 3D indoor scene understanding and reconstruction.
+
+# 2. Related Works
+
+# 2.1. Indoor Instance Shape Dataset
+
+Recently, many advances have been seen in learning-based 3D object and scene reconstruction from images and videos. However, numerous challenges persist due to the limitations of existing datasets.
+
+These learning-based approaches are usually trained either on existing synthetic datasets or real-world datasets. While synthetic datasets are demonstrated valuable for training models, they lack realism. Large synthetic object collections like ShapeNet[5] and ABO[10] provide diverse 3D models but lack environment context. Synthetic scene datasets such as 3D-Front[14], Replica[45], and Structured3D[63] possess complete synthetic environments with CAD annotations for objects. However, models trained on these datasets often struggle to generalize with real inputs due to substantial domain gaps[53].
+
+Some works [2, 29, 34, 46, 53, 54] annotate CAD
+
+<table><tr><td>Dataset</td><td>Aligned</td><td>#Scenes</td><td>#CADs</td><td>Sensor Type</td><td>Annotation Method</td></tr><tr><td>Scan2CAD [2]</td><td>-</td><td>1,506</td><td>3,049</td><td>RGB-D</td><td>Retrieval</td></tr><tr><td>CAD-Estate [29]</td><td>-</td><td>19,512</td><td>12,024</td><td>RGB</td><td>Retrieval</td></tr><tr><td>IKEA [16]</td><td>✓</td><td>null</td><td>90</td><td>RGB</td><td>Retrieval</td></tr><tr><td>Pix3D [46]</td><td>✓</td><td>null</td><td>219</td><td>RGB</td><td>Retrieval</td></tr><tr><td>ScanSalon [53]</td><td>✓</td><td>413</td><td>800</td><td>RGB-D</td><td>Artist</td></tr><tr><td>Aria&#x27;s Digital Twin [34]</td><td>✓</td><td>2</td><td>370</td><td>RGB-D</td><td>Artist</td></tr><tr><td>LASA (Ours)</td><td>✓</td><td>920</td><td>10,412</td><td>RGB-D</td><td>Artist</td></tr></table>
+
+Table 1. Comparisons with existing 3D indoor datasets with instance shape annotations
+
+models on real-world data to bridge the domain gaps. Scan2CAD [2] and CAD-estate [29] have provided scanned object-CAD pairs by retrieving them from ShapeNet [5] and are further manually aligned to the real-world scenes. However, these retrieved CAD models lack alignment with real objects, potentially biasing data-driven reconstruction methods towards inferior reconstruction. This motivates us to build a real-world dataset with well-aligned CAD annotations. Aria's Digital Twin [34] and ScanSalon [53] provide such CADs though, the limited quantities restrict their application for data-hungry tasks. Datasets such as Pix3d [46] and PASCAL3D+ [54] supply single-view images with aligned shapes but are limited in scene modalities lacking point cloud and multi-view images.
+
+# 2.2. 3D Shape Reconstruction
+
+Object-level Reconstruction Existing approaches leverage images or partial point clouds as input. Images based reconstruction methods accept either single-view [6, 17, 19, 20, 25, 27, 30, 31, 33, 35, 50, 55, 57, 62, 64] or sparse multiview images [4, 9, 39, 56, 59] as inputs for shape reconstruction. They extract 2D image features and utilize them for shape reconstruction. Some [27, 43] leverage 2D pixel-aligned local features for reconstruction, demonstrating appealing performance for high-quality reconstruction. Other works [1, 8, 12, 26, 40, 52, 58, 61] conduct shape reconstruction from noisy, incomplete partial point clouds. Both paradigms have their advantages, with image-based methods perceiving rich 2D appearance features, while point-based methods process native 3D signals. [21] proposed to combine both inputs to fuse their advantages. Our proposed approach also accepts both inputs, focusing on effectively aggregating and aligning local features from both input sources. Since diffusion model [7, 19, 44, 51, 61, 64] have demonstrated strong capabilities in both shape generation and reconstruction, we opt for a diffusion model for robust and high-quality reconstruction.
+
+Instance-level Scene Reconstruction Recent instance scene reconstruction methods [13, 18, 21-23, 28, 32, 47, 48] follow a detect-then-reconstruct pipeline from a single scan. First, these methods use a 3D object detector to localize objects in either scene scans or videos. Subsequently, the detected 3D objects are fed into a 3D shape reconstruction
+
+![](images/a9e8e291f691372d1661d76b3bf441b41a5f83b739e2d63fbde559d6887cebf2.jpg)  
+Figure 2. Visual comparison between aligned and unaligned CAD annotations
+
+module individually to obtain object shapes. Finally, the reconstructed 3D object shapes are placed back at their original locations to obtain a reconstruction of the full scene. These methods commonly utilize the Scan2CAD [2] dataset for training, where the inferior alignment limits their reconstruction quality. In contrast, the CAD models in our LASA dataset are manually crafted by artists to guarantee alignment, which we hope can lay a foundation for future research in this area.
+
+# 3. LASA Dataset
+
+LASA is a large-scale dataset that contains 10,412 unique CAD models covering 920 scenes across 17 categories. Rather than relying on a pre-existing CAD database to annotate scenes, LASA engages professional artists to manually create aligned CAD models with 3D scans. Our annotations provide precise and consistent (as shown in Fig. 2) training data for data-driven reconstruction algorithms.
+
+# 3.1. Data Annotation
+
+LASA is built upon the 3D laser scans from ArkitScenes since it is accurate with high resolution, which is critical for
+
+high-fidelity CAD annotations.
+
+Data Preprocessing. Each laser scan from ArkitScenes is exceptionally dense with  $1\mathrm{GB}+$  data storage. To improve annotation efficiency, we downsample the scans to a 4mm density. Since ArkitScenes does not publicly provide alignment transformations between the laser scans and the RGB-D scans, we utilize a coarse-to-fine registration method to calculate the transformation matrix (see our supplemental for details). With the transformation matrix, we align the laser data with the RGB-D sequence coordinates from ArkitScenes. We then use ArkitScenes' 3D bounding box annotations to partition the aligned laser point clouds for each single object. These segmented point clouds are transformed into the canonical space. Furthermore, for each object, we select 2-5 frames from RGB-D scans that maximize the 2D projection area of its 3D bounding box. These selected frames serve as references for annotation.
+
+Shape Annotation. The CAD annotation process involves a team of 35 artists working over 4 months. With preprocessed point clouds and reference images, each artist spent approximately 69 minutes designing a single model. Each model is annotated with Autodesk Maya or Cinema 4D.
+
+Shape Verification. We involve a shape verification procedure for annotation quality control. This procedure has both algorithmic validation and manual reviews to thoroughly evaluate CAD model's accuracy against ground truth scans and images. Our multi-step verification process includes
+
+- Senior Review: After initial annotations, 6 senior designers reviewed every CAD model to verify quality, accuracy, and reliability by manually cross-checking against the 3D scans. Any models that failed to meet the standards were flagged for rework.  
+- Geometry Alignment: We matched the CAD models to aligned laser scans and calculated the unidirectional Chamfer distance between them. This quantified the raw geometric alignment error for the CAD surface compared to the ground truth scan.  
+- View Alignment: We also verified alignment in the pixel level, where we rendered 112,639 images across all scenes by positioning the CAD models in the view frustum of RGB-D sensors. Crowd workers performed a manual inspection to check if the rendered views overlay on the real images. They checked for inconsistencies along object edges and intricate details which would indicate misalignment. This pixel-level evaluation ensured precise alignment. Any rendering mismatches were fixed by re-annotating the CAD model.
+
+# 3.2. Dataset Statistics
+
+Tab. 1 shows the statistics of LASA compared to the existing datasets. LASA contains a comparable number of unique CAD models to CAD-Estate [29], which was previously the largest scene CAD dataset. However, LASA pro
+
+vides better CAD annotation quality against their retrieved CAD models. Additionally, LASA demonstrates greater shape diversity than Scan2CAD [2], with over 3 times as many unique CAD models.
+
+Among all aligned datasets, LASA stands out with a total of 10,412 CADs. This is 13 times more than ScanSalon [53] and 28 times more than Aria's Digital Twin dataset[34]. Unlike IKEA [16] and Pix3D [46] which are annotated on single-view RGB images, LASA captures full RGB-D sequences. This enables a wider range of downstream applications compared to static image datasets.
+
+Furthermore, we compare LASA with Scan2CAD in terms of alignment quality by measuring the Chamfer distance between CAD annotation and the scene scans, which are 0.161 vs 0.269. LASA provides much better aligned data.
+
+# 4. Instance-level Scene reconstruction
+
+We propose a Diffusion-based Cross-modal Shape Reconstruction method (DisCo). DisCo is a diffusion-based model to pursue high-fidelity 3D shape reconstruction from partial point clouds and multi-view images. Various representation including latent sets [61], volumetric grids [7, 64], and triplanes [19, 39, 51] are popular choice for diffusion model. We opt for the triplane since its efficiency enables higher output resolution compared to volumetric grids; while reserving 3D structure compared to latent sets. We employ latent triplane diffusion, where a triplane variational auto-encoder (VAE) first encodes shape into triplane latent space (in Sec. 4.1). Subsequently, a triplane diffusion model operates on this latent space for 3D shape reconstruction conditioned on both partial points and multi-view images (in Sec. 4.2). The overall pipeline of DisCo is shown in the upper part of Fig. 3.
+
+It has been demonstrated that using multiple input modalities (images and scans) presents complementary benefits for semantic scene completion [21]. In DisCo, we also fuse image and point features and introduce Hybrid Feature Aggregation Layer (in Sec. 4.3). In this layer, we utilize a hybrid representation combining a triplane and a volumetric grid. This combination facilitates efficient local feature aggregation and feature alignment from both partial point clouds and multi-view images.
+
+# 4.1. Triplane Variational Auto-Encoder
+
+To conduct a latent triplane diffusion, the first step is to learn an encoder capable of encoding shapes in a triplane latent space. The Triplane VAE [19] comprises an encoder  $\psi_{enc}$  and a decoder  $\psi_{dec}$ . The encoder processes inputs and encodes them into latent space, while the decoder recovers shape from the latent representation. Surface point cloud  $\mathbf{P} \in \mathbb{R}^{K \times 3}$  sampled from a ground truth shape, serves as inputs to  $\psi_{enc}$ .  $K = 20,000$  in our experiment. These points are projected onto a triplane and subsequently processed by
+
+![](images/0b51d3c5063ba281352084f533b9cf9ce768d10f3b7df4ed39c53f869f3a8be0.jpg)  
+Figure 3. Pipeline of our DisCo. Firstly, a triplane VAE model is trained to encode shape into triplane latent space (top-left). Subsequently, a triplane diffusion model is trained in this latent space for conditional shape reconstruction (top-right). A novel Hybrid Feature Aggregation Layer is proposed to effectively aggregate and align local features in both partial points cloud and multi-view images (bottom).
+
+a PointNet to form a triplane feature map. Followed by a UNet [41], the encoder  $\psi_{enc}$  outputs a normal distribution  $\mathcal{N}(\mu, \sigma^2)$ , where  $\mu, \sigma \in \mathbb{R}^{H \times W \times 3 \times C}$ . A latent triplane  $T_0 \in \mathbb{R}^{H \times W \times 3 \times C}$  can be sampled from this distribution. The above process can be summarized as:
+
+$$
+T _ {0} \sim \mathcal {N} (\mu , \sigma^ {2}) \quad \mu , \sigma = \psi_ {\text {e n c}} (\mathbf {P}) \tag {1}
+$$
+
+The occupancy field is chosen as the shape representation. The decoder  $\psi_{dec}$  takes a point  $p$  in space and the triplane latent  $T_0$  as inputs, yielding the occupancy of this point. Specifically, A UNet model first refines  $T_0$  and outputs a triplane feature map. Then, point  $p$  is projected onto this triplane feature map, where features are sampled using bilinear interpolation. These sampled features are fed into MLPs which outputs the occupancy prediction  $\tilde{o}$ . The training of the VAE model is supervised by reconstruction loss and KL divergence loss as  $\mathcal{L}_{vae} = \| \tilde{o} - o_{gt} \|_2^2 + \lambda_{kl} \mathcal{L}_{kl}$ . In our experiment,  $\lambda_{kl} = 0.025$ . As in [51], the network layers in both  $\psi_{enc}$  and  $\psi_{dec}$  adopt 3d aware convolution for triplane processing.
+
+The reconstruction is conducted in canonical object space. During training, augmentation such as random shifting, rotating and scaling are applied, so that it will be more robust to inaccurate objects' pose during inference.
+
+# 4.2. Triplane Diffusion for reconstruction
+
+Our approach employs latent triplane diffusion to reconstruct shapes based on partial point clouds and multi-view images as conditions. Specifically, a 2D UNet model serves as a denoise function  $D(\cdot)$ . This model comprises cascades of residual convolutional block and Hybrid Feature Aggregation Layer with 3d aware convolution. we introduce a novel Hybrid Feature Aggregation Layer, designed to fos
+
+ter effective interaction between local features derived from partial point clouds and multi-view images. We use continuous diffusion steps as in [24]. The forward diffusion process during training is defined as  $T_{\sigma} = T_{0} + n$ , where  $n \sim \mathcal{N}(0, \sigma^{2}\mathbf{I})$ ,  $\sigma$  indicates the diffusion steps, and also the deviation of the noise added. The denoise UNet takes a noisy triplane latent  $T_{\sigma}$  as input, and outputs a denoised triplane latent  $T_{\text{denoise}}$ . We follow the diffusion formulation in EDM [24], the objective function during training is:
+
+$$
+\mathbb {E} _ {\sigma , n, T _ {0}} \lambda_ {\sigma} \| D (T _ {0} + n, \sigma , c) - T _ {0} \| _ {2} ^ {2} \quad n \sim \mathcal {N} (0, \sigma^ {2} \mathbf {I}) \tag {2}
+$$
+
+Here  $c$  denotes the conditional inputs. In our case, they are partial point clouds and multi-view images.  $\lambda_{\sigma}$  denotes a loss normalization factor. Inference can be conducted through sampling from noise triplane as in EDM [24].
+
+During training our diffusion model, we implement a strategy to first pretrain on synthetic datasets, then fine-tune on LASA dataset. We leverage ShapeNet [5], ABO [10], and 3D-Future [15] dataset to synthesize partial point cloud and render images by embedding CAD models in HM3D scene[38, 60]. This strategy enhances both the robustness and the performance of our method, enabling more effective real-world object reconstruction.
+
+# 4.3. Hybrid Feature Aggregation Layer
+
+The objective of the Hybrid Feature Aggregation Layer is to aggregate and align local features from two input modalities to the triplane space. Points-triplane interaction is implemented by projecting points onto the triplane. However, such interaction becomes challenging when fusing images and triplanes. An alternative way is to expand the triplane into a volumetric grid and project the grids to images. This motivates us to propose this Hybrid Feature Aggregation
+
+Table 2. Quantitative comparison on shape reconstruction. Evaluation metrics are mIoU / Chamfer L2 / F-score respectively. Higher mIoU and F-score are better while lower Chamfer L2 is better. Chamfer L2 is scaled by 1,000. LAS doesn't have mIoU value since it uses a surface occupancy representation.  
+
+<table><tr><td>Method</td><td>Chair</td><td>Sofa</td><td>Table</td><td>Cabinet</td><td>Bed</td><td>Shelf</td></tr><tr><td>IFNet</td><td>28.9 / 19.8 / 25.2</td><td>66.1 / 3.61 / 31.1</td><td>28.3 / 21.4 / 27.4</td><td>73.8 / 3.20 / 36.6</td><td>64.0 / 2.95 / 28.8</td><td>17.2 / 5.24 / 29.6</td></tr><tr><td>LAS-pts</td><td>- / 13.2 / 22.6</td><td>- / 4.47 / 22.9</td><td>- / 19.5 / 23.9</td><td>- / 4.81 / 22.1</td><td>- / 4.77 / 25.8</td><td>- / 4.70 / 26.8</td></tr><tr><td>LAS-pts+imgs</td><td>- / 10.7 / 24.1</td><td>- / 3.76 / 24.1</td><td>- / 15.7 / 24.6</td><td>- / 4.56 / 24.4</td><td>- / 4.58 / 26.5</td><td>- / 4.35 / 27.2</td></tr><tr><td>3DShape2VecSec</td><td>32.5 / 6.43 / 25.6</td><td>66.7 / 3.39 / 27.6</td><td>30.9 / 12.9 / 25.3</td><td>68.1 / 4.09 / 23.7</td><td>62.3 / 3.69 / 30.5</td><td>22.3 / 3.79 / 32.0</td></tr><tr><td>Ours-pts</td><td>33.4 / 5.68 / 26.6</td><td>68.8 / 3.21 / 29.0</td><td>38.0 / 10.5 / 32.2</td><td>72.3 / 3.63 / 36.5</td><td>54.0 / 2.97 / 34.1</td><td>23.2 / 3.68 / 36.5</td></tr><tr><td>Ours-pts+imgs</td><td>38.6 / 3.57 / 31.0</td><td>70.7 / 2.88 / 31.6</td><td>41.5 / 6.52 / 36.1</td><td>75.1 / 3.10 / 37.0</td><td>62.5 / 2.62 / 35.4</td><td>24.5 / 3.45 / 37.5</td></tr></table>
+
+Layer, introducing a hybrid representation that facilitates both points-triplane and images-triplane interactions.
+
+As in the bottom part of Fig. 3, inputs of this layer are partial point cloud  $\tilde{P}$ , k posed images  $I_{i}, i \in 1,2\dots k$ , and triplane feature  $\tilde{T}_l$  from the l-th convolutional layer. It begins with the aggregation of local features from partial points, achieved by projecting them onto the triplane and incorporating a PointNet layer. Image features map is first extracted using pretrained Vision Transformer. Then, the triplane expands into a volumetric grids  $G_{l} \in \mathbb{R}^{H \times W \times L \times C}$ . The volumetric grids are then projected to k images using their camera poses, and image local features are sampled using bi-linear interpolation.
+
+To fuse features from multiple images, we employ a transformer. Specifically, the voxel feature serves as the query, while the sampled image feature serves as the key and value. The transformer outputs a volumetric grid attended with local image features from multi-view images. Finally, the volumetric grid is flattened back to a triplane by pooling, producing an output triplane feature map. This process ensures the effective aggregation and alignment of local features from diverse input modalities.
+
+# 5. Occupancy-guided 3D Object Detection
+
+3D object detection takes scene scans as input and parses the scene objects into 3D bounding boxes. In real-world scenarios, object scans are often incomplete and sparse due to occlusion, inaccurate sensors, and limited views during capture, making objects hard to recognize. To address it, we propose an Occupancy-Guided 3D Object Detection (OccGOD) approach that utilizes shape completeness prior for better scene understanding. We generate scene-level occupancy ground truth from LASA's fully-covered annotations. Specifically, scenes are partitioned into numerous  $384 \times 384 \times 96$  voxel grids, with a resolution of  $4 \mathrm{~cm}$ . All CAD models are then placed back into the scene, on which the surface points are densely sampled at  $2 \mathrm{~cm}$  intervals. Subsequently, we iterate through each point, marking their corresponding voxel to be occupied.
+
+Our methodology follows a simple 'plug-and-play' manner. It is compatible with any detection method based on a 3D
+
+structured representation like volumetric grids [42, 49]. For ease of use, we built our OccGOD upon Cagroup3D [49]. In addition to the original backbone and bounding box prediction head, we introduce an occupancy head and augment the bounding box prediction head with another two output parameters for orientation regression. The occupancy heads takes backbone features as inputs, and output the occupancy of each voxel. More details of network design are in the supplemental. To further explore occupancy representations, we concatenate the features from the occupancy head with the backbone's features during ROI pooling for second-stage bounding box prediction. The occupancy head is supervised with a binary cross-entropy loss function with scene-level occupancy labels from LASA.
+
+Our proposed OccGOD predicts a complete foreground structure to guide the bounding box detection. By leveraging the complete scene context, it achieves significant gains in detecting occluded and sparse objects compared to baseline methods.
+
+# 6. Experiment
+
+# 6.1. Experiment Setup
+
+For indoor object reconstruction, we employ mean Intersection over Union (mIoU), L2 chamfer distance, and  $1\%$  F-score. We first normalize both results and ground-truth CAD into the interval from -0.5 to 0.5, and compute the above metrics between them. The experiment is conducted over 6 categories merged from 17 categories in LASA dataset.
+
+For 3D object detection, we assess mean average precision (mAP) and mean average recall (mAR) with an IoU threshold at 0.5. Evaluations for both object reconstruction and 3D object detection are performed on LASA's test set.
+
+# 6.2. Evaluation on Indoor Object Reconstruction
+
+In this session, we compare our methods with existing baselines. We choose IFNet [8] and two state-of-the-art diffusion-based methods, LAS Diffusion [64] and 3DShape2VecSet [61], for comparison. We first pretrain all methods on synthetic dataset [5, 10, 15], then finetune them
+
+![](images/55fedb28b91e3e2955b818b8399779d65cb623cd29c9364bf20d76ab3bd56183.jpg)  
+Figure 4. Qualitative comparison between our method and IFNet, 3DShape2Vecset, and LAS.
+
+on LASA. IFNet and 3DShape2VecSet receive point clouds as inputs. For LAS Diffusion, we extend it into two versions: with point clouds as input (LAS-pts), and with both point clouds and images as input (LAS-pts+imgs). We compare them with our DisCo with two variants: 1) with partial point clouds only (Ours-pts); 2) with both modalities (Ours-pts+imgs). The quantitative and qualitative comparisons are shown in Tab. 2 and Fig. 4. Our method achieves state-of-the-art performance both quantitatively and qualitatively.
+
+# 6.3. Ablation Study
+
+Real-world Performance Boost using LASA We investigate the impact of our LASA dataset on real-world object reconstruction through three training setups: training from scratch on LASA (w/o pretrain), training on synthetic datasets only (w/o finetune), and pretraining on synthetic
+
+datasets followed by finetuning on LASA (full). The quantitative comparison is in Tab. 4. The table shows that finetuning on LASA significantly improves real-world reconstruction, with pretraining on synthetic data followed by finetuning on real strategy achieving the best performance.
+
+Effectiveness of Hybrid Feature Aggregation Layer We verify the effectiveness of the Hybrid Feature Aggregation (HFA) layer in aggregating and aligning local features from both partial points and multi-view images. We compare it against not using the expanded grids to project onto the images. Specifically, the latter directly projects the triplane's pixels to the images. The quantitative comparison is shown in Tab. 5. The decent improvement of the HFA layer verifies its powerfulness in fusing multi-modal features.
+
+Robustness to inaccurate detection We further investigate how inaccurate detection results could affect the re
+
+Table 3. Quantitative comparison between the state-of-the-art (CAGroup3D) and our OccGOD. Oriented bounding boxes are predicted. Evaluation metrics are mAP / mAR. Higher mAP / mAR indicates better performance.  
+
+<table><tr><td>@IoU &gt; 0.50</td><td>Chair</td><td>Table</td><td>Cabinet</td><td>Refrigerator</td><td>Shelf</td><td>Bed</td><td>Sink</td><td>Washer</td><td>Bathtub</td></tr><tr><td>CaGroup3D</td><td>92.05 / 93.09</td><td>46.68 / 66.37</td><td>33.93 / 54.64</td><td>90.56 / 91.22</td><td>35.12 / 57.54</td><td>67.31 / 73.89</td><td>64.03 / 74.15</td><td>87.77 / 89.39</td><td>27.99 / 45.97</td></tr><tr><td>Our OccGOD</td><td>92.57 / 93.25</td><td>49.17 / 66.76</td><td>35.05 / 55.90</td><td>90.45 / 91.89</td><td>38.15 / 58.19</td><td>70.78 / 78.33</td><td>70.30 / 78.74</td><td>86.27 / 88.64</td><td>26.56 / 46.77</td></tr><tr><td>@IoU &gt; 0.50</td><td>Toilet</td><td>Oven</td><td>Dishwasher</td><td>Fireplace</td><td>Stool</td><td>TV Monitor</td><td>Sofa</td><td>Stove</td><td>Overall</td></tr><tr><td>CAGroup3D</td><td>50.94 / 68.99</td><td>78.93 / 81.28</td><td>92.19 / 92.86</td><td>28.21 / 45.19</td><td>70.69 / 80.78</td><td>1.16 / 6.63</td><td>46.32 / 65.51</td><td>33.32 / 41.73</td><td>55.72 / 66.43</td></tr><tr><td>Our OccGOD</td><td>59.41 / 74.68</td><td>79.54 / 82.19</td><td>90.96 / 92.75</td><td>30.22 / 46.15</td><td>71.61 / 80.78</td><td>0.73 / 5.19</td><td>47.65 / 64.98</td><td>35.64 / 41.73</td><td>57.36 / 67.47</td></tr></table>
+
+Table 4. Quantitative comparison on different training setups. The evaluation metrics are mIoU / chamfer L2 / F-score respectively.  
+
+<table><tr><td>Strategy</td><td>Chair</td><td>Sofa</td><td>Table</td></tr><tr><td>w/o pretrain</td><td>35.6 / 4.35 / 27.4</td><td>66.7 / 3.80 / 26.0</td><td>36.7 / 8.20 / 30.4</td></tr><tr><td>w/o finetune</td><td>25.0 / 10.8 / 23.5</td><td>66.7 / 5.11 / 26.8</td><td>30.9 / 12.5 / 26.1</td></tr><tr><td>full</td><td>38.6 / 3.57/ 31.0</td><td>70.7/ 2.88/ 31.6</td><td>41.5 / 6.52 / 36.1</td></tr><tr><td></td><td>Cabinet</td><td>Bed</td><td>Shelf</td></tr><tr><td>w/o pretrain</td><td>72.6 / 3.49 / 34.2</td><td>66.0 / 2.21 / 30.6</td><td>14.8 / 4.76 / 30.5</td></tr><tr><td>w/o finetune</td><td>67.2 / 5.22 / 29.1</td><td>55.3 / 3.38 / 29.0</td><td>23.9 / 4.18 / 30.8</td></tr><tr><td>full</td><td>75.1 / 3.10 / 37.0</td><td>62.5 / 2.62 / 35.4</td><td>24.5 / 3.45 / 37.5</td></tr></table>
+
+Table 5. Quantitative comparison between HFA layer and direct triplane projection. The evaluation metrics are mIoU / chamfer L2 / F-score respectively.  
+
+<table><tr><td>Method</td><td>Chair</td><td>Sofa</td></tr><tr><td>Triplane project</td><td>38.1 / 3.95 / 30.6</td><td>70.0 / 3.03 / 30.8</td></tr><tr><td>HFA layer</td><td>38.6 / 3.57 / 31.0</td><td>70.7 / 2.88 / 31.6</td></tr></table>
+
+Table 6. Quantitative comparison between reconstruction using GT 3D bounding boxes and noisy bounding boxes. Evaluation metrics are mIoU / chamfer L2 / F-score respectively.  
+
+<table><tr><td>Detection type</td><td>Chair</td><td>Sofa</td><td>Table</td></tr><tr><td>noisy_bbox</td><td>38.7 / 3.77 / 31.3</td><td>70.2 / 2.90 / 31.8</td><td>40.6 / 7.42 / 34.4</td></tr><tr><td>GT_bbox</td><td>38.6 / 3.57 / 31.0</td><td>70.7/ 2.88/ 31.6</td><td>41.5 / 6.52 / 36.1</td></tr><tr><td></td><td>Cabinet</td><td>Bed</td><td>Shelf</td></tr><tr><td>noisy_bbox</td><td>73.1 / 3.70 / 34.4</td><td>65.5 / 2.64 / 36.2</td><td>24.1 / 3.85 / 36.0</td></tr><tr><td>GT_bbox</td><td>75.1 / 3.10 / 37.0</td><td>62.5 / 2.62 / 35.4</td><td>24.5 / 3.45 / 37.5</td></tr></table>
+
+construction. An experiment is conducted by randomly rotating between -10 and 10 degrees, scaling between 0.8 and 1.1, and shifting the center between  $-10\%$  and  $10\%$  for each object. The quantitative results are shown in Tab. 6. We observe that, with considerable disturbances on object poses, our method achieves robust accuracy.
+
+Effectiveness of scene-level occupancy to OccGOD Tab. 3 compares the baseline (Cagroup3D) and our proposed OccGOD. Cagroup3D achieves an mAP of 55.72 and an mAR of 66.43 with an IOU threshold of 0.5. Our OccGOD enhances the baseline, improving mAP by 1.64 and mAR by 1.04. Notable increases occurred for larger
+
+furniture like tables (+2.42 in AP), toilets (+8.47 in AP and +5.69 in AR), shelves (+3.03 in AP), beds (+3.47 in AP and 4.44 in AR), and sinks (+6.27 in AP and 4.59 in AR).
+
+# 7. Conclusion
+
+We have introduced a new dataset LASA, a Large-scale Aligned Shape Annotation Dataset. In this work, we have illustrated the substantial benefits LASA brings to the community, particularly in the realms of indoor instance-level scene reconstruction and 3D object detection. Empowered by LASA, we propose a novel Diffusion-based CrossModal Shape Reconstruction approach, namely DisCo, and an Occupancy-guided 3D Object Detection method, namely OccGOD. In DisCo, we design a novel Hybrid Feature Aggregation Layer to effectively fuse and align local features from two input modalities - partial point clouds and multiview images. In OccGOD, we leverage the scene-level occupancy labels provided by LASA, to enhance 3D object detection by learning object completeness priors. Extensive experiments demonstrated that, with the support of LASA, both methods achieve state-of-the-art performance in real-world scenarios.
+
+We firmly believe that the large-scale and well-aligned features of LASA present better annotation quality and quantity, laying a foundation for many 3D downstream applications, including 3D understanding and reconstruction.
+
+# 8. Acknowledgements
+
+The work was supported in part by Guangdong Provincial Outstanding Youth Project No. 2023B1515020055, the Basic Research Project No. HZQB-KCZYZ-2021067 of Hetao Shenzhen-HK S&T Cooperation Zone, NSFC-62172348, the National Key R&D Program of China with grant No. 2018YFB1800800, by Shenzhen Outstanding Talents Training Fund 202002, by Guangdong Research Projects No. 2017ZT07X152 and No. 2019CX01X104, by Key Area R&D Program of Guangdong Province (Grant No. 2018B030338001), by the Guangdong Provincial Key Laboratory of Future Networks of Intelligence (Grant No. 2022B1212010001), and by Shenzhen Key Laboratory of Big Data and Artificial Intelligence (Grant No. ZDSYS201707251409055). It is also partly supported by NSFC-61931024 and Shenzhen General Project No. JCYJ20220530143604010.
+
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+        "text": "LASIL: Learner-Aware Supervised Imitation Learning For Long-term Microscopic Traffic Simulation",
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+        "text": "Ke Guo $^{1,2,3}$ , Zhenwei Miao $^{1*}$ , Wei Jing $^{1}$ , Weiwei Liu $^{1}$ , Weizi Li $^{4}$ , Dayang Hao $^{1}$ , Jia Pan $^{2,3}$ $^{1}$ Alibaba Group  $^{2}$ The University of Hong Kong  \n $^{3}$ Centre for Transformative Garment Production, Hong Kong  $^{4}$ University of Tennessee, Knoxville  \nu3006612@connect.hku.hk, zhenwei.mzw@alibaba-inc.com  \n21wjing@gmail.com, 11932061@zju.edu.cn, weizili@utk.edu, jpan@cs.hku.hk",
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+        "text": "Microscopic traffic simulation plays a crucial role in transportation engineering by providing insights into individual vehicle behavior and overall traffic flow. However, creating a realistic simulator that accurately replicates human driving behaviors in various traffic conditions presents significant challenges. Traditional simulators relying on heuristic models often fail to deliver accurate simulations due to the complexity of real-world traffic environments. Due to the covariate shift issue, existing imitation learning-based simulators often fail to generate stable long-term simulations. In this paper, we propose a novel approach called learner-aware supervised imitation learning to address the covariate shift problem in multi-agent imitation learning. By leveraging a variational autoencoder simultaneously modeling the expert and learner state distribution, our approach augments expert states such that the augmented state is aware of learner state distribution. Our method, applied to urban traffic simulation, demonstrates significant improvements over existing state-of-the-art baselines in both short-term microscopic and long-term macroscopic realism when evaluated on the real-world dataset pNEUMA.",
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+        "text": "1. Introduction",
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+        "text": "Microscopic traffic simulation is a cornerstone in transportation engineering. It enables engineers to predict and analyze individual vehicle behavior, providing crucial insights into how alterations in road structures or traffic management strategies might influence overall traffic flow; it allows for the testing of diverse scenarios without disrupting real-world traffic; and it enhances safety by pinpointing potential hazards and devising strategies to mitigate risks. By leveraging simulations, engineers can optimize traffic flow,",
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+        "text": "reduce congestion, and enhance overall efficiency, proving particularly advantageous in designing or enhancing road networks. Using the simulation data, policymakers and urban planners can make informed decisions aligned with community needs regarding transportation infrastructure.",
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+        "text": "However, generating realistic and accurate simulations that can simultaneously replicate the microscopic response of human drivers in various traffic conditions and long-term macroscopic traffic statistics is challenging. In recent years, significant efforts have been invested in developing realistic traffic simulators with the goal to accurately model human driving behaviors. Traditional traffic simulators, such as SUMO [24], AIMSUN [2], and MITSIM [44], typically rely on heuristic car-following models like the Intelligent Driver Model (IDM) [42]. However, despite carefully calibrating parameters, the rule-based models often fail to deliver accurate simulations due to the complexity of real-world traffic environments [12, 30]. Factors such as the road structure, neighboring vehicles, and even driver psychology can influence the decisions of human drivers, making it challenging to achieve accurate simulations [7, 27, 43].",
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+        "text": "In pursuit of realistic traffic simulations, researchers have turned to neural networks to represent the driving model through imitation learning (IL) from human demonstrations. Most traffic simulation approaches [4, 34, 41] leverage behavior cloning (BC) [32] to learn a driving policy by minimizing the disparity between the model output and the human demonstrations in training data. However, BC is hindered by covariate shift [37], where the state induced by the learner's policy progressively diverges from the expert's distribution. Existing BC-based simulators have succeeded in short-term (less than 20 seconds) simulation applications like autonomous driving tests but often fail to generate stable long-term simulations.",
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+        "text": "To address covariate shift, existing methods such as DAGger [37], DART [25], and ADAPS [28] incorporate supervisor (humans or principled simulations) corrections",
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+    {
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+        "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
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+        "text": "*Zhenwei Miao is the corresponding author.",
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+    {
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+    {
+        "type": "text",
+        "text": "at the learner's or perturbed expert's states. However, human supervision can be problematic due to intensive labor and judgment errors, and principled simulations may not account for heterogeneous driving behaviors. Recent traffic simulators [40, 46] propose using inverse reinforcement learning (IRL). These methods, such as generative adversarial imitation learning (GAIL) [17] and adversarial inverse reinforcement learning (AIRL) [13], learn a reward function using a discriminator neural network within Generative Adversarial Networks (GANs) [14]. The policy network is trained to maximize the learned reward through online reinforcement learning (RL), enabling agents to handle out-of-distribution states. However, directly applying GAIL to traffic simulation can be problematic [5]. The dynamic nature of the environment in the multi-agent system can lead to noises during policy learning, resulting in highly biased estimated gradients. Furthermore, training the discriminator in GAIL is challenging due to the instability and sensitivity of hyperparameters during min-max optimization.",
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+        "type": "text",
+        "text": "To address the issue of covariate shift in multi-agent imitation learning without depending on costly expert supervision or unstable discriminators and multi-agent RL, we propose Learner-Aware Supervised Imitation Learning (LASIL) for tackling the covariate shift problem during policy learning. We mitigate the distribution shift between expert and learner state distribution by augmenting the expert state distribution. However, there is no expert supervision at any augmented state, so we ensure that an augmented state is close to an expert state such that the future trajectory of the expert state can serve as the target trajectory for the augmented state to constrain the learner within the expert state distribution. Hence, our goal is to augment the expert state to cover the learner's state distribution while remaining close to the original expert state distribution. To achieve this, we use a variational autoencoder (VAE) [21] to simultaneously model the distributions of both the expert and learner states. By minimizing the VAE's latent space regularization loss of modeling both distributions, we project the expert and learner states into a unified latent space. And by minimizing the VAE's reconstruction loss, the resulting reconstruction leveraging such learnt latent space will resemble both expert and learner state distribution. As a result, when inputting expert states into the trained VAE, we obtain a learner-aware augmented expert state.",
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+        "type": "text",
+        "text": "In practice, we divide an agent's state into two parts: past trajectory and context, i.e., other features in the state including vehicle type, waypoints, and destination. We observe that the distribution of the context is consistent regardless of a learnt policy due to the static features of traffic conditions embedded in the context, leading to less covariate shift. Therefore, we propose a context-conditioned VAE to model the context-conditioned trajectory distribution of both expert and learner states. The decoder of the context-",
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+        "text": "In summary, our contributions are as follows:",
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+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- We propose learner-aware supervised imitation learning (LASIL) to achieve stable learning and alleviate covariate shift in multi-agent imitation learning.",
+            "- We propose a learner-aware data augmentation method based on a context-conditioned VAE that generates learner-aware augmented expert states.",
+            "- Our approach is tailored for urban traffic simulation. To the best of our knowledge, it is the first imitation learning-based traffic simulator that can reproduce long-term (more than 10 minutes) stable microscopic simulation, achieving  $40\\mathrm{x}$  simulation length improvements over previous state-of-the-art [4, 41, 46].",
+            "- We evaluate our method on the real-world dataset pNEUMA [3] with over half a million trajectories. Our approach outperforms state-of-the-art baselines in both short-term microscopic and long-term macroscopic simulations. The code is available at https://github.com/Kguo-cs/LSAIL."
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+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
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+        "type": "text",
+        "text": "2.1. Imitation learning",
+        "text_level": 1,
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Existing imitation learning (IL) methods can be broadly categorized into behavior cloning (BC) and inverse reinforcement learning (IRL) approaches. BC [32] learns a policy in a supervised fashion by minimizing the discrepancy between the learner's actions and those of an expert. However, BC suffers from the issue of covariate shift, where the state distribution induced by the learner's policy gradually deviates from that of the expert. To address this, methods like DAGger [37] and DART [25] request supervisor corrections at the learner's or perturbed expert's states. Our method follows a similar supervised learning approach to DAGger and DART, but does not require access to an expert policy.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Due to the challenges in obtaining expert supervision, recent IRL-based methods utilize feedback from a neural network-based discriminator to handle covariate shift. Typically, these methods involve an iterative process alternating between reward estimation and reinforcement learning. Earlier IRL-based methods [15, 35, 39, 47] require frequent dynamic programming processes, while recent adversarial IL approaches integrate reward function learning with policy learning using a GAN formulation. However, both GAN and RL training processes are known to be unstable, sensitive to hyperparameters, and have poor sample efficiency [9]. Moreover, the discriminator can easily exploit insignificant differences between expert and policy samples, leading to undesirable performance [45]. In contrast, our method avoids the min-max optimization problem and the sample-inefficient RL process, requiring minimal",
+        "bbox": [
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+        "page_idx": 1
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+    {
+        "type": "page_number",
+        "text": "15387",
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "fine-tuning. Instead, we utilize the real future trajectory as the target state to learn corrective behavior.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2.2. Imitation Learning-based Traffic simulation",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Recent traffic simulators focus on enhancing realism by leveraging imitation learning (IL) from human driving demonstrations, which extend traditional BC and IRL methods to tackle the challenging multi-agent IL problem.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "BC-based traffic simulators like TrafficSim [41] and SimNet [4] typically begin by training a prediction model and subsequently adjust the predicted trajectories to prevent collisions and adhere to traffic regulations during simulation. However, BC-based methods face challenges in achieving long-term simulation due to the covariate shift problem. To mitigate this issue, we augment expert state based on the policy distribution, enabling stable long-term simulation. Additionally, we enhance performance by modifying the predicted trajectory during simulation through road projection and ensuring smoothness from the current state. Notably, we skip the computationally intensive collision removal operation, prioritizing the capture of macroscopic long-term influence over micro-level details.",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "IRL-based simulators learn the underlying reward function of human driving behavior and derive the driving policy by maximizing the learned reward. While adversarial IRL methods theoretically address the covariate shift of BC in a single-agent context through online interaction, its performance deteriorates in the multi-agent IL domain due to the dynamic environment, complicating the training process. To tackle this challenge, approaches like PS-GAIL [40] and PS-ARIL [46] adopt two-stage learning and gradually introduce vehicles to the environment. Nonetheless, these methods still exhibit significant undesirable traffic phenomena, such as off-road driving, collisions, and abrupt braking. Building upon PS-GAIL, the reward-augmented imitation learning (RAIL) method [5, 22] penalizes undesirable phenomena by introducing a hand-crafted reward. However, maximizing the new reward does not guarantee the recovery of human-like trajectories. Despite numerous enhancements to the original GAIL framework, these IRL-based methods often struggle to produce stable long-term traffic flow, as evidenced in our experiments. In contrast, our method is a supervised learning approach, leading to faster, simpler, and more stable learning of driving policies.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3. Background",
+        "text_level": 1,
+        "bbox": [
+            76,
+            776,
+            205,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1. Markov Decision Process",
+        "text_level": 1,
+        "bbox": [
+            76,
+            801,
+            305,
+            816
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "We model the human driving process using a Markov decision process (MDP) denoted as  $\\mathcal{M} = \\{\\mathcal{S},\\mathcal{A},\\mathcal{T},r\\}$ , incorporating a time horizon of  $T$ , where  $\\mathcal{S}$  and  $\\mathcal{A}$  represent the continuous state and action spaces respectively. A stochastic function  $\\mathcal{T}:S\\times \\mathcal{A}\\times \\mathcal{S}\\rightarrow [0,1]$  describes the system",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "dynamics, and  $r: \\mathcal{S} \\times \\mathcal{A} \\to \\mathbb{R}$  is a reward function. The policy  $\\pi(\\boldsymbol{a} | s)$  determines the probability of selecting an action  $a$  at a state  $s$ , and a trajectory  $\\tau = (s_0, \\boldsymbol{a}_0, \\dots, s_T, \\boldsymbol{a}_T)$  represents a sequence of state-action pairs. The marginal state distribution of a policy  $\\pi$  is computed as  $\\rho^{\\pi}(s) = \\frac{1}{D} \\sum_{s \\in \\mathcal{D}_{\\pi}} \\delta_s$ , where  $\\mathcal{D}_{\\pi}$  denotes the set of states of size  $D$  in trajectories induced by the policy  $\\pi$ , and  $\\delta_s$  signifies a Dirac distribution centered on  $s$ . Similarly, the marginal state-action distribution  $\\rho^{\\pi}(s, \\boldsymbol{a})$  is computed.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.2. Imitation Learning",
+        "text_level": 1,
+        "bbox": [
+            500,
+            257,
+            683,
+            273
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In the application of IL for learning a driving policy, we assume that all agents adopt the same policy. The objective is to learn a policy  $\\pi$  that minimizes the  $f$ -divergence between the marginal state-action distribution of the expert's demonstrations  $\\rho^{\\exp}(s,a)$  and the learner policy's distribution  $\\rho^{\\pi}(s,a)$ . For example, BC optimizes the policy to minimize the Kullback-Leibler (KL) divergence at the expert state distribution  $\\mathbb{E}_{\\rho^{\\exp}(s)}[\\mathrm{KL}(\\pi^{\\exp}(a|s)\\| \\pi (a|s))]$ , while DAgger minimizes  $\\mathbb{E}_{\\rho^{\\pi}(s)}[\\mathrm{KL}(\\pi^{\\exp}(a|s)\\| \\pi (a|s))]$ . On the other hand, GAIL minimizes the Jensen-Shannon divergence  $D_{\\mathrm{JS}}(\\rho^{\\exp}(s,a)\\| \\rho^{\\pi}(s,a))$ , while AIRL minimizes the KL divergence  $\\mathrm{KL}(\\rho^{\\pi}(s,a)\\| \\rho^{\\exp}(s,a))$ .",
+        "bbox": [
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+            287,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "However, GAIL and AIRL often exhibit unsatisfactory practical performance due to their optimization processes' instability and sample inefficiency, which involve GANs and RL. In contrast, BC only requires simple and stable supervised learning but suffers from the covariate shift issue, as it only minimizes the policy difference at the expert state distribution without guaranteeing performance at the learner state distribution. DAGger addresses the covariate shift problem but requires access to the expert policy. To mitigate the covariate shift problem without depending on the expert policy, we propose maximizing the transition probability  $\\mathbb{E}_{\\boldsymbol{s} \\sim \\rho^{\\exp}(\\boldsymbol{s}), \\boldsymbol{s} + \\epsilon \\sim \\rho^{\\pi}(\\boldsymbol{s})}[\\mathcal{T}(\\boldsymbol{s} + \\epsilon, \\pi(\\boldsymbol{s} + \\epsilon), \\boldsymbol{s}')]$ , where  $\\epsilon$  is a small augmentation term. Note that our policy learns to predict the distribution of the next state  $s'$  instead of the action. Our approach assumes that when the expert's original future trajectory can serve as supervision to guide the agent back towards the expert distribution.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.3. Variational Autoencoder",
+        "text_level": 1,
+        "bbox": [
+            500,
+            763,
+            723,
+            779
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The VAE defines a generative model given by  $p_{\\theta}(\\pmb{x}, \\pmb{z}) = p(\\pmb{z}) p_{\\theta}(\\pmb{x} | \\pmb{z})$ , where  $\\pmb{z}$  is the latent variable with prior distribution  $p(\\pmb{z})$ , and  $p_{\\theta}(\\pmb{x} | \\pmb{z})$  represents the conditional distribution modeling the likelihood of data  $\\pmb{x}$  given  $\\pmb{z}$ . The learning objective is to maximize the training samples' marginal log-likelihood  $\\log p_{\\theta}(\\pmb{x})$ . However, due to the intractability of marginalization, VAE maximizes the variational lower",
+        "bbox": [
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+            900
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "15388",
+        "bbox": [
+            480,
+            944,
+            517,
+            955
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "bound using  $q_{\\phi}(\\pmb {z}|\\pmb {x})$  as the approximate posterior:",
+        "bbox": [
+            76,
+            90,
+            413,
+            107
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\log p _ {\\theta} (\\boldsymbol {x}) \\\\ \\geq \\mathbb {E} _ {\\boldsymbol {z} \\sim q _ {\\phi} (\\boldsymbol {z} | \\boldsymbol {x})} [ \\log p _ {\\theta} (\\boldsymbol {x} | \\boldsymbol {z}) ] - \\operatorname {K L} \\left(q _ {\\phi} (\\boldsymbol {z} | \\boldsymbol {x}) \\| p (\\boldsymbol {z})\\right) \\tag {1} \\\\ := - \\mathcal {L} _ {\\text {r e c}} (\\boldsymbol {x}) - \\mathcal {L} _ {\\mathrm {K L}} (\\boldsymbol {x}), \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            94,
+            116,
+            468,
+            172
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathcal{L}_{\\mathrm{rec}}(\\boldsymbol{x})$  represents the reconstruction loss, which penalizes the network for creating outputs different from the input.  $\\mathcal{L}_{\\mathrm{KL}}(\\boldsymbol{x})$  represents the KL divergence loss to make a continuous and smooth latent space, allowing easy random sampling and interpolation. Intuitively, this KL loss encourages the encoder to distribute all encodings evenly around the center of the latent space.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4. Method",
+        "text_level": 1,
+        "bbox": [
+            76,
+            299,
+            168,
+            314
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In Fig. 1, we present an overview of our method. Our model comprises three modules: a VAE-based data augmentation module, a policy network, and a post-processing (LQR and on-road projection) module. During training, we augment each expert data by generating a learner-aware augmented expert state through the VAE's reconstruction of its past trajectory. Using this augmented state along with the original future trajectory, we train the learner's policy network through supervised learning. During simulation, we roll out the policy network with several post-processing steps including sampling, projecting the trajectories onto the road, and smoothing the projected trajectories.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4.1. State Representation",
+        "text_level": 1,
+        "bbox": [
+            76,
+            513,
+            272,
+            530
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "As human drivers make decisions mainly depending on their surrounding information, we build a graph to model the traffic system with each driving agent as its node.",
+        "bbox": [
+            75,
+            537,
+            468,
+            583
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Node: The state of each agent can be divided into two components: the past trajectory  $s_p$  and the context  $s_c$ . In practice, the past trajectory is composed of the agent's positions at several past time steps, including the current time step. The context includes its type, nearby waypoints' positions and corresponding road width, the traffic light status of the road it is traveling on, and destination. The waypoints are composed of the center points of the routing roads with a fixed interval. We transform each agent's state into its individual coordinate system to learn a policy with transformation invariance. To reduce the implicit covariate shift, we set each agent's current position adding a Gaussian perturbation as the origin and the  $x$ -axis directions pointing towards the agent's destination like [16].",
+        "bbox": [
+            75,
+            584,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Edge: When each agent's state coordinates are transformed from the global coordinate system to their individual coordinate system, information about the relative positions among agents is lost. However, a traffic model needs the relative information of agents to understand how they interact with each other. To preserve these relationships, we introduce directed edges between neighboring agents. The",
+        "bbox": [
+            75,
+            795,
+            468,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "edge feature is the relative position of the destination node's coordinate origin in the source node's coordinate system.",
+        "bbox": [
+            498,
+            90,
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+            121
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4.2. Learner-aware Data Augmentation",
+        "text_level": 1,
+        "bbox": [
+            498,
+            130,
+            805,
+            146
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "To address the covariate shift issue between the expert and learner state distributions, we propose to minimize the expert's and learner's embedded state distribution difference. In practice, we propose utilizing the same VAE to model the expert and learner state distributions simultaneously. As both the expert and learner state are projected to the same latent space, the distribution of the state reconstructed from the joint latent space can resemble both distributions.",
+        "bbox": [
+            496,
+            152,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In contrast to the past trajectory, the context distribution is more challenging to model but exhibits less covariate shift. Therefore, we propose using a context-conditioned VAE to specifically model the context-conditioned trajectory distribution rather than the state distribution. For each expert or learner state represented as  $s = (s_p, s_c)$ , we employ an encoder  $q_{\\phi}(z | s_p, s_c)$  to obtain the latent variable distribution. We can sample a latent variable  $z$  from this distribution by applying the reparameterization trick. Subsequently, a decoder  $p_{\\theta}(s_p | z, s_c)$  is used to reconstruct the distribution of the past trajectory  $s_p$  given  $z$  and  $s_c$ . The VAE is trained to maximize the variational lower bound, which incorporates the context-conditioned log-likelihood of both the expert and learner past trajectories:",
+        "bbox": [
+            496,
+            275,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {V A E} = \\mathbb {E} _ {\\boldsymbol {s} \\sim \\rho^ {\\exp}} \\left[ \\mathcal {L} \\left(\\boldsymbol {s} _ {p} \\mid \\boldsymbol {s} _ {c}\\right) \\right] + \\lambda \\mathbb {E} _ {\\boldsymbol {s} \\sim \\rho^ {\\pi}} \\left[ \\mathcal {L} \\left(\\boldsymbol {s} _ {p} \\mid \\boldsymbol {s} _ {c}\\right) \\right]. \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            511,
+            497,
+            890,
+            515
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Here,  $\\lambda$  is a hyperparameter that controls the degree to which the augmented context-conditioned past trajectory distribution aligns with the learner's context-conditioned past trajectory distribution. The term  $\\mathcal{L}(s_p|s_c)$  is given by:",
+        "bbox": [
+            496,
+            525,
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+            588
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\mathcal {L} \\left(\\boldsymbol {s} _ {p} \\mid \\boldsymbol {s} _ {c}\\right) = \\mathbb {E} _ {\\boldsymbol {z} \\sim q _ {\\phi} \\left(\\boldsymbol {z} \\mid \\boldsymbol {s} _ {p}, \\boldsymbol {s} _ {c}\\right)} \\left[ \\log p _ {\\theta} \\left(\\boldsymbol {s} _ {p} \\mid \\boldsymbol {z}, \\boldsymbol {s} _ {c}\\right) \\right] \\\\ - \\operatorname {K L} \\left(q _ {\\phi} (\\boldsymbol {z} | \\boldsymbol {s} _ {p}, \\boldsymbol {s} _ {c}) \\| p (\\boldsymbol {z})\\right). \\tag {3} \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            547,
+            598,
+            890,
+            635
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "For simplicity, we assume  $p_{\\theta}$  and  $q_{\\phi}$  as multivariate normal distributions with diagonal variance matrices. The prior distribution  $p(z)$  is set as an isotropic unit Gaussian  $\\mathcal{N}(\\mathbf{0},\\mathbf{I})$",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4.3. Edge-enhanced Graph Attention Network",
+        "text_level": 1,
+        "bbox": [
+            498,
+            700,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We build all models in our approach including the VAE encoder, decoder, and learner's policy network based on an edge-enhanced graph attention (EGAT) network [11, 33], which model interactions by aggregating neighboring node and edge information using an attention mechanism. The node features in the first layer are obtained by embedding the node input with a fully connected layer and the node features in the other layers are calculated by:",
+        "bbox": [
+            496,
+            724,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\boldsymbol {h} _ {i} ^ {l} = \\sigma \\left(\\sum_ {j \\in \\mathcal {N} _ {i}} \\alpha_ {i j} ^ {l} \\boldsymbol {W} ^ {l} \\left[ \\boldsymbol {h} _ {i} ^ {(l - 1)} \\| \\boldsymbol {e} _ {i j} \\| \\boldsymbol {h} _ {j} ^ {(l - 1)} \\right]\\right), \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            537,
+            854,
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+            904
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "15389",
+        "bbox": [
+            480,
+            944,
+            517,
+            955
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/c52e0a4a753e710f5e0703f22977e3dbee94a3e67553d93d5b4a19ad522866d7.jpg",
+        "image_caption": [
+            "Figure 1. Overview of our approach. The processes with purple and red arrows handle only expert or learner data, respectively, while the processes represented by black arrows apply to both data. Each state is a multi-agent state represented by a graph. Each model, including the VAE encoder, decoder, and policy network, is implemented using an EGAT network."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            76,
+            88,
+            893,
+            335
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $h_i^l$  is the feature of node  $i$  in the  $l$ th layer,  $e_{ij}$  is the coordinate origin's position of node  $j$  relative to node  $i$ ,  $\\| \\cdot \\|$  means the concatenation,  $W^l$  is the learnable weight matrix,  $\\mathcal{N}_i$  is the set of the first-order neighbors of node  $i$  (including the node itself), and  $\\sigma$  is a non-linear activation function. The attention coefficient  $\\alpha_{ij}^l$  indicates the importance of node  $j$  to node  $i$ , considering both node and edge features, and is computed as:",
+        "bbox": [
+            76,
+            383,
+            473,
+            507
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\alpha_ {i j} ^ {l} = \\operatorname {s o f t m a x} _ {j} \\left(\\sigma \\left(\\left(\\boldsymbol {w} ^ {l}\\right) ^ {T} \\left[ \\boldsymbol {h} _ {i} ^ {(l - 1)} \\| \\boldsymbol {e} _ {i j} \\| \\boldsymbol {h} _ {j} ^ {(l - 1)} \\right]\\right)\\right), \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            84,
+            516,
+            468,
+            544
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\boldsymbol{w}^l$  is a learnable weight vector, and normalization is performed on the weights across all neighbors of node  $i$  using a softmax function. After passing through multiple EGAT layers, the node features at the last layer is fed into a fully connected layer to obtain the outputs of the network.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.4. Policy Loss",
+        "text_level": 1,
+        "bbox": [
+            76,
+            642,
+            200,
+            657
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "To train the learner's policy network, we first sample a learner-aware augmented expert state from the context-conditioned VAE for each expert state. Then, the policy network predicts its future position distribution over  $T$  time steps, denoted as  $p(\\hat{p}_1^m, \\hat{p}_2^m, \\dots, \\hat{p}_T^m)$ , which is assumed to be a product of multi-variable Gaussian distributions:",
+        "bbox": [
+            75,
+            666,
+            468,
+            756
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\np \\left(\\hat {\\boldsymbol {p}} _ {1} ^ {m}, \\hat {\\boldsymbol {p}} _ {2} ^ {m}, \\dots , \\hat {\\boldsymbol {p}} _ {T} ^ {m}\\right) = \\prod_ {t = 1} ^ {T} \\mathcal {N} \\left(\\hat {\\boldsymbol {\\mu}} _ {t} ^ {m}, \\hat {\\boldsymbol {\\Sigma}} _ {t} ^ {m}\\right), \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            138,
+            768,
+            468,
+            811
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\hat{\\pmb{\\mu}}_t^m$  and  $\\hat{\\Sigma}_t^m$  represent the mean and covariance matrix of the predicted position  $\\hat{\\pmb{p}}_t^m$  at future time step  $t$ . We assume that there is no correlation between the position distributions at different future time steps. To learn the policy network, we minimize the negative log-likelihood (NLL)",
+        "bbox": [
+            75,
+            824,
+            470,
+            902
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "loss of all agents' ground-truth future trajectories:",
+        "bbox": [
+            498,
+            383,
+            830,
+            401
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {N L L} = - \\sum_ {m = 1} ^ {M} \\sum_ {t = 1} ^ {T} \\log \\left(\\mathcal {N} \\left(\\boldsymbol {p} _ {t} ^ {m} - \\hat {\\boldsymbol {\\mu}} _ {t} ^ {m}, \\hat {\\boldsymbol {\\Sigma}} _ {t} ^ {m}\\right)\\right), \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            540,
+            409,
+            890,
+            450
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\pmb{p}_t^m$  denotes the ground truth position of agent  $m$  at future time step  $t$ , and  $M$  is the total number of agents.",
+        "bbox": [
+            498,
+            458,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.5. Simulation Process",
+        "text_level": 1,
+        "bbox": [
+            500,
+            496,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "During training, we simultaneously simulate (roll out) the learned policy network iteratively to get learner state samples. Instead of directly updating each agent to its predicted position, we apply several post-processing steps to the prediction for better realism. Firstly, we sample from the distribution, and then project each sampled position onto the nearest on-road point. Then, we smooth the projected trajectory with a linear-quadratic regulator (LQR) [1] by minimizing the total commutative quadratic cost of a linear dynamic system described by:",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\left[ \\begin{array}{l} \\tilde {\\boldsymbol {p}} _ {t + 1} ^ {m} \\\\ \\tilde {\\boldsymbol {v}} _ {t + 1} ^ {m} \\end{array} \\right] = \\left[ \\begin{array}{c c} \\boldsymbol {I} & \\boldsymbol {D} \\\\ 0 & \\boldsymbol {I} \\end{array} \\right] \\left[ \\begin{array}{l} \\tilde {\\boldsymbol {p}} _ {t} ^ {m} \\\\ \\tilde {\\boldsymbol {v}} _ {t} ^ {m} \\end{array} \\right] + \\left[ \\begin{array}{c} \\boldsymbol {D} ^ {2} \\\\ \\boldsymbol {D} \\end{array} \\right] \\tilde {\\boldsymbol {a}} _ {t} ^ {m}, \\tag {8}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+            678,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $D$  is a diagonal matrix with the interval of each time step as diagonal entries, and  $\\tilde{\\boldsymbol{p}}_t^m$ ,  $\\tilde{\\boldsymbol{v}}_t^m$ ,  $\\tilde{\\boldsymbol{a}}_t^m$  represent the LQR-planned position, velocity, and acceleration. The system is subject to a quadratic cost function given by:",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {J} = \\sum_ {m = 1} ^ {M} \\sum_ {t = 1} ^ {T} \\| \\tilde {\\boldsymbol {p}} _ {t} ^ {m} - \\bar {\\boldsymbol {p}} _ {t} ^ {m} \\| ^ {2} + \\eta_ {\\boldsymbol {a}} \\| \\tilde {\\boldsymbol {a}} _ {t} ^ {m} \\| ^ {2}, \\tag {9}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where the projected predicted position  $\\bar{\\pmb{p}}_m^t$  is considered as the target pose, and the hyper-parameter  $\\eta_{\\mathbf{a}}$  is used to penalize high acceleration. Finally, each agent is updated to the first position of the planned trajectory.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "15390",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.6. Training Process",
+        "text_level": 1,
+        "bbox": [
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+            90,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "At each training step, the policy network is trained to maximize the probability of the expert's future trajectory using its context state and history trajectory augmented by the VAE as input. Simultaneously, the VAE is iteratively trained to reconstruct the expert and learner data. The expert data are the same as the policy network's training data before augmentation. The learner data is sampled from a replay buffer. Every  $N$  training steps, we empty the replay buffer and roll out the current policy with post-processing for  $S$  time steps to generate the learner data and store it in the replay buffer. During the roll-out, we start at a random time step in the training dataset and apply our model in a closed-loop manner. At each time step during the rollout, we sample a future trajectory for each vehicle from the Gaussian distribution predicted by our policy network, project the predicted trajectory onto the road, smooth the on-road trajectory with LQR, and finally update the vehicle to the first position of the smoothed trajectory.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5. Experiment",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5.1. Dataset",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We utilize a real-world urban dataset called pNEUMA [3], which was collected by 10 drones in Athens over a span of 4 days. The dataset encompasses over half a million vehicle trajectories within a large area encompassing over  $100\\mathrm{km}$  of lanes and approximately 100 intersections. The recordings were conducted at 5 intervals each day, with each period lasting about 15 minutes and a data collection time interval of 0.04 seconds. To enhance computational efficiency, we adopt a time step of 0.4 seconds. The dataset is divided into a training set, comprising recordings from the first 3 days, and a validation/test set, consisting of recordings from the final day. Notably, we choose not to utilize other popular traffic datasets like NGSIM [8] or HighD [23] or autonomous driving datasets like Lyft [18] or nuPlan [6], as they only encompass samll-scale scenarios. This limitation makes it inadequate for evaluate macroscopic realism.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5.2. Metrics",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We evaluate the realism of our simulator by measuring the similarity between the simulation result and real data. During evaluation, each vehicle enters the simulator at its first recorded time and position, and is controlled by our simulator to complete its recorded route. When an agent reaches its final recorded position, it is removed from the simulator.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Short-term microscopic: Following [5, 40], we conduct a short-term microscopic evaluation by simulating for 20 seconds from a random time step in the test dataset. We first measure the similarity between the simulated and real",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "data using position and velocity RMSE metrics given by:",
+        "bbox": [
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+            90,
+            885,
+            107
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathrm {R M S E} = \\frac {1}{T _ {s}} \\sum_ {t = 1} ^ {T _ {s}} \\sqrt {\\frac {1}{M} \\sum_ {m = 1} ^ {M} \\| \\boldsymbol {s} _ {t} ^ {m} - \\hat {\\boldsymbol {s}} _ {t} ^ {m} \\| ^ {2}}, \\tag {10}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            537,
+            116,
+            890,
+            164
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where  $s_t^m$  and  $\\hat{s}_t^m$  were the real and simulated value of the position or velocity of the agent  $m$  at time step  $t$ , respectively.  $T_s$  was the total simulated time steps, and  $M$  was the total simulated agent number. Besides, we measure the minimum Average Displace Error (minADE) to not penalize reasonable trajectory unlike the real one:",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\min  A D E _ {N} = \\frac {1}{M} \\sum_ {m = 1} ^ {M} \\min  _ {\\hat {\\boldsymbol {s}} _ {n}} \\frac {1}{T _ {s}} \\sum_ {t = 1} ^ {T _ {s}} \\| \\boldsymbol {s} _ {t} ^ {m} - \\hat {\\boldsymbol {s}} _ {t, n} ^ {m} \\| ^ {2}, \\tag {11}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            514,
+            273,
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+            316
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where  $N = 20$  is roll-out times. We also calculate the off-road rate (the avarage proportion of vehicles that deviate more than  $1.5\\mathrm{m}$  from the road over all time steps). The common collision rate metric is not used because we focus on the long-term impact and the dataset does not provide accurate vehicle size and heading information.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Long-term macroscopic: we also evaluate our model's long-term macroscopic accuracy on five periods for 800 seconds from its initial recording time. To measure the long-term performance, we use two standard macroscopic metrics for traffic flow data [29, 36, 38], namely road density and speed RMSE, in addition to the off-road rate. The density of a road at a time step is calculated by dividing the number of vehicles on the road by its total lane length, assuming that all lanes have the same width. Meanwhile, the road speed is computed as the mean speed of all vehicles on the road. To quantify the similarity between the simulated and ground truth values, we still use RMSE, where the variable  $M$  becomes the total number of roads.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5.3. Performance",
+        "text_level": 1,
+        "bbox": [
+            500,
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+            635
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We compare our method against state-of-the-art baselines:",
+        "bbox": [
+            500,
+            643,
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+            657
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "SUMO [24]: we use the IDM model [42] as the car-following model and mobil [19] as the lane-changing model. We tune the IDM's parameters for 6 types of vehicle by minimizing the MSE between the IDM calculated acceleration and real acceleration using an Adam optimizer [20].",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "BC [32]: we learn our model directly by the BC method.",
+        "bbox": [
+            517,
+            734,
+            890,
+            750
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "MARL [26]: we train our model using IPPO [10] as the Multi-Agent RL algorithm, where the reward function is composed of three parts: a displacement reward (average distance between agent trajectory with GT trajectory), an off-road penalty and a terminal reward.",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "MARL+BC [31]: we add a behavior cloning term in the loss function while learning the policy with MARL.",
+        "bbox": [
+            496,
+            825,
+            890,
+            854
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "PS-GAIL [40]: we let all vehicles share the same policy parameter and critic parameter and learn the policy using reward functions computed by GAIL.",
+        "bbox": [
+            496,
+            854,
+            890,
+            900
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "15391",
+        "bbox": [
+            480,
+            944,
+            517,
+            955
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/0268c0a1fa53ed225ecb6bfcfbb35d7df3d3f48b8af73efc045b67907470045d.jpg",
+        "table_caption": [
+            "Table 1. Comparison with baselines and ablated models on microscopic metrics for 20 seconds."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>Position RMSE(m)</td><td>Velocity RMSE(m/s)</td><td>minADE20(m)</td><td>Off-road(%)</td></tr><tr><td>SUMO [24]</td><td>41.25</td><td>7.00</td><td>24.20</td><td>0</td></tr><tr><td>BC [32]</td><td>40.08±1.61</td><td>6.74±0.37</td><td>22.02±3.98</td><td>33.43±3.10</td></tr><tr><td>MARL [26]</td><td>48.66±1.54</td><td>8.92±0.67</td><td>40.07±1.26</td><td>3.70±0.40</td></tr><tr><td>MARL+BC [31]</td><td>29.78±0.42</td><td>4.54±0.14</td><td>22.07±0.21</td><td>11.14±1.17</td></tr><tr><td>PS-GAIL [40]</td><td>34.78±0.43</td><td>5.33±0.12</td><td>27.86±0.33</td><td>7.65±0.32</td></tr><tr><td>RAIL [5]</td><td>31.62±0.65</td><td>5.51±0.09</td><td>24.51±0.41</td><td>2.57±0.47</td></tr><tr><td>LASIL (ours)</td><td>19.21±0.44</td><td>3.02±0.07</td><td>12.79±0.32</td><td>0.28±0.01</td></tr><tr><td>w/o Augmentation</td><td>21.62±0.54</td><td>3.34±0.14</td><td>13.81±0.37</td><td>1.31±0.18</td></tr><tr><td>w/o Context-conditioned</td><td>23.03±0.87</td><td>3.73±0.12</td><td>14.94±0.43</td><td>0.51±0.04</td></tr><tr><td>w/o On-road Projection</td><td>22.53±0.42</td><td>3.26±0.10</td><td>14.42±0.33</td><td>1.74±0.60</td></tr><tr><td>w/o LQR</td><td>22.62±0.43</td><td>4.05±0.15</td><td>14.02±0.28</td><td>0.22±0.02</td></tr></table>",
+        "bbox": [
+            122,
+            103,
+            848,
+            299
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/f9b8def84aa564045cc8cd26e7540397c1fc332b7a0e7a8cddf50f4bae582c4f.jpg",
+        "table_caption": [
+            "Table 2. Comparison with baselines and ablated models on macroscopic metrics for 800 seconds."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>Road Density RMSE(veh/km)</td><td>Road Speed RMSE(m/s)</td><td>Off-road(%)</td></tr><tr><td>SUMO [24]</td><td>52.70</td><td>5.52</td><td>0</td></tr><tr><td>BC [32]</td><td>61.51±1.53</td><td>5.38±0.21</td><td>42.15±5.25</td></tr><tr><td>MARL [26]</td><td>90.59±2.65</td><td>5.27±0.48</td><td>4.63±0.64</td></tr><tr><td>MARL+BC [31]</td><td>43.60±2.80</td><td>4.01±0.13</td><td>22.73±5.62</td></tr><tr><td>PS-GAIL [40]</td><td>54.06±1.23</td><td>4.03±0.05</td><td>13.24±3.20</td></tr><tr><td>RAIL [5]</td><td>54.45±1.89</td><td>3.89±0.11</td><td>2.92±0.38</td></tr><tr><td>LASIL (ours)</td><td>45.13±0.25</td><td>3.17±0.14</td><td>0.34±0.03</td></tr><tr><td>w/o Augmentation</td><td>55.65±0.44</td><td>3.73±0.23</td><td>9.62±1.40</td></tr><tr><td>w/o Context-conditioned</td><td>55.98±0.51</td><td>4.48±0.19</td><td>0.64±0.08</td></tr><tr><td>w/o On-road Projection</td><td>52.90±0.54</td><td>3.59±0.20</td><td>11.33±2.37</td></tr><tr><td>w/o LQR</td><td>61.68±0.96</td><td>3.54±0.16</td><td>0.47±0.07</td></tr></table>",
+        "bbox": [
+            129,
+            319,
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+            515
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "RAIL [5]: we learn the model as PS-GAIL but with additional displacement, off-road and terminal rewards.",
+        "bbox": [
+            76,
+            520,
+            468,
+            550
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We train and evaluate each model five times to obtain the mean and standard deviation (std) of various metrics. Note that we do not apply on-road projection and LQR for baselines. We evaluate both short-term and long-term performance, as shown in Tab. 1 and Tab. 2, respectively. Our method achieves better results than all baselines in terms of position and velocity RMSE, road density and speed RMSE, with minor off-road rate.",
+        "bbox": [
+            75,
+            551,
+            468,
+            672
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5.4. Ablation Study",
+        "text_level": 1,
+        "bbox": [
+            76,
+            681,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We conducted a series of ablation experiments to assess the individual contributions of crucial components in our approach, whose results are presented in Tab. 1 and Tab. 2.",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Augmentation: By removing our VAE module and directly learning the original expert state and action, we analyze the importance of our data augmentation technique. The results demonstrate that augmentation plays a vital role in improving both short-term and long-term simulation performance by mitigating covariate shift.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Context-conditioned VAE: To emphasize the significance of modeling the context-conditioned trajectory distribution rather than the whole state distribution, we replaced our context-conditioned VAE with a naive VAE that directly",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "models the expert and learner state distribution. The observed drop in performance demonstrates the challenges in reconstructing the context distribution.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "On-road projection: Our ablation study on the on-road projection module aims to show its impact on reducing the off-road rate. The results show that the on-road projection module leads to a notable decrease in the off-road rate and moderate improvements in other performance metrics.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "LQR: Removing LQR module allows us to evaluate its effectiveness. While LQR led to a higher short-term off-road rate due to more constrained movement (driving off-road due to inertia), its removal deteriorates other short-term and long-term metrics, because LQR can smooth the trajectory, thus leads to more realistic simulations.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5.5. Qualitative Result",
+        "text_level": 1,
+        "bbox": [
+            500,
+            766,
+            678,
+            782
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "In Fig. 2, we present the mean road density and speed for real-world data, SUMO simulation, and our proposed method over all time steps. The results demonstrate that our proposed method surpasses the capabilities of the SUMO simulator at replicating long-term macroscopic traffic patterns due to our model's enhanced ability to replicate the typical microscopic driving behaviors over a long period.",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "15392",
+        "bbox": [
+            480,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/7fe78b129460e56077e2dacba9ddc2df6714e3b7076b387f2f8e7ad5ec3de2b5.jpg",
+        "image_caption": [
+            "Figure 2. Mean density and speed on each road over all time steps in the long-term evaluation. Our method's density and speed hot-maps have a more similar color to the ground-truth one compared with the SUMO's."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            101,
+            87,
+            861,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "6. Conclusion",
+        "text_level": 1,
+        "bbox": [
+            76,
+            678,
+            194,
+            694
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "In conclusion, we have addressed the challenge of creating a realistic traffic simulator that accurately models human driving behaviors in various traffic conditions. Traditional imitation learning-based simulators often fail to deliver accurate long-term simulations due to the covariate shift problem in multi-agent imitation learning. To tackle this issue, we proposed a learner-aware supervised imitation learning method, which leverages a context-conditioned VAE to generate learner-aware augmented expert states. We leverage a context-conditioned VAE to simultaneously reconstruct the expert and learner state. This approach enables the reproduction of long-term stable microscopic traffic simulations, marking a significant advancement in the field of urban",
+        "bbox": [
+            75,
+            703,
+            470,
+            900
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "traffic simulation. Our method has demonstrated superior performance over existing state-of-the-art simulators when evaluated on the real-world dataset pNEUMA, achieving better short-term microscopic and long-term macroscopic similarity to real-world data than state-of-the-art baselines.",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "7. Acknowledgements",
+        "text_level": 1,
+        "bbox": [
+            500,
+            768,
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+            787
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "This research project is partially supported by the Innovation and Technology Commission of the HKSAR Government under the InnoHK initiative, Hong Kong General Research Fund (11202119 and 11208718), Innovation and Technology Commission (GHP/126/21GD), and Guangdong, Hong Kong and Macao Joint Innovation Project (2023A0505010016).",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "page_number",
+        "text": "15393",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
+            78,
+            89,
+            173,
+            104
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "list",
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2024/LASIL_ Learner-Aware Supervised Imitation Learning For Long-term Microscopic Traffic Simulation/44a62bf3-d838-46a8-bbd5-a317e9666352_model.json

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+            "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+        },
+        {
+            "type": "title",
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+            "content": "LASIL: Learner-Aware Supervised Imitation Learning For Long-term Microscopic Traffic Simulation"
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+            "type": "text",
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+            "content": "Ke Guo\\(^{1,2,3}\\), Zhenwei Miao\\(^{1*}\\), Wei Jing\\(^{1}\\), Weiwei Liu\\(^{1}\\), Weizi Li\\(^{4}\\), Dayang Hao\\(^{1}\\), Jia Pan\\(^{2,3}\\)  \n\\(^{1}\\)Alibaba Group \\(^{2}\\)The University of Hong Kong  \n\\(^{3}\\)Centre for Transformative Garment Production, Hong Kong \\(^{4}\\)University of Tennessee, Knoxville  \nu3006612@connect.hku.hk, zhenwei.mzw@alibaba-inc.com  \n21wjing@gmail.com, 11932061@zju.edu.cn, weizili@utk.edu, jpan@cs.hku.hk"
+        },
+        {
+            "type": "title",
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+            "content": "Abstract"
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+            "bbox": [
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+            "content": "Microscopic traffic simulation plays a crucial role in transportation engineering by providing insights into individual vehicle behavior and overall traffic flow. However, creating a realistic simulator that accurately replicates human driving behaviors in various traffic conditions presents significant challenges. Traditional simulators relying on heuristic models often fail to deliver accurate simulations due to the complexity of real-world traffic environments. Due to the covariate shift issue, existing imitation learning-based simulators often fail to generate stable long-term simulations. In this paper, we propose a novel approach called learner-aware supervised imitation learning to address the covariate shift problem in multi-agent imitation learning. By leveraging a variational autoencoder simultaneously modeling the expert and learner state distribution, our approach augments expert states such that the augmented state is aware of learner state distribution. Our method, applied to urban traffic simulation, demonstrates significant improvements over existing state-of-the-art baselines in both short-term microscopic and long-term macroscopic realism when evaluated on the real-world dataset pNEUMA."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "angle": 0,
+            "content": "1. Introduction"
+        },
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+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "Microscopic traffic simulation is a cornerstone in transportation engineering. It enables engineers to predict and analyze individual vehicle behavior, providing crucial insights into how alterations in road structures or traffic management strategies might influence overall traffic flow; it allows for the testing of diverse scenarios without disrupting real-world traffic; and it enhances safety by pinpointing potential hazards and devising strategies to mitigate risks. By leveraging simulations, engineers can optimize traffic flow,"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.329,
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+            ],
+            "angle": 0,
+            "content": "reduce congestion, and enhance overall efficiency, proving particularly advantageous in designing or enhancing road networks. Using the simulation data, policymakers and urban planners can make informed decisions aligned with community needs regarding transportation infrastructure."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": "However, generating realistic and accurate simulations that can simultaneously replicate the microscopic response of human drivers in various traffic conditions and long-term macroscopic traffic statistics is challenging. In recent years, significant efforts have been invested in developing realistic traffic simulators with the goal to accurately model human driving behaviors. Traditional traffic simulators, such as SUMO [24], AIMSUN [2], and MITSIM [44], typically rely on heuristic car-following models like the Intelligent Driver Model (IDM) [42]. However, despite carefully calibrating parameters, the rule-based models often fail to deliver accurate simulations due to the complexity of real-world traffic environments [12, 30]. Factors such as the road structure, neighboring vehicles, and even driver psychology can influence the decisions of human drivers, making it challenging to achieve accurate simulations [7, 27, 43]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
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+            ],
+            "angle": 0,
+            "content": "In pursuit of realistic traffic simulations, researchers have turned to neural networks to represent the driving model through imitation learning (IL) from human demonstrations. Most traffic simulation approaches [4, 34, 41] leverage behavior cloning (BC) [32] to learn a driving policy by minimizing the disparity between the model output and the human demonstrations in training data. However, BC is hindered by covariate shift [37], where the state induced by the learner's policy progressively diverges from the expert's distribution. Existing BC-based simulators have succeeded in short-term (less than 20 seconds) simulation applications like autonomous driving tests but often fail to generate stable long-term simulations."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "To address covariate shift, existing methods such as DAGger [37], DART [25], and ADAPS [28] incorporate supervisor (humans or principled simulations) corrections"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.096,
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+            ],
+            "angle": 0,
+            "content": "*Zhenwei Miao is the corresponding author."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
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+            "angle": 0,
+            "content": "15386"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.473,
+                0.38
+            ],
+            "angle": 0,
+            "content": "at the learner's or perturbed expert's states. However, human supervision can be problematic due to intensive labor and judgment errors, and principled simulations may not account for heterogeneous driving behaviors. Recent traffic simulators [40, 46] propose using inverse reinforcement learning (IRL). These methods, such as generative adversarial imitation learning (GAIL) [17] and adversarial inverse reinforcement learning (AIRL) [13], learn a reward function using a discriminator neural network within Generative Adversarial Networks (GANs) [14]. The policy network is trained to maximize the learned reward through online reinforcement learning (RL), enabling agents to handle out-of-distribution states. However, directly applying GAIL to traffic simulation can be problematic [5]. The dynamic nature of the environment in the multi-agent system can lead to noises during policy learning, resulting in highly biased estimated gradients. Furthermore, training the discriminator in GAIL is challenging due to the instability and sensitivity of hyperparameters during min-max optimization."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.384,
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+            ],
+            "angle": 0,
+            "content": "To address the issue of covariate shift in multi-agent imitation learning without depending on costly expert supervision or unstable discriminators and multi-agent RL, we propose Learner-Aware Supervised Imitation Learning (LASIL) for tackling the covariate shift problem during policy learning. We mitigate the distribution shift between expert and learner state distribution by augmenting the expert state distribution. However, there is no expert supervision at any augmented state, so we ensure that an augmented state is close to an expert state such that the future trajectory of the expert state can serve as the target trajectory for the augmented state to constrain the learner within the expert state distribution. Hence, our goal is to augment the expert state to cover the learner's state distribution while remaining close to the original expert state distribution. To achieve this, we use a variational autoencoder (VAE) [21] to simultaneously model the distributions of both the expert and learner states. By minimizing the VAE's latent space regularization loss of modeling both distributions, we project the expert and learner states into a unified latent space. And by minimizing the VAE's reconstruction loss, the resulting reconstruction leveraging such learnt latent space will resemble both expert and learner state distribution. As a result, when inputting expert states into the trained VAE, we obtain a learner-aware augmented expert state."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": "In practice, we divide an agent's state into two parts: past trajectory and context, i.e., other features in the state including vehicle type, waypoints, and destination. We observe that the distribution of the context is consistent regardless of a learnt policy due to the static features of traffic conditions embedded in the context, leading to less covariate shift. Therefore, we propose a context-conditioned VAE to model the context-conditioned trajectory distribution of both expert and learner states. The decoder of the context-"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.122
+            ],
+            "angle": 0,
+            "content": "conditioned VAE will receive both the latent variable and the context, and yield only the trajectory information."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "In summary, our contributions are as follows:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.14,
+                0.891,
+                0.184
+            ],
+            "angle": 0,
+            "content": "- We propose learner-aware supervised imitation learning (LASIL) to achieve stable learning and alleviate covariate shift in multi-agent imitation learning."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.185,
+                0.892,
+                0.229
+            ],
+            "angle": 0,
+            "content": "- We propose a learner-aware data augmentation method based on a context-conditioned VAE that generates learner-aware augmented expert states."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.23,
+                0.892,
+                0.319
+            ],
+            "angle": 0,
+            "content": "- Our approach is tailored for urban traffic simulation. To the best of our knowledge, it is the first imitation learning-based traffic simulator that can reproduce long-term (more than 10 minutes) stable microscopic simulation, achieving \\(40\\mathrm{x}\\) simulation length improvements over previous state-of-the-art [4, 41, 46]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.32,
+                0.892,
+                0.41
+            ],
+            "angle": 0,
+            "content": "- We evaluate our method on the real-world dataset pNEUMA [3] with over half a million trajectories. Our approach outperforms state-of-the-art baselines in both short-term microscopic and long-term macroscopic simulations. The code is available at https://github.com/Kguo-cs/LSAIL."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.5,
+                0.14,
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+                0.41
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+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "angle": 0,
+            "content": "2. Related Work"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.453,
+                0.677,
+                0.469
+            ],
+            "angle": 0,
+            "content": "2.1. Imitation learning"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.477,
+                0.892,
+                0.658
+            ],
+            "angle": 0,
+            "content": "Existing imitation learning (IL) methods can be broadly categorized into behavior cloning (BC) and inverse reinforcement learning (IRL) approaches. BC [32] learns a policy in a supervised fashion by minimizing the discrepancy between the learner's actions and those of an expert. However, BC suffers from the issue of covariate shift, where the state distribution induced by the learner's policy gradually deviates from that of the expert. To address this, methods like DAGger [37] and DART [25] request supervisor corrections at the learner's or perturbed expert's states. Our method follows a similar supervised learning approach to DAGger and DART, but does not require access to an expert policy."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.66,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Due to the challenges in obtaining expert supervision, recent IRL-based methods utilize feedback from a neural network-based discriminator to handle covariate shift. Typically, these methods involve an iterative process alternating between reward estimation and reinforcement learning. Earlier IRL-based methods [15, 35, 39, 47] require frequent dynamic programming processes, while recent adversarial IL approaches integrate reward function learning with policy learning using a GAN formulation. However, both GAN and RL training processes are known to be unstable, sensitive to hyperparameters, and have poor sample efficiency [9]. Moreover, the discriminator can easily exploit insignificant differences between expert and policy samples, leading to undesirable performance [45]. In contrast, our method avoids the min-max optimization problem and the sample-inefficient RL process, requiring minimal"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "15387"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.092,
+                0.47,
+                0.122
+            ],
+            "angle": 0,
+            "content": "fine-tuning. Instead, we utilize the real future trajectory as the target state to learn corrective behavior."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.133,
+                0.453,
+                0.149
+            ],
+            "angle": 0,
+            "content": "2.2. Imitation Learning-based Traffic simulation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.156,
+                0.469,
+                0.217
+            ],
+            "angle": 0,
+            "content": "Recent traffic simulators focus on enhancing realism by leveraging imitation learning (IL) from human driving demonstrations, which extend traditional BC and IRL methods to tackle the challenging multi-agent IL problem."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.217,
+                0.469,
+                0.428
+            ],
+            "angle": 0,
+            "content": "BC-based traffic simulators like TrafficSim [41] and SimNet [4] typically begin by training a prediction model and subsequently adjust the predicted trajectories to prevent collisions and adhere to traffic regulations during simulation. However, BC-based methods face challenges in achieving long-term simulation due to the covariate shift problem. To mitigate this issue, we augment expert state based on the policy distribution, enabling stable long-term simulation. Additionally, we enhance performance by modifying the predicted trajectory during simulation through road projection and ensuring smoothness from the current state. Notably, we skip the computationally intensive collision removal operation, prioritizing the capture of macroscopic long-term influence over micro-level details."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.429,
+                0.47,
+                0.761
+            ],
+            "angle": 0,
+            "content": "IRL-based simulators learn the underlying reward function of human driving behavior and derive the driving policy by maximizing the learned reward. While adversarial IRL methods theoretically address the covariate shift of BC in a single-agent context through online interaction, its performance deteriorates in the multi-agent IL domain due to the dynamic environment, complicating the training process. To tackle this challenge, approaches like PS-GAIL [40] and PS-ARIL [46] adopt two-stage learning and gradually introduce vehicles to the environment. Nonetheless, these methods still exhibit significant undesirable traffic phenomena, such as off-road driving, collisions, and abrupt braking. Building upon PS-GAIL, the reward-augmented imitation learning (RAIL) method [5, 22] penalizes undesirable phenomena by introducing a hand-crafted reward. However, maximizing the new reward does not guarantee the recovery of human-like trajectories. Despite numerous enhancements to the original GAIL framework, these IRL-based methods often struggle to produce stable long-term traffic flow, as evidenced in our experiments. In contrast, our method is a supervised learning approach, leading to faster, simpler, and more stable learning of driving policies."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.777,
+                0.206,
+                0.793
+            ],
+            "angle": 0,
+            "content": "3. Background"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.802,
+                0.307,
+                0.817
+            ],
+            "angle": 0,
+            "content": "3.1. Markov Decision Process"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.825,
+                0.469,
+                0.901
+            ],
+            "angle": 0,
+            "content": "We model the human driving process using a Markov decision process (MDP) denoted as \\(\\mathcal{M} = \\{\\mathcal{S},\\mathcal{A},\\mathcal{T},r\\}\\), incorporating a time horizon of \\(T\\), where \\(\\mathcal{S}\\) and \\(\\mathcal{A}\\) represent the continuous state and action spaces respectively. A stochastic function \\(\\mathcal{T}:S\\times \\mathcal{A}\\times \\mathcal{S}\\rightarrow [0,1]\\) describes the system"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.092,
+                0.892,
+                0.228
+            ],
+            "angle": 0,
+            "content": "dynamics, and \\(r: \\mathcal{S} \\times \\mathcal{A} \\to \\mathbb{R}\\) is a reward function. The policy \\(\\pi(\\boldsymbol{a} | s)\\) determines the probability of selecting an action \\(a\\) at a state \\(s\\), and a trajectory \\(\\tau = (s_0, \\boldsymbol{a}_0, \\dots, s_T, \\boldsymbol{a}_T)\\) represents a sequence of state-action pairs. The marginal state distribution of a policy \\(\\pi\\) is computed as \\(\\rho^{\\pi}(s) = \\frac{1}{D} \\sum_{s \\in \\mathcal{D}_{\\pi}} \\delta_s\\), where \\(\\mathcal{D}_{\\pi}\\) denotes the set of states of size \\(D\\) in trajectories induced by the policy \\(\\pi\\), and \\(\\delta_s\\) signifies a Dirac distribution centered on \\(s\\). Similarly, the marginal state-action distribution \\(\\rho^{\\pi}(s, \\boldsymbol{a})\\) is computed."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.258,
+                0.684,
+                0.274
+            ],
+            "angle": 0,
+            "content": "3.2. Imitation Learning"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.289,
+                0.892,
+                0.472
+            ],
+            "angle": 0,
+            "content": "In the application of IL for learning a driving policy, we assume that all agents adopt the same policy. The objective is to learn a policy \\(\\pi\\) that minimizes the \\(f\\)-divergence between the marginal state-action distribution of the expert's demonstrations \\(\\rho^{\\exp}(s,a)\\) and the learner policy's distribution \\(\\rho^{\\pi}(s,a)\\). For example, BC optimizes the policy to minimize the Kullback-Leibler (KL) divergence at the expert state distribution \\(\\mathbb{E}_{\\rho^{\\exp}(s)}[\\mathrm{KL}(\\pi^{\\exp}(a|s)\\| \\pi (a|s))]\\), while DAgger minimizes \\(\\mathbb{E}_{\\rho^{\\pi}(s)}[\\mathrm{KL}(\\pi^{\\exp}(a|s)\\| \\pi (a|s))]\\). On the other hand, GAIL minimizes the Jensen-Shannon divergence \\(D_{\\mathrm{JS}}(\\rho^{\\exp}(s,a)\\| \\rho^{\\pi}(s,a))\\), while AIRL minimizes the KL divergence \\(\\mathrm{KL}(\\rho^{\\pi}(s,a)\\| \\rho^{\\exp}(s,a))\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.478,
+                0.892,
+                0.734
+            ],
+            "angle": 0,
+            "content": "However, GAIL and AIRL often exhibit unsatisfactory practical performance due to their optimization processes' instability and sample inefficiency, which involve GANs and RL. In contrast, BC only requires simple and stable supervised learning but suffers from the covariate shift issue, as it only minimizes the policy difference at the expert state distribution without guaranteeing performance at the learner state distribution. DAGger addresses the covariate shift problem but requires access to the expert policy. To mitigate the covariate shift problem without depending on the expert policy, we propose maximizing the transition probability \\(\\mathbb{E}_{\\boldsymbol{s} \\sim \\rho^{\\exp}(\\boldsymbol{s}), \\boldsymbol{s} + \\epsilon \\sim \\rho^{\\pi}(\\boldsymbol{s})}[\\mathcal{T}(\\boldsymbol{s} + \\epsilon, \\pi(\\boldsymbol{s} + \\epsilon), \\boldsymbol{s}')]\\), where \\(\\epsilon\\) is a small augmentation term. Note that our policy learns to predict the distribution of the next state \\(s'\\) instead of the action. Our approach assumes that when the expert's original future trajectory can serve as supervision to guide the agent back towards the expert distribution."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.765,
+                0.724,
+                0.78
+            ],
+            "angle": 0,
+            "content": "3.3. Variational Autoencoder"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.795,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "The VAE defines a generative model given by \\( p_{\\theta}(\\pmb{x}, \\pmb{z}) = p(\\pmb{z}) p_{\\theta}(\\pmb{x} | \\pmb{z}) \\), where \\( \\pmb{z} \\) is the latent variable with prior distribution \\( p(\\pmb{z}) \\), and \\( p_{\\theta}(\\pmb{x} | \\pmb{z}) \\) represents the conditional distribution modeling the likelihood of data \\( \\pmb{x} \\) given \\( \\pmb{z} \\). The learning objective is to maximize the training samples' marginal log-likelihood \\( \\log p_{\\theta}(\\pmb{x}) \\). However, due to the intractability of marginalization, VAE maximizes the variational lower"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "15388"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.092,
+                0.414,
+                0.108
+            ],
+            "angle": 0,
+            "content": "bound using \\(q_{\\phi}(\\pmb {z}|\\pmb {x})\\) as the approximate posterior:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.096,
+                0.117,
+                0.469,
+                0.173
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} \\log p _ {\\theta} (\\boldsymbol {x}) \\\\ \\geq \\mathbb {E} _ {\\boldsymbol {z} \\sim q _ {\\phi} (\\boldsymbol {z} | \\boldsymbol {x})} [ \\log p _ {\\theta} (\\boldsymbol {x} | \\boldsymbol {z}) ] - \\operatorname {K L} \\left(q _ {\\phi} (\\boldsymbol {z} | \\boldsymbol {x}) \\| p (\\boldsymbol {z})\\right) \\tag {1} \\\\ := - \\mathcal {L} _ {\\text {r e c}} (\\boldsymbol {x}) - \\mathcal {L} _ {\\mathrm {K L}} (\\boldsymbol {x}), \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.182,
+                0.47,
+                0.289
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathcal{L}_{\\mathrm{rec}}(\\boldsymbol{x})\\) represents the reconstruction loss, which penalizes the network for creating outputs different from the input. \\(\\mathcal{L}_{\\mathrm{KL}}(\\boldsymbol{x})\\) represents the KL divergence loss to make a continuous and smooth latent space, allowing easy random sampling and interpolation. Intuitively, this KL loss encourages the encoder to distribute all encodings evenly around the center of the latent space."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.3,
+                0.169,
+                0.315
+            ],
+            "angle": 0,
+            "content": "4. Method"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.326,
+                0.47,
+                0.508
+            ],
+            "angle": 0,
+            "content": "In Fig. 1, we present an overview of our method. Our model comprises three modules: a VAE-based data augmentation module, a policy network, and a post-processing (LQR and on-road projection) module. During training, we augment each expert data by generating a learner-aware augmented expert state through the VAE's reconstruction of its past trajectory. Using this augmented state along with the original future trajectory, we train the learner's policy network through supervised learning. During simulation, we roll out the policy network with several post-processing steps including sampling, projecting the trajectories onto the road, and smoothing the projected trajectories."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.515,
+                0.274,
+                0.531
+            ],
+            "angle": 0,
+            "content": "4.1. State Representation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.539,
+                0.469,
+                0.584
+            ],
+            "angle": 0,
+            "content": "As human drivers make decisions mainly depending on their surrounding information, we build a graph to model the traffic system with each driving agent as its node."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.585,
+                0.469,
+                0.795
+            ],
+            "angle": 0,
+            "content": "Node: The state of each agent can be divided into two components: the past trajectory \\( s_p \\) and the context \\( s_c \\). In practice, the past trajectory is composed of the agent's positions at several past time steps, including the current time step. The context includes its type, nearby waypoints' positions and corresponding road width, the traffic light status of the road it is traveling on, and destination. The waypoints are composed of the center points of the routing roads with a fixed interval. We transform each agent's state into its individual coordinate system to learn a policy with transformation invariance. To reduce the implicit covariate shift, we set each agent's current position adding a Gaussian perturbation as the origin and the \\( x \\)-axis directions pointing towards the agent's destination like [16]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.796,
+                0.469,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Edge: When each agent's state coordinates are transformed from the global coordinate system to their individual coordinate system, information about the relative positions among agents is lost. However, a traffic model needs the relative information of agents to understand how they interact with each other. To preserve these relationships, we introduce directed edges between neighboring agents. The"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.092,
+                0.892,
+                0.122
+            ],
+            "angle": 0,
+            "content": "edge feature is the relative position of the destination node's coordinate origin in the source node's coordinate system."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.131,
+                0.806,
+                0.147
+            ],
+            "angle": 0,
+            "content": "4.2. Learner-aware Data Augmentation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.154,
+                0.892,
+                0.275
+            ],
+            "angle": 0,
+            "content": "To address the covariate shift issue between the expert and learner state distributions, we propose to minimize the expert's and learner's embedded state distribution difference. In practice, we propose utilizing the same VAE to model the expert and learner state distributions simultaneously. As both the expert and learner state are projected to the same latent space, the distribution of the state reconstructed from the joint latent space can resemble both distributions."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.276,
+                0.892,
+                0.487
+            ],
+            "angle": 0,
+            "content": "In contrast to the past trajectory, the context distribution is more challenging to model but exhibits less covariate shift. Therefore, we propose using a context-conditioned VAE to specifically model the context-conditioned trajectory distribution rather than the state distribution. For each expert or learner state represented as \\( s = (s_p, s_c) \\), we employ an encoder \\( q_{\\phi}(z | s_p, s_c) \\) to obtain the latent variable distribution. We can sample a latent variable \\( z \\) from this distribution by applying the reparameterization trick. Subsequently, a decoder \\( p_{\\theta}(s_p | z, s_c) \\) is used to reconstruct the distribution of the past trajectory \\( s_p \\) given \\( z \\) and \\( s_c \\). The VAE is trained to maximize the variational lower bound, which incorporates the context-conditioned log-likelihood of both the expert and learner past trajectories:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.513,
+                0.498,
+                0.892,
+                0.516
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {V A E} = \\mathbb {E} _ {\\boldsymbol {s} \\sim \\rho^ {\\exp}} \\left[ \\mathcal {L} \\left(\\boldsymbol {s} _ {p} \\mid \\boldsymbol {s} _ {c}\\right) \\right] + \\lambda \\mathbb {E} _ {\\boldsymbol {s} \\sim \\rho^ {\\pi}} \\left[ \\mathcal {L} \\left(\\boldsymbol {s} _ {p} \\mid \\boldsymbol {s} _ {c}\\right) \\right]. \\tag {2}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.526,
+                0.892,
+                0.589
+            ],
+            "angle": 0,
+            "content": "Here, \\(\\lambda\\) is a hyperparameter that controls the degree to which the augmented context-conditioned past trajectory distribution aligns with the learner's context-conditioned past trajectory distribution. The term \\(\\mathcal{L}(s_p|s_c)\\) is given by:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.548,
+                0.599,
+                0.891,
+                0.636
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} \\mathcal {L} \\left(\\boldsymbol {s} _ {p} \\mid \\boldsymbol {s} _ {c}\\right) = \\mathbb {E} _ {\\boldsymbol {z} \\sim q _ {\\phi} \\left(\\boldsymbol {z} \\mid \\boldsymbol {s} _ {p}, \\boldsymbol {s} _ {c}\\right)} \\left[ \\log p _ {\\theta} \\left(\\boldsymbol {s} _ {p} \\mid \\boldsymbol {z}, \\boldsymbol {s} _ {c}\\right) \\right] \\\\ - \\operatorname {K L} \\left(q _ {\\phi} (\\boldsymbol {z} | \\boldsymbol {s} _ {p}, \\boldsymbol {s} _ {c}) \\| p (\\boldsymbol {z})\\right). \\tag {3} \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.647,
+                0.892,
+                0.694
+            ],
+            "angle": 0,
+            "content": "For simplicity, we assume \\(p_{\\theta}\\) and \\(q_{\\phi}\\) as multivariate normal distributions with diagonal variance matrices. The prior distribution \\(p(z)\\) is set as an isotropic unit Gaussian \\(\\mathcal{N}(\\mathbf{0},\\mathbf{I})\\)"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.701,
+                0.858,
+                0.718
+            ],
+            "angle": 0,
+            "content": "4.3. Edge-enhanced Graph Attention Network"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.725,
+                0.892,
+                0.846
+            ],
+            "angle": 0,
+            "content": "We build all models in our approach including the VAE encoder, decoder, and learner's policy network based on an edge-enhanced graph attention (EGAT) network [11, 33], which model interactions by aggregating neighboring node and edge information using an attention mechanism. The node features in the first layer are obtained by embedding the node input with a fully connected layer and the node features in the other layers are calculated by:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.538,
+                0.856,
+                0.892,
+                0.905
+            ],
+            "angle": 0,
+            "content": "\\[\n\\boldsymbol {h} _ {i} ^ {l} = \\sigma \\left(\\sum_ {j \\in \\mathcal {N} _ {i}} \\alpha_ {i j} ^ {l} \\boldsymbol {W} ^ {l} \\left[ \\boldsymbol {h} _ {i} ^ {(l - 1)} \\| \\boldsymbol {e} _ {i j} \\| \\boldsymbol {h} _ {j} ^ {(l - 1)} \\right]\\right), \\tag {4}\n\\]"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "15389"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.078,
+                0.089,
+                0.895,
+                0.337
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.339,
+                0.895,
+                0.381
+            ],
+            "angle": 0,
+            "content": "Figure 1. Overview of our approach. The processes with purple and red arrows handle only expert or learner data, respectively, while the processes represented by black arrows apply to both data. Each state is a multi-agent state represented by a graph. Each model, including the VAE encoder, decoder, and policy network, is implemented using an EGAT network."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.385,
+                0.474,
+                0.508
+            ],
+            "angle": 0,
+            "content": "where \\( h_i^l \\) is the feature of node \\( i \\) in the \\( l \\)th layer, \\( e_{ij} \\) is the coordinate origin's position of node \\( j \\) relative to node \\( i \\), \\( \\| \\cdot \\| \\) means the concatenation, \\( W^l \\) is the learnable weight matrix, \\( \\mathcal{N}_i \\) is the set of the first-order neighbors of node \\( i \\) (including the node itself), and \\( \\sigma \\) is a non-linear activation function. The attention coefficient \\( \\alpha_{ij}^l \\) indicates the importance of node \\( j \\) to node \\( i \\), considering both node and edge features, and is computed as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.085,
+                0.517,
+                0.47,
+                0.545
+            ],
+            "angle": 0,
+            "content": "\\[\n\\alpha_ {i j} ^ {l} = \\operatorname {s o f t m a x} _ {j} \\left(\\sigma \\left(\\left(\\boldsymbol {w} ^ {l}\\right) ^ {T} \\left[ \\boldsymbol {h} _ {i} ^ {(l - 1)} \\| \\boldsymbol {e} _ {i j} \\| \\boldsymbol {h} _ {j} ^ {(l - 1)} \\right]\\right)\\right), \\tag {5}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.556,
+                0.47,
+                0.633
+            ],
+            "angle": 0,
+            "content": "where \\(\\boldsymbol{w}^l\\) is a learnable weight vector, and normalization is performed on the weights across all neighbors of node \\(i\\) using a softmax function. After passing through multiple EGAT layers, the node features at the last layer is fed into a fully connected layer to obtain the outputs of the network."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.643,
+                0.202,
+                0.659
+            ],
+            "angle": 0,
+            "content": "4.4. Policy Loss"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.667,
+                0.47,
+                0.757
+            ],
+            "angle": 0,
+            "content": "To train the learner's policy network, we first sample a learner-aware augmented expert state from the context-conditioned VAE for each expert state. Then, the policy network predicts its future position distribution over \\( T \\) time steps, denoted as \\( p(\\hat{p}_1^m, \\hat{p}_2^m, \\dots, \\hat{p}_T^m) \\), which is assumed to be a product of multi-variable Gaussian distributions:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.14,
+                0.77,
+                0.47,
+                0.812
+            ],
+            "angle": 0,
+            "content": "\\[\np \\left(\\hat {\\boldsymbol {p}} _ {1} ^ {m}, \\hat {\\boldsymbol {p}} _ {2} ^ {m}, \\dots , \\hat {\\boldsymbol {p}} _ {T} ^ {m}\\right) = \\prod_ {t = 1} ^ {T} \\mathcal {N} \\left(\\hat {\\boldsymbol {\\mu}} _ {t} ^ {m}, \\hat {\\boldsymbol {\\Sigma}} _ {t} ^ {m}\\right), \\tag {6}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.825,
+                0.471,
+                0.903
+            ],
+            "angle": 0,
+            "content": "where \\(\\hat{\\pmb{\\mu}}_t^m\\) and \\(\\hat{\\Sigma}_t^m\\) represent the mean and covariance matrix of the predicted position \\(\\hat{\\pmb{p}}_t^m\\) at future time step \\(t\\). We assume that there is no correlation between the position distributions at different future time steps. To learn the policy network, we minimize the negative log-likelihood (NLL)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.385,
+                0.831,
+                0.402
+            ],
+            "angle": 0,
+            "content": "loss of all agents' ground-truth future trajectories:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.542,
+                0.41,
+                0.892,
+                0.452
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {N L L} = - \\sum_ {m = 1} ^ {M} \\sum_ {t = 1} ^ {T} \\log \\left(\\mathcal {N} \\left(\\boldsymbol {p} _ {t} ^ {m} - \\hat {\\boldsymbol {\\mu}} _ {t} ^ {m}, \\hat {\\boldsymbol {\\Sigma}} _ {t} ^ {m}\\right)\\right), \\tag {7}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.459,
+                0.894,
+                0.49
+            ],
+            "angle": 0,
+            "content": "where \\( \\pmb{p}_t^m \\) denotes the ground truth position of agent \\( m \\) at future time step \\( t \\), and \\( M \\) is the total number of agents."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.497,
+                0.684,
+                0.512
+            ],
+            "angle": 0,
+            "content": "4.5. Simulation Process"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.52,
+                0.895,
+                0.672
+            ],
+            "angle": 0,
+            "content": "During training, we simultaneously simulate (roll out) the learned policy network iteratively to get learner state samples. Instead of directly updating each agent to its predicted position, we apply several post-processing steps to the prediction for better realism. Firstly, we sample from the distribution, and then project each sampled position onto the nearest on-road point. Then, we smooth the projected trajectory with a linear-quadratic regulator (LQR) [1] by minimizing the total commutative quadratic cost of a linear dynamic system described by:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.521,
+                0.679,
+                0.892,
+                0.715
+            ],
+            "angle": 0,
+            "content": "\\[\n\\left[ \\begin{array}{l} \\tilde {\\boldsymbol {p}} _ {t + 1} ^ {m} \\\\ \\tilde {\\boldsymbol {v}} _ {t + 1} ^ {m} \\end{array} \\right] = \\left[ \\begin{array}{c c} \\boldsymbol {I} & \\boldsymbol {D} \\\\ 0 & \\boldsymbol {I} \\end{array} \\right] \\left[ \\begin{array}{l} \\tilde {\\boldsymbol {p}} _ {t} ^ {m} \\\\ \\tilde {\\boldsymbol {v}} _ {t} ^ {m} \\end{array} \\right] + \\left[ \\begin{array}{c} \\boldsymbol {D} ^ {2} \\\\ \\boldsymbol {D} \\end{array} \\right] \\tilde {\\boldsymbol {a}} _ {t} ^ {m}, \\tag {8}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.721,
+                0.894,
+                0.782
+            ],
+            "angle": 0,
+            "content": "where \\(D\\) is a diagonal matrix with the interval of each time step as diagonal entries, and \\(\\tilde{\\boldsymbol{p}}_t^m\\), \\(\\tilde{\\boldsymbol{v}}_t^m\\), \\(\\tilde{\\boldsymbol{a}}_t^m\\) represent the LQR-planned position, velocity, and acceleration. The system is subject to a quadratic cost function given by:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.558,
+                0.79,
+                0.892,
+                0.832
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {J} = \\sum_ {m = 1} ^ {M} \\sum_ {t = 1} ^ {T} \\| \\tilde {\\boldsymbol {p}} _ {t} ^ {m} - \\bar {\\boldsymbol {p}} _ {t} ^ {m} \\| ^ {2} + \\eta_ {\\boldsymbol {a}} \\| \\tilde {\\boldsymbol {a}} _ {t} ^ {m} \\| ^ {2}, \\tag {9}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.84,
+                0.894,
+                0.902
+            ],
+            "angle": 0,
+            "content": "where the projected predicted position \\(\\bar{\\pmb{p}}_m^t\\) is considered as the target pose, and the hyper-parameter \\(\\eta_{\\mathbf{a}}\\) is used to penalize high acceleration. Finally, each agent is updated to the first position of the planned trajectory."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.52,
+                0.958
+            ],
+            "angle": 0,
+            "content": "15390"
+        }
+    ],
+    [
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.091,
+                0.245,
+                0.108
+            ],
+            "angle": 0,
+            "content": "4.6. Training Process"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.116,
+                0.473,
+                0.391
+            ],
+            "angle": 0,
+            "content": "At each training step, the policy network is trained to maximize the probability of the expert's future trajectory using its context state and history trajectory augmented by the VAE as input. Simultaneously, the VAE is iteratively trained to reconstruct the expert and learner data. The expert data are the same as the policy network's training data before augmentation. The learner data is sampled from a replay buffer. Every \\( N \\) training steps, we empty the replay buffer and roll out the current policy with post-processing for \\( S \\) time steps to generate the learner data and store it in the replay buffer. During the roll-out, we start at a random time step in the training dataset and apply our model in a closed-loop manner. At each time step during the rollout, we sample a future trajectory for each vehicle from the Gaussian distribution predicted by our policy network, project the predicted trajectory onto the road, smooth the on-road trajectory with LQR, and finally update the vehicle to the first position of the smoothed trajectory."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.41,
+                0.203,
+                0.427
+            ],
+            "angle": 0,
+            "content": "5. Experiment"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.437,
+                0.173,
+                0.451
+            ],
+            "angle": 0,
+            "content": "5.1. Dataset"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.463,
+                0.473,
+                0.706
+            ],
+            "angle": 0,
+            "content": "We utilize a real-world urban dataset called pNEUMA [3], which was collected by 10 drones in Athens over a span of 4 days. The dataset encompasses over half a million vehicle trajectories within a large area encompassing over \\(100\\mathrm{km}\\) of lanes and approximately 100 intersections. The recordings were conducted at 5 intervals each day, with each period lasting about 15 minutes and a data collection time interval of 0.04 seconds. To enhance computational efficiency, we adopt a time step of 0.4 seconds. The dataset is divided into a training set, comprising recordings from the first 3 days, and a validation/test set, consisting of recordings from the final day. Notably, we choose not to utilize other popular traffic datasets like NGSIM [8] or HighD [23] or autonomous driving datasets like Lyft [18] or nuPlan [6], as they only encompass samll-scale scenarios. This limitation makes it inadequate for evaluate macroscopic realism."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.721,
+                0.174,
+                0.736
+            ],
+            "angle": 0,
+            "content": "5.2. Metrics"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.747,
+                0.47,
+                0.839
+            ],
+            "angle": 0,
+            "content": "We evaluate the realism of our simulator by measuring the similarity between the simulation result and real data. During evaluation, each vehicle enters the simulator at its first recorded time and position, and is controlled by our simulator to complete its recorded route. When an agent reaches its final recorded position, it is removed from the simulator."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.84,
+                0.471,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Short-term microscopic: Following [5, 40], we conduct a short-term microscopic evaluation by simulating for 20 seconds from a random time step in the test dataset. We first measure the similarity between the simulated and real"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.092,
+                0.887,
+                0.108
+            ],
+            "angle": 0,
+            "content": "data using position and velocity RMSE metrics given by:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.539,
+                0.117,
+                0.892,
+                0.165
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathrm {R M S E} = \\frac {1}{T _ {s}} \\sum_ {t = 1} ^ {T _ {s}} \\sqrt {\\frac {1}{M} \\sum_ {m = 1} ^ {M} \\| \\boldsymbol {s} _ {t} ^ {m} - \\hat {\\boldsymbol {s}} _ {t} ^ {m} \\| ^ {2}}, \\tag {10}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.174,
+                0.894,
+                0.266
+            ],
+            "angle": 0,
+            "content": "where \\( s_t^m \\) and \\( \\hat{s}_t^m \\) were the real and simulated value of the position or velocity of the agent \\( m \\) at time step \\( t \\), respectively. \\( T_s \\) was the total simulated time steps, and \\( M \\) was the total simulated agent number. Besides, we measure the minimum Average Displace Error (minADE) to not penalize reasonable trajectory unlike the real one:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.515,
+                0.275,
+                0.892,
+                0.317
+            ],
+            "angle": 0,
+            "content": "\\[\n\\min  A D E _ {N} = \\frac {1}{M} \\sum_ {m = 1} ^ {M} \\min  _ {\\hat {\\boldsymbol {s}} _ {n}} \\frac {1}{T _ {s}} \\sum_ {t = 1} ^ {T _ {s}} \\| \\boldsymbol {s} _ {t} ^ {m} - \\hat {\\boldsymbol {s}} _ {t, n} ^ {m} \\| ^ {2}, \\tag {11}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.325,
+                0.892,
+                0.416
+            ],
+            "angle": 0,
+            "content": "where \\( N = 20 \\) is roll-out times. We also calculate the off-road rate (the avarage proportion of vehicles that deviate more than \\( 1.5\\mathrm{m} \\) from the road over all time steps). The common collision rate metric is not used because we focus on the long-term impact and the dataset does not provide accurate vehicle size and heading information."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.416,
+                0.893,
+                0.612
+            ],
+            "angle": 0,
+            "content": "Long-term macroscopic: we also evaluate our model's long-term macroscopic accuracy on five periods for 800 seconds from its initial recording time. To measure the long-term performance, we use two standard macroscopic metrics for traffic flow data [29, 36, 38], namely road density and speed RMSE, in addition to the off-road rate. The density of a road at a time step is calculated by dividing the number of vehicles on the road by its total lane length, assuming that all lanes have the same width. Meanwhile, the road speed is computed as the mean speed of all vehicles on the road. To quantify the similarity between the simulated and ground truth values, we still use RMSE, where the variable \\( M \\) becomes the total number of roads."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.621,
+                0.637,
+                0.636
+            ],
+            "angle": 0,
+            "content": "5.3. Performance"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.645,
+                0.885,
+                0.659
+            ],
+            "angle": 0,
+            "content": "We compare our method against state-of-the-art baselines:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.66,
+                0.892,
+                0.735
+            ],
+            "angle": 0,
+            "content": "SUMO [24]: we use the IDM model [42] as the car-following model and mobil [19] as the lane-changing model. We tune the IDM's parameters for 6 types of vehicle by minimizing the MSE between the IDM calculated acceleration and real acceleration using an Adam optimizer [20]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.519,
+                0.735,
+                0.891,
+                0.75
+            ],
+            "angle": 0,
+            "content": "BC [32]: we learn our model directly by the BC method."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.75,
+                0.892,
+                0.825
+            ],
+            "angle": 0,
+            "content": "MARL [26]: we train our model using IPPO [10] as the Multi-Agent RL algorithm, where the reward function is composed of three parts: a displacement reward (average distance between agent trajectory with GT trajectory), an off-road penalty and a terminal reward."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.826,
+                0.892,
+                0.855
+            ],
+            "angle": 0,
+            "content": "MARL+BC [31]: we add a behavior cloning term in the loss function while learning the policy with MARL."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.856,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "PS-GAIL [40]: we let all vehicles share the same policy parameter and critic parameter and learn the policy using reward functions computed by GAIL."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.518,
+                0.957
+            ],
+            "angle": 0,
+            "content": "15391"
+        }
+    ],
+    [
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.202,
+                0.09,
+                0.768,
+                0.103
+            ],
+            "angle": 0,
+            "content": "Table 1. Comparison with baselines and ablated models on microscopic metrics for 20 seconds."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.124,
+                0.104,
+                0.849,
+                0.3
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Model</td><td>Position RMSE(m)</td><td>Velocity RMSE(m/s)</td><td>minADE20(m)</td><td>Off-road(%)</td></tr><tr><td>SUMO [24]</td><td>41.25</td><td>7.00</td><td>24.20</td><td>0</td></tr><tr><td>BC [32]</td><td>40.08±1.61</td><td>6.74±0.37</td><td>22.02±3.98</td><td>33.43±3.10</td></tr><tr><td>MARL [26]</td><td>48.66±1.54</td><td>8.92±0.67</td><td>40.07±1.26</td><td>3.70±0.40</td></tr><tr><td>MARL+BC [31]</td><td>29.78±0.42</td><td>4.54±0.14</td><td>22.07±0.21</td><td>11.14±1.17</td></tr><tr><td>PS-GAIL [40]</td><td>34.78±0.43</td><td>5.33±0.12</td><td>27.86±0.33</td><td>7.65±0.32</td></tr><tr><td>RAIL [5]</td><td>31.62±0.65</td><td>5.51±0.09</td><td>24.51±0.41</td><td>2.57±0.47</td></tr><tr><td>LASIL (ours)</td><td>19.21±0.44</td><td>3.02±0.07</td><td>12.79±0.32</td><td>0.28±0.01</td></tr><tr><td>w/o Augmentation</td><td>21.62±0.54</td><td>3.34±0.14</td><td>13.81±0.37</td><td>1.31±0.18</td></tr><tr><td>w/o Context-conditioned</td><td>23.03±0.87</td><td>3.73±0.12</td><td>14.94±0.43</td><td>0.51±0.04</td></tr><tr><td>w/o On-road Projection</td><td>22.53±0.42</td><td>3.26±0.10</td><td>14.42±0.33</td><td>1.74±0.60</td></tr><tr><td>w/o LQR</td><td>22.62±0.43</td><td>4.05±0.15</td><td>14.02±0.28</td><td>0.22±0.02</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.197,
+                0.305,
+                0.773,
+                0.318
+            ],
+            "angle": 0,
+            "content": "Table 2. Comparison with baselines and ablated models on macroscopic metrics for 800 seconds."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.13,
+                0.32,
+                0.842,
+                0.516
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Model</td><td>Road Density RMSE(veh/km)</td><td>Road Speed RMSE(m/s)</td><td>Off-road(%)</td></tr><tr><td>SUMO [24]</td><td>52.70</td><td>5.52</td><td>0</td></tr><tr><td>BC [32]</td><td>61.51±1.53</td><td>5.38±0.21</td><td>42.15±5.25</td></tr><tr><td>MARL [26]</td><td>90.59±2.65</td><td>5.27±0.48</td><td>4.63±0.64</td></tr><tr><td>MARL+BC [31]</td><td>43.60±2.80</td><td>4.01±0.13</td><td>22.73±5.62</td></tr><tr><td>PS-GAIL [40]</td><td>54.06±1.23</td><td>4.03±0.05</td><td>13.24±3.20</td></tr><tr><td>RAIL [5]</td><td>54.45±1.89</td><td>3.89±0.11</td><td>2.92±0.38</td></tr><tr><td>LASIL (ours)</td><td>45.13±0.25</td><td>3.17±0.14</td><td>0.34±0.03</td></tr><tr><td>w/o Augmentation</td><td>55.65±0.44</td><td>3.73±0.23</td><td>9.62±1.40</td></tr><tr><td>w/o Context-conditioned</td><td>55.98±0.51</td><td>4.48±0.19</td><td>0.64±0.08</td></tr><tr><td>w/o On-road Projection</td><td>52.90±0.54</td><td>3.59±0.20</td><td>11.33±2.37</td></tr><tr><td>w/o LQR</td><td>61.68±0.96</td><td>3.54±0.16</td><td>0.47±0.07</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.521,
+                0.47,
+                0.551
+            ],
+            "angle": 0,
+            "content": "RAIL [5]: we learn the model as PS-GAIL but with additional displacement, off-road and terminal rewards."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.552,
+                0.47,
+                0.673
+            ],
+            "angle": 0,
+            "content": "We train and evaluate each model five times to obtain the mean and standard deviation (std) of various metrics. Note that we do not apply on-road projection and LQR for baselines. We evaluate both short-term and long-term performance, as shown in Tab. 1 and Tab. 2, respectively. Our method achieves better results than all baselines in terms of position and velocity RMSE, road density and speed RMSE, with minor off-road rate."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.682,
+                0.231,
+                0.699
+            ],
+            "angle": 0,
+            "content": "5.4. Ablation Study"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.705,
+                0.47,
+                0.75
+            ],
+            "angle": 0,
+            "content": "We conducted a series of ablation experiments to assess the individual contributions of crucial components in our approach, whose results are presented in Tab. 1 and Tab. 2."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.75,
+                0.471,
+                0.84
+            ],
+            "angle": 0,
+            "content": "Augmentation: By removing our VAE module and directly learning the original expert state and action, we analyze the importance of our data augmentation technique. The results demonstrate that augmentation plays a vital role in improving both short-term and long-term simulation performance by mitigating covariate shift."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.84,
+                0.471,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Context-conditioned VAE: To emphasize the significance of modeling the context-conditioned trajectory distribution rather than the whole state distribution, we replaced our context-conditioned VAE with a naive VAE that directly"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.521,
+                0.892,
+                0.567
+            ],
+            "angle": 0,
+            "content": "models the expert and learner state distribution. The observed drop in performance demonstrates the challenges in reconstructing the context distribution."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.572,
+                0.892,
+                0.648
+            ],
+            "angle": 0,
+            "content": "On-road projection: Our ablation study on the on-road projection module aims to show its impact on reducing the off-road rate. The results show that the on-road projection module leads to a notable decrease in the off-road rate and moderate improvements in other performance metrics."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.652,
+                0.892,
+                0.743
+            ],
+            "angle": 0,
+            "content": "LQR: Removing LQR module allows us to evaluate its effectiveness. While LQR led to a higher short-term off-road rate due to more constrained movement (driving off-road due to inertia), its removal deteriorates other short-term and long-term metrics, because LQR can smooth the trajectory, thus leads to more realistic simulations."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.767,
+                0.679,
+                0.783
+            ],
+            "angle": 0,
+            "content": "5.5. Qualitative Result"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.795,
+                0.892,
+                0.903
+            ],
+            "angle": 0,
+            "content": "In Fig. 2, we present the mean road density and speed for real-world data, SUMO simulation, and our proposed method over all time steps. The results demonstrate that our proposed method surpasses the capabilities of the SUMO simulator at replicating long-term macroscopic traffic patterns due to our model's enhanced ability to replicate the typical microscopic driving behaviors over a long period."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.52,
+                0.957
+            ],
+            "angle": 0,
+            "content": "15392"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.102,
+                0.088,
+                0.862,
+                0.646
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.647,
+                0.892,
+                0.675
+            ],
+            "angle": 0,
+            "content": "Figure 2. Mean density and speed on each road over all time steps in the long-term evaluation. Our method's density and speed hot-maps have a more similar color to the ground-truth one compared with the SUMO's."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.679,
+                0.196,
+                0.695
+            ],
+            "angle": 0,
+            "content": "6. Conclusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.704,
+                0.471,
+                0.901
+            ],
+            "angle": 0,
+            "content": "In conclusion, we have addressed the challenge of creating a realistic traffic simulator that accurately models human driving behaviors in various traffic conditions. Traditional imitation learning-based simulators often fail to deliver accurate long-term simulations due to the covariate shift problem in multi-agent imitation learning. To tackle this issue, we proposed a learner-aware supervised imitation learning method, which leverages a context-conditioned VAE to generate learner-aware augmented expert states. We leverage a context-conditioned VAE to simultaneously reconstruct the expert and learner state. This approach enables the reproduction of long-term stable microscopic traffic simulations, marking a significant advancement in the field of urban"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.68,
+                0.892,
+                0.755
+            ],
+            "angle": 0,
+            "content": "traffic simulation. Our method has demonstrated superior performance over existing state-of-the-art simulators when evaluated on the real-world dataset pNEUMA, achieving better short-term microscopic and long-term macroscopic similarity to real-world data than state-of-the-art baselines."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.77,
+                0.688,
+                0.788
+            ],
+            "angle": 0,
+            "content": "7. Acknowledgements"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
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+            "content": "This research project is partially supported by the Innovation and Technology Commission of the HKSAR Government under the InnoHK initiative, Hong Kong General Research Fund (11202119 and 11208718), Innovation and Technology Commission (GHP/126/21GD), and Guangdong, Hong Kong and Macao Joint Innovation Project (2023A0505010016)."
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2024/LASIL_ Learner-Aware Supervised Imitation Learning For Long-term Microscopic Traffic Simulation/44a62bf3-d838-46a8-bbd5-a317e9666352_origin.pdf

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2024/LASIL_ Learner-Aware Supervised Imitation Learning For Long-term Microscopic Traffic Simulation/full.md

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+# LASIL: Learner-Aware Supervised Imitation Learning For Long-term Microscopic Traffic Simulation
+
+Ke Guo $^{1,2,3}$ , Zhenwei Miao $^{1*}$ , Wei Jing $^{1}$ , Weiwei Liu $^{1}$ , Weizi Li $^{4}$ , Dayang Hao $^{1}$ , Jia Pan $^{2,3}$ $^{1}$ Alibaba Group  $^{2}$ The University of Hong Kong  
+ $^{3}$ Centre for Transformative Garment Production, Hong Kong  $^{4}$ University of Tennessee, Knoxville  
+u3006612@connect.hku.hk, zhenwei.mzw@alibaba-inc.com  
+21wjing@gmail.com, 11932061@zju.edu.cn, weizili@utk.edu, jpan@cs.hku.hk
+
+# Abstract
+
+Microscopic traffic simulation plays a crucial role in transportation engineering by providing insights into individual vehicle behavior and overall traffic flow. However, creating a realistic simulator that accurately replicates human driving behaviors in various traffic conditions presents significant challenges. Traditional simulators relying on heuristic models often fail to deliver accurate simulations due to the complexity of real-world traffic environments. Due to the covariate shift issue, existing imitation learning-based simulators often fail to generate stable long-term simulations. In this paper, we propose a novel approach called learner-aware supervised imitation learning to address the covariate shift problem in multi-agent imitation learning. By leveraging a variational autoencoder simultaneously modeling the expert and learner state distribution, our approach augments expert states such that the augmented state is aware of learner state distribution. Our method, applied to urban traffic simulation, demonstrates significant improvements over existing state-of-the-art baselines in both short-term microscopic and long-term macroscopic realism when evaluated on the real-world dataset pNEUMA.
+
+# 1. Introduction
+
+Microscopic traffic simulation is a cornerstone in transportation engineering. It enables engineers to predict and analyze individual vehicle behavior, providing crucial insights into how alterations in road structures or traffic management strategies might influence overall traffic flow; it allows for the testing of diverse scenarios without disrupting real-world traffic; and it enhances safety by pinpointing potential hazards and devising strategies to mitigate risks. By leveraging simulations, engineers can optimize traffic flow,
+
+reduce congestion, and enhance overall efficiency, proving particularly advantageous in designing or enhancing road networks. Using the simulation data, policymakers and urban planners can make informed decisions aligned with community needs regarding transportation infrastructure.
+
+However, generating realistic and accurate simulations that can simultaneously replicate the microscopic response of human drivers in various traffic conditions and long-term macroscopic traffic statistics is challenging. In recent years, significant efforts have been invested in developing realistic traffic simulators with the goal to accurately model human driving behaviors. Traditional traffic simulators, such as SUMO [24], AIMSUN [2], and MITSIM [44], typically rely on heuristic car-following models like the Intelligent Driver Model (IDM) [42]. However, despite carefully calibrating parameters, the rule-based models often fail to deliver accurate simulations due to the complexity of real-world traffic environments [12, 30]. Factors such as the road structure, neighboring vehicles, and even driver psychology can influence the decisions of human drivers, making it challenging to achieve accurate simulations [7, 27, 43].
+
+In pursuit of realistic traffic simulations, researchers have turned to neural networks to represent the driving model through imitation learning (IL) from human demonstrations. Most traffic simulation approaches [4, 34, 41] leverage behavior cloning (BC) [32] to learn a driving policy by minimizing the disparity between the model output and the human demonstrations in training data. However, BC is hindered by covariate shift [37], where the state induced by the learner's policy progressively diverges from the expert's distribution. Existing BC-based simulators have succeeded in short-term (less than 20 seconds) simulation applications like autonomous driving tests but often fail to generate stable long-term simulations.
+
+To address covariate shift, existing methods such as DAGger [37], DART [25], and ADAPS [28] incorporate supervisor (humans or principled simulations) corrections
+
+at the learner's or perturbed expert's states. However, human supervision can be problematic due to intensive labor and judgment errors, and principled simulations may not account for heterogeneous driving behaviors. Recent traffic simulators [40, 46] propose using inverse reinforcement learning (IRL). These methods, such as generative adversarial imitation learning (GAIL) [17] and adversarial inverse reinforcement learning (AIRL) [13], learn a reward function using a discriminator neural network within Generative Adversarial Networks (GANs) [14]. The policy network is trained to maximize the learned reward through online reinforcement learning (RL), enabling agents to handle out-of-distribution states. However, directly applying GAIL to traffic simulation can be problematic [5]. The dynamic nature of the environment in the multi-agent system can lead to noises during policy learning, resulting in highly biased estimated gradients. Furthermore, training the discriminator in GAIL is challenging due to the instability and sensitivity of hyperparameters during min-max optimization.
+
+To address the issue of covariate shift in multi-agent imitation learning without depending on costly expert supervision or unstable discriminators and multi-agent RL, we propose Learner-Aware Supervised Imitation Learning (LASIL) for tackling the covariate shift problem during policy learning. We mitigate the distribution shift between expert and learner state distribution by augmenting the expert state distribution. However, there is no expert supervision at any augmented state, so we ensure that an augmented state is close to an expert state such that the future trajectory of the expert state can serve as the target trajectory for the augmented state to constrain the learner within the expert state distribution. Hence, our goal is to augment the expert state to cover the learner's state distribution while remaining close to the original expert state distribution. To achieve this, we use a variational autoencoder (VAE) [21] to simultaneously model the distributions of both the expert and learner states. By minimizing the VAE's latent space regularization loss of modeling both distributions, we project the expert and learner states into a unified latent space. And by minimizing the VAE's reconstruction loss, the resulting reconstruction leveraging such learnt latent space will resemble both expert and learner state distribution. As a result, when inputting expert states into the trained VAE, we obtain a learner-aware augmented expert state.
+
+In practice, we divide an agent's state into two parts: past trajectory and context, i.e., other features in the state including vehicle type, waypoints, and destination. We observe that the distribution of the context is consistent regardless of a learnt policy due to the static features of traffic conditions embedded in the context, leading to less covariate shift. Therefore, we propose a context-conditioned VAE to model the context-conditioned trajectory distribution of both expert and learner states. The decoder of the context-
+
+conditioned VAE will receive both the latent variable and the context, and yield only the trajectory information.
+
+In summary, our contributions are as follows:
+
+- We propose learner-aware supervised imitation learning (LASIL) to achieve stable learning and alleviate covariate shift in multi-agent imitation learning.  
+- We propose a learner-aware data augmentation method based on a context-conditioned VAE that generates learner-aware augmented expert states.  
+- Our approach is tailored for urban traffic simulation. To the best of our knowledge, it is the first imitation learning-based traffic simulator that can reproduce long-term (more than 10 minutes) stable microscopic simulation, achieving  $40\mathrm{x}$  simulation length improvements over previous state-of-the-art [4, 41, 46].  
+- We evaluate our method on the real-world dataset pNEUMA [3] with over half a million trajectories. Our approach outperforms state-of-the-art baselines in both short-term microscopic and long-term macroscopic simulations. The code is available at https://github.com/Kguo-cs/LSAIL.
+
+# 2. Related Work
+
+# 2.1. Imitation learning
+
+Existing imitation learning (IL) methods can be broadly categorized into behavior cloning (BC) and inverse reinforcement learning (IRL) approaches. BC [32] learns a policy in a supervised fashion by minimizing the discrepancy between the learner's actions and those of an expert. However, BC suffers from the issue of covariate shift, where the state distribution induced by the learner's policy gradually deviates from that of the expert. To address this, methods like DAGger [37] and DART [25] request supervisor corrections at the learner's or perturbed expert's states. Our method follows a similar supervised learning approach to DAGger and DART, but does not require access to an expert policy.
+
+Due to the challenges in obtaining expert supervision, recent IRL-based methods utilize feedback from a neural network-based discriminator to handle covariate shift. Typically, these methods involve an iterative process alternating between reward estimation and reinforcement learning. Earlier IRL-based methods [15, 35, 39, 47] require frequent dynamic programming processes, while recent adversarial IL approaches integrate reward function learning with policy learning using a GAN formulation. However, both GAN and RL training processes are known to be unstable, sensitive to hyperparameters, and have poor sample efficiency [9]. Moreover, the discriminator can easily exploit insignificant differences between expert and policy samples, leading to undesirable performance [45]. In contrast, our method avoids the min-max optimization problem and the sample-inefficient RL process, requiring minimal
+
+fine-tuning. Instead, we utilize the real future trajectory as the target state to learn corrective behavior.
+
+# 2.2. Imitation Learning-based Traffic simulation
+
+Recent traffic simulators focus on enhancing realism by leveraging imitation learning (IL) from human driving demonstrations, which extend traditional BC and IRL methods to tackle the challenging multi-agent IL problem.
+
+BC-based traffic simulators like TrafficSim [41] and SimNet [4] typically begin by training a prediction model and subsequently adjust the predicted trajectories to prevent collisions and adhere to traffic regulations during simulation. However, BC-based methods face challenges in achieving long-term simulation due to the covariate shift problem. To mitigate this issue, we augment expert state based on the policy distribution, enabling stable long-term simulation. Additionally, we enhance performance by modifying the predicted trajectory during simulation through road projection and ensuring smoothness from the current state. Notably, we skip the computationally intensive collision removal operation, prioritizing the capture of macroscopic long-term influence over micro-level details.
+
+IRL-based simulators learn the underlying reward function of human driving behavior and derive the driving policy by maximizing the learned reward. While adversarial IRL methods theoretically address the covariate shift of BC in a single-agent context through online interaction, its performance deteriorates in the multi-agent IL domain due to the dynamic environment, complicating the training process. To tackle this challenge, approaches like PS-GAIL [40] and PS-ARIL [46] adopt two-stage learning and gradually introduce vehicles to the environment. Nonetheless, these methods still exhibit significant undesirable traffic phenomena, such as off-road driving, collisions, and abrupt braking. Building upon PS-GAIL, the reward-augmented imitation learning (RAIL) method [5, 22] penalizes undesirable phenomena by introducing a hand-crafted reward. However, maximizing the new reward does not guarantee the recovery of human-like trajectories. Despite numerous enhancements to the original GAIL framework, these IRL-based methods often struggle to produce stable long-term traffic flow, as evidenced in our experiments. In contrast, our method is a supervised learning approach, leading to faster, simpler, and more stable learning of driving policies.
+
+# 3. Background
+
+# 3.1. Markov Decision Process
+
+We model the human driving process using a Markov decision process (MDP) denoted as  $\mathcal{M} = \{\mathcal{S},\mathcal{A},\mathcal{T},r\}$ , incorporating a time horizon of  $T$ , where  $\mathcal{S}$  and  $\mathcal{A}$  represent the continuous state and action spaces respectively. A stochastic function  $\mathcal{T}:S\times \mathcal{A}\times \mathcal{S}\rightarrow [0,1]$  describes the system
+
+dynamics, and  $r: \mathcal{S} \times \mathcal{A} \to \mathbb{R}$  is a reward function. The policy  $\pi(\boldsymbol{a} | s)$  determines the probability of selecting an action  $a$  at a state  $s$ , and a trajectory  $\tau = (s_0, \boldsymbol{a}_0, \dots, s_T, \boldsymbol{a}_T)$  represents a sequence of state-action pairs. The marginal state distribution of a policy  $\pi$  is computed as  $\rho^{\pi}(s) = \frac{1}{D} \sum_{s \in \mathcal{D}_{\pi}} \delta_s$ , where  $\mathcal{D}_{\pi}$  denotes the set of states of size  $D$  in trajectories induced by the policy  $\pi$ , and  $\delta_s$  signifies a Dirac distribution centered on  $s$ . Similarly, the marginal state-action distribution  $\rho^{\pi}(s, \boldsymbol{a})$  is computed.
+
+# 3.2. Imitation Learning
+
+In the application of IL for learning a driving policy, we assume that all agents adopt the same policy. The objective is to learn a policy  $\pi$  that minimizes the  $f$ -divergence between the marginal state-action distribution of the expert's demonstrations  $\rho^{\exp}(s,a)$  and the learner policy's distribution  $\rho^{\pi}(s,a)$ . For example, BC optimizes the policy to minimize the Kullback-Leibler (KL) divergence at the expert state distribution  $\mathbb{E}_{\rho^{\exp}(s)}[\mathrm{KL}(\pi^{\exp}(a|s)\| \pi (a|s))]$ , while DAgger minimizes  $\mathbb{E}_{\rho^{\pi}(s)}[\mathrm{KL}(\pi^{\exp}(a|s)\| \pi (a|s))]$ . On the other hand, GAIL minimizes the Jensen-Shannon divergence  $D_{\mathrm{JS}}(\rho^{\exp}(s,a)\| \rho^{\pi}(s,a))$ , while AIRL minimizes the KL divergence  $\mathrm{KL}(\rho^{\pi}(s,a)\| \rho^{\exp}(s,a))$ .
+
+However, GAIL and AIRL often exhibit unsatisfactory practical performance due to their optimization processes' instability and sample inefficiency, which involve GANs and RL. In contrast, BC only requires simple and stable supervised learning but suffers from the covariate shift issue, as it only minimizes the policy difference at the expert state distribution without guaranteeing performance at the learner state distribution. DAGger addresses the covariate shift problem but requires access to the expert policy. To mitigate the covariate shift problem without depending on the expert policy, we propose maximizing the transition probability  $\mathbb{E}_{\boldsymbol{s} \sim \rho^{\exp}(\boldsymbol{s}), \boldsymbol{s} + \epsilon \sim \rho^{\pi}(\boldsymbol{s})}[\mathcal{T}(\boldsymbol{s} + \epsilon, \pi(\boldsymbol{s} + \epsilon), \boldsymbol{s}')]$ , where  $\epsilon$  is a small augmentation term. Note that our policy learns to predict the distribution of the next state  $s'$  instead of the action. Our approach assumes that when the expert's original future trajectory can serve as supervision to guide the agent back towards the expert distribution.
+
+# 3.3. Variational Autoencoder
+
+The VAE defines a generative model given by  $p_{\theta}(\pmb{x}, \pmb{z}) = p(\pmb{z}) p_{\theta}(\pmb{x} | \pmb{z})$ , where  $\pmb{z}$  is the latent variable with prior distribution  $p(\pmb{z})$ , and  $p_{\theta}(\pmb{x} | \pmb{z})$  represents the conditional distribution modeling the likelihood of data  $\pmb{x}$  given  $\pmb{z}$ . The learning objective is to maximize the training samples' marginal log-likelihood  $\log p_{\theta}(\pmb{x})$ . However, due to the intractability of marginalization, VAE maximizes the variational lower
+
+bound using  $q_{\phi}(\pmb {z}|\pmb {x})$  as the approximate posterior:
+
+$$
+\begin{array}{l} \log p _ {\theta} (\boldsymbol {x}) \\ \geq \mathbb {E} _ {\boldsymbol {z} \sim q _ {\phi} (\boldsymbol {z} | \boldsymbol {x})} [ \log p _ {\theta} (\boldsymbol {x} | \boldsymbol {z}) ] - \operatorname {K L} \left(q _ {\phi} (\boldsymbol {z} | \boldsymbol {x}) \| p (\boldsymbol {z})\right) \tag {1} \\ := - \mathcal {L} _ {\text {r e c}} (\boldsymbol {x}) - \mathcal {L} _ {\mathrm {K L}} (\boldsymbol {x}), \\ \end{array}
+$$
+
+where  $\mathcal{L}_{\mathrm{rec}}(\boldsymbol{x})$  represents the reconstruction loss, which penalizes the network for creating outputs different from the input.  $\mathcal{L}_{\mathrm{KL}}(\boldsymbol{x})$  represents the KL divergence loss to make a continuous and smooth latent space, allowing easy random sampling and interpolation. Intuitively, this KL loss encourages the encoder to distribute all encodings evenly around the center of the latent space.
+
+# 4. Method
+
+In Fig. 1, we present an overview of our method. Our model comprises three modules: a VAE-based data augmentation module, a policy network, and a post-processing (LQR and on-road projection) module. During training, we augment each expert data by generating a learner-aware augmented expert state through the VAE's reconstruction of its past trajectory. Using this augmented state along with the original future trajectory, we train the learner's policy network through supervised learning. During simulation, we roll out the policy network with several post-processing steps including sampling, projecting the trajectories onto the road, and smoothing the projected trajectories.
+
+# 4.1. State Representation
+
+As human drivers make decisions mainly depending on their surrounding information, we build a graph to model the traffic system with each driving agent as its node.
+
+Node: The state of each agent can be divided into two components: the past trajectory  $s_p$  and the context  $s_c$ . In practice, the past trajectory is composed of the agent's positions at several past time steps, including the current time step. The context includes its type, nearby waypoints' positions and corresponding road width, the traffic light status of the road it is traveling on, and destination. The waypoints are composed of the center points of the routing roads with a fixed interval. We transform each agent's state into its individual coordinate system to learn a policy with transformation invariance. To reduce the implicit covariate shift, we set each agent's current position adding a Gaussian perturbation as the origin and the  $x$ -axis directions pointing towards the agent's destination like [16].
+
+Edge: When each agent's state coordinates are transformed from the global coordinate system to their individual coordinate system, information about the relative positions among agents is lost. However, a traffic model needs the relative information of agents to understand how they interact with each other. To preserve these relationships, we introduce directed edges between neighboring agents. The
+
+edge feature is the relative position of the destination node's coordinate origin in the source node's coordinate system.
+
+# 4.2. Learner-aware Data Augmentation
+
+To address the covariate shift issue between the expert and learner state distributions, we propose to minimize the expert's and learner's embedded state distribution difference. In practice, we propose utilizing the same VAE to model the expert and learner state distributions simultaneously. As both the expert and learner state are projected to the same latent space, the distribution of the state reconstructed from the joint latent space can resemble both distributions.
+
+In contrast to the past trajectory, the context distribution is more challenging to model but exhibits less covariate shift. Therefore, we propose using a context-conditioned VAE to specifically model the context-conditioned trajectory distribution rather than the state distribution. For each expert or learner state represented as  $s = (s_p, s_c)$ , we employ an encoder  $q_{\phi}(z | s_p, s_c)$  to obtain the latent variable distribution. We can sample a latent variable  $z$  from this distribution by applying the reparameterization trick. Subsequently, a decoder  $p_{\theta}(s_p | z, s_c)$  is used to reconstruct the distribution of the past trajectory  $s_p$  given  $z$  and  $s_c$ . The VAE is trained to maximize the variational lower bound, which incorporates the context-conditioned log-likelihood of both the expert and learner past trajectories:
+
+$$
+\mathcal {L} _ {V A E} = \mathbb {E} _ {\boldsymbol {s} \sim \rho^ {\exp}} \left[ \mathcal {L} \left(\boldsymbol {s} _ {p} \mid \boldsymbol {s} _ {c}\right) \right] + \lambda \mathbb {E} _ {\boldsymbol {s} \sim \rho^ {\pi}} \left[ \mathcal {L} \left(\boldsymbol {s} _ {p} \mid \boldsymbol {s} _ {c}\right) \right]. \tag {2}
+$$
+
+Here,  $\lambda$  is a hyperparameter that controls the degree to which the augmented context-conditioned past trajectory distribution aligns with the learner's context-conditioned past trajectory distribution. The term  $\mathcal{L}(s_p|s_c)$  is given by:
+
+$$
+\begin{array}{l} \mathcal {L} \left(\boldsymbol {s} _ {p} \mid \boldsymbol {s} _ {c}\right) = \mathbb {E} _ {\boldsymbol {z} \sim q _ {\phi} \left(\boldsymbol {z} \mid \boldsymbol {s} _ {p}, \boldsymbol {s} _ {c}\right)} \left[ \log p _ {\theta} \left(\boldsymbol {s} _ {p} \mid \boldsymbol {z}, \boldsymbol {s} _ {c}\right) \right] \\ - \operatorname {K L} \left(q _ {\phi} (\boldsymbol {z} | \boldsymbol {s} _ {p}, \boldsymbol {s} _ {c}) \| p (\boldsymbol {z})\right). \tag {3} \\ \end{array}
+$$
+
+For simplicity, we assume  $p_{\theta}$  and  $q_{\phi}$  as multivariate normal distributions with diagonal variance matrices. The prior distribution  $p(z)$  is set as an isotropic unit Gaussian  $\mathcal{N}(\mathbf{0},\mathbf{I})$
+
+# 4.3. Edge-enhanced Graph Attention Network
+
+We build all models in our approach including the VAE encoder, decoder, and learner's policy network based on an edge-enhanced graph attention (EGAT) network [11, 33], which model interactions by aggregating neighboring node and edge information using an attention mechanism. The node features in the first layer are obtained by embedding the node input with a fully connected layer and the node features in the other layers are calculated by:
+
+$$
+\boldsymbol {h} _ {i} ^ {l} = \sigma \left(\sum_ {j \in \mathcal {N} _ {i}} \alpha_ {i j} ^ {l} \boldsymbol {W} ^ {l} \left[ \boldsymbol {h} _ {i} ^ {(l - 1)} \| \boldsymbol {e} _ {i j} \| \boldsymbol {h} _ {j} ^ {(l - 1)} \right]\right), \tag {4}
+$$
+
+![](images/c52e0a4a753e710f5e0703f22977e3dbee94a3e67553d93d5b4a19ad522866d7.jpg)  
+Figure 1. Overview of our approach. The processes with purple and red arrows handle only expert or learner data, respectively, while the processes represented by black arrows apply to both data. Each state is a multi-agent state represented by a graph. Each model, including the VAE encoder, decoder, and policy network, is implemented using an EGAT network.
+
+where  $h_i^l$  is the feature of node  $i$  in the  $l$ th layer,  $e_{ij}$  is the coordinate origin's position of node  $j$  relative to node  $i$ ,  $\| \cdot \|$  means the concatenation,  $W^l$  is the learnable weight matrix,  $\mathcal{N}_i$  is the set of the first-order neighbors of node  $i$  (including the node itself), and  $\sigma$  is a non-linear activation function. The attention coefficient  $\alpha_{ij}^l$  indicates the importance of node  $j$  to node  $i$ , considering both node and edge features, and is computed as:
+
+$$
+\alpha_ {i j} ^ {l} = \operatorname {s o f t m a x} _ {j} \left(\sigma \left(\left(\boldsymbol {w} ^ {l}\right) ^ {T} \left[ \boldsymbol {h} _ {i} ^ {(l - 1)} \| \boldsymbol {e} _ {i j} \| \boldsymbol {h} _ {j} ^ {(l - 1)} \right]\right)\right), \tag {5}
+$$
+
+where  $\boldsymbol{w}^l$  is a learnable weight vector, and normalization is performed on the weights across all neighbors of node  $i$  using a softmax function. After passing through multiple EGAT layers, the node features at the last layer is fed into a fully connected layer to obtain the outputs of the network.
+
+# 4.4. Policy Loss
+
+To train the learner's policy network, we first sample a learner-aware augmented expert state from the context-conditioned VAE for each expert state. Then, the policy network predicts its future position distribution over  $T$  time steps, denoted as  $p(\hat{p}_1^m, \hat{p}_2^m, \dots, \hat{p}_T^m)$ , which is assumed to be a product of multi-variable Gaussian distributions:
+
+$$
+p \left(\hat {\boldsymbol {p}} _ {1} ^ {m}, \hat {\boldsymbol {p}} _ {2} ^ {m}, \dots , \hat {\boldsymbol {p}} _ {T} ^ {m}\right) = \prod_ {t = 1} ^ {T} \mathcal {N} \left(\hat {\boldsymbol {\mu}} _ {t} ^ {m}, \hat {\boldsymbol {\Sigma}} _ {t} ^ {m}\right), \tag {6}
+$$
+
+where  $\hat{\pmb{\mu}}_t^m$  and  $\hat{\Sigma}_t^m$  represent the mean and covariance matrix of the predicted position  $\hat{\pmb{p}}_t^m$  at future time step  $t$ . We assume that there is no correlation between the position distributions at different future time steps. To learn the policy network, we minimize the negative log-likelihood (NLL)
+
+loss of all agents' ground-truth future trajectories:
+
+$$
+\mathcal {L} _ {N L L} = - \sum_ {m = 1} ^ {M} \sum_ {t = 1} ^ {T} \log \left(\mathcal {N} \left(\boldsymbol {p} _ {t} ^ {m} - \hat {\boldsymbol {\mu}} _ {t} ^ {m}, \hat {\boldsymbol {\Sigma}} _ {t} ^ {m}\right)\right), \tag {7}
+$$
+
+where  $\pmb{p}_t^m$  denotes the ground truth position of agent  $m$  at future time step  $t$ , and  $M$  is the total number of agents.
+
+# 4.5. Simulation Process
+
+During training, we simultaneously simulate (roll out) the learned policy network iteratively to get learner state samples. Instead of directly updating each agent to its predicted position, we apply several post-processing steps to the prediction for better realism. Firstly, we sample from the distribution, and then project each sampled position onto the nearest on-road point. Then, we smooth the projected trajectory with a linear-quadratic regulator (LQR) [1] by minimizing the total commutative quadratic cost of a linear dynamic system described by:
+
+$$
+\left[ \begin{array}{l} \tilde {\boldsymbol {p}} _ {t + 1} ^ {m} \\ \tilde {\boldsymbol {v}} _ {t + 1} ^ {m} \end{array} \right] = \left[ \begin{array}{c c} \boldsymbol {I} & \boldsymbol {D} \\ 0 & \boldsymbol {I} \end{array} \right] \left[ \begin{array}{l} \tilde {\boldsymbol {p}} _ {t} ^ {m} \\ \tilde {\boldsymbol {v}} _ {t} ^ {m} \end{array} \right] + \left[ \begin{array}{c} \boldsymbol {D} ^ {2} \\ \boldsymbol {D} \end{array} \right] \tilde {\boldsymbol {a}} _ {t} ^ {m}, \tag {8}
+$$
+
+where  $D$  is a diagonal matrix with the interval of each time step as diagonal entries, and  $\tilde{\boldsymbol{p}}_t^m$ ,  $\tilde{\boldsymbol{v}}_t^m$ ,  $\tilde{\boldsymbol{a}}_t^m$  represent the LQR-planned position, velocity, and acceleration. The system is subject to a quadratic cost function given by:
+
+$$
+\mathcal {J} = \sum_ {m = 1} ^ {M} \sum_ {t = 1} ^ {T} \| \tilde {\boldsymbol {p}} _ {t} ^ {m} - \bar {\boldsymbol {p}} _ {t} ^ {m} \| ^ {2} + \eta_ {\boldsymbol {a}} \| \tilde {\boldsymbol {a}} _ {t} ^ {m} \| ^ {2}, \tag {9}
+$$
+
+where the projected predicted position  $\bar{\pmb{p}}_m^t$  is considered as the target pose, and the hyper-parameter  $\eta_{\mathbf{a}}$  is used to penalize high acceleration. Finally, each agent is updated to the first position of the planned trajectory.
+
+# 4.6. Training Process
+
+At each training step, the policy network is trained to maximize the probability of the expert's future trajectory using its context state and history trajectory augmented by the VAE as input. Simultaneously, the VAE is iteratively trained to reconstruct the expert and learner data. The expert data are the same as the policy network's training data before augmentation. The learner data is sampled from a replay buffer. Every  $N$  training steps, we empty the replay buffer and roll out the current policy with post-processing for  $S$  time steps to generate the learner data and store it in the replay buffer. During the roll-out, we start at a random time step in the training dataset and apply our model in a closed-loop manner. At each time step during the rollout, we sample a future trajectory for each vehicle from the Gaussian distribution predicted by our policy network, project the predicted trajectory onto the road, smooth the on-road trajectory with LQR, and finally update the vehicle to the first position of the smoothed trajectory.
+
+# 5. Experiment
+
+# 5.1. Dataset
+
+We utilize a real-world urban dataset called pNEUMA [3], which was collected by 10 drones in Athens over a span of 4 days. The dataset encompasses over half a million vehicle trajectories within a large area encompassing over  $100\mathrm{km}$  of lanes and approximately 100 intersections. The recordings were conducted at 5 intervals each day, with each period lasting about 15 minutes and a data collection time interval of 0.04 seconds. To enhance computational efficiency, we adopt a time step of 0.4 seconds. The dataset is divided into a training set, comprising recordings from the first 3 days, and a validation/test set, consisting of recordings from the final day. Notably, we choose not to utilize other popular traffic datasets like NGSIM [8] or HighD [23] or autonomous driving datasets like Lyft [18] or nuPlan [6], as they only encompass samll-scale scenarios. This limitation makes it inadequate for evaluate macroscopic realism.
+
+# 5.2. Metrics
+
+We evaluate the realism of our simulator by measuring the similarity between the simulation result and real data. During evaluation, each vehicle enters the simulator at its first recorded time and position, and is controlled by our simulator to complete its recorded route. When an agent reaches its final recorded position, it is removed from the simulator.
+
+Short-term microscopic: Following [5, 40], we conduct a short-term microscopic evaluation by simulating for 20 seconds from a random time step in the test dataset. We first measure the similarity between the simulated and real
+
+data using position and velocity RMSE metrics given by:
+
+$$
+\mathrm {R M S E} = \frac {1}{T _ {s}} \sum_ {t = 1} ^ {T _ {s}} \sqrt {\frac {1}{M} \sum_ {m = 1} ^ {M} \| \boldsymbol {s} _ {t} ^ {m} - \hat {\boldsymbol {s}} _ {t} ^ {m} \| ^ {2}}, \tag {10}
+$$
+
+where  $s_t^m$  and  $\hat{s}_t^m$  were the real and simulated value of the position or velocity of the agent  $m$  at time step  $t$ , respectively.  $T_s$  was the total simulated time steps, and  $M$  was the total simulated agent number. Besides, we measure the minimum Average Displace Error (minADE) to not penalize reasonable trajectory unlike the real one:
+
+$$
+\min  A D E _ {N} = \frac {1}{M} \sum_ {m = 1} ^ {M} \min  _ {\hat {\boldsymbol {s}} _ {n}} \frac {1}{T _ {s}} \sum_ {t = 1} ^ {T _ {s}} \| \boldsymbol {s} _ {t} ^ {m} - \hat {\boldsymbol {s}} _ {t, n} ^ {m} \| ^ {2}, \tag {11}
+$$
+
+where  $N = 20$  is roll-out times. We also calculate the off-road rate (the avarage proportion of vehicles that deviate more than  $1.5\mathrm{m}$  from the road over all time steps). The common collision rate metric is not used because we focus on the long-term impact and the dataset does not provide accurate vehicle size and heading information.
+
+Long-term macroscopic: we also evaluate our model's long-term macroscopic accuracy on five periods for 800 seconds from its initial recording time. To measure the long-term performance, we use two standard macroscopic metrics for traffic flow data [29, 36, 38], namely road density and speed RMSE, in addition to the off-road rate. The density of a road at a time step is calculated by dividing the number of vehicles on the road by its total lane length, assuming that all lanes have the same width. Meanwhile, the road speed is computed as the mean speed of all vehicles on the road. To quantify the similarity between the simulated and ground truth values, we still use RMSE, where the variable  $M$  becomes the total number of roads.
+
+# 5.3. Performance
+
+We compare our method against state-of-the-art baselines:
+
+SUMO [24]: we use the IDM model [42] as the car-following model and mobil [19] as the lane-changing model. We tune the IDM's parameters for 6 types of vehicle by minimizing the MSE between the IDM calculated acceleration and real acceleration using an Adam optimizer [20].
+
+BC [32]: we learn our model directly by the BC method.
+
+MARL [26]: we train our model using IPPO [10] as the Multi-Agent RL algorithm, where the reward function is composed of three parts: a displacement reward (average distance between agent trajectory with GT trajectory), an off-road penalty and a terminal reward.
+
+MARL+BC [31]: we add a behavior cloning term in the loss function while learning the policy with MARL.
+
+PS-GAIL [40]: we let all vehicles share the same policy parameter and critic parameter and learn the policy using reward functions computed by GAIL.
+
+Table 1. Comparison with baselines and ablated models on microscopic metrics for 20 seconds.  
+
+<table><tr><td>Model</td><td>Position RMSE(m)</td><td>Velocity RMSE(m/s)</td><td>minADE20(m)</td><td>Off-road(%)</td></tr><tr><td>SUMO [24]</td><td>41.25</td><td>7.00</td><td>24.20</td><td>0</td></tr><tr><td>BC [32]</td><td>40.08±1.61</td><td>6.74±0.37</td><td>22.02±3.98</td><td>33.43±3.10</td></tr><tr><td>MARL [26]</td><td>48.66±1.54</td><td>8.92±0.67</td><td>40.07±1.26</td><td>3.70±0.40</td></tr><tr><td>MARL+BC [31]</td><td>29.78±0.42</td><td>4.54±0.14</td><td>22.07±0.21</td><td>11.14±1.17</td></tr><tr><td>PS-GAIL [40]</td><td>34.78±0.43</td><td>5.33±0.12</td><td>27.86±0.33</td><td>7.65±0.32</td></tr><tr><td>RAIL [5]</td><td>31.62±0.65</td><td>5.51±0.09</td><td>24.51±0.41</td><td>2.57±0.47</td></tr><tr><td>LASIL (ours)</td><td>19.21±0.44</td><td>3.02±0.07</td><td>12.79±0.32</td><td>0.28±0.01</td></tr><tr><td>w/o Augmentation</td><td>21.62±0.54</td><td>3.34±0.14</td><td>13.81±0.37</td><td>1.31±0.18</td></tr><tr><td>w/o Context-conditioned</td><td>23.03±0.87</td><td>3.73±0.12</td><td>14.94±0.43</td><td>0.51±0.04</td></tr><tr><td>w/o On-road Projection</td><td>22.53±0.42</td><td>3.26±0.10</td><td>14.42±0.33</td><td>1.74±0.60</td></tr><tr><td>w/o LQR</td><td>22.62±0.43</td><td>4.05±0.15</td><td>14.02±0.28</td><td>0.22±0.02</td></tr></table>
+
+Table 2. Comparison with baselines and ablated models on macroscopic metrics for 800 seconds.  
+
+<table><tr><td>Model</td><td>Road Density RMSE(veh/km)</td><td>Road Speed RMSE(m/s)</td><td>Off-road(%)</td></tr><tr><td>SUMO [24]</td><td>52.70</td><td>5.52</td><td>0</td></tr><tr><td>BC [32]</td><td>61.51±1.53</td><td>5.38±0.21</td><td>42.15±5.25</td></tr><tr><td>MARL [26]</td><td>90.59±2.65</td><td>5.27±0.48</td><td>4.63±0.64</td></tr><tr><td>MARL+BC [31]</td><td>43.60±2.80</td><td>4.01±0.13</td><td>22.73±5.62</td></tr><tr><td>PS-GAIL [40]</td><td>54.06±1.23</td><td>4.03±0.05</td><td>13.24±3.20</td></tr><tr><td>RAIL [5]</td><td>54.45±1.89</td><td>3.89±0.11</td><td>2.92±0.38</td></tr><tr><td>LASIL (ours)</td><td>45.13±0.25</td><td>3.17±0.14</td><td>0.34±0.03</td></tr><tr><td>w/o Augmentation</td><td>55.65±0.44</td><td>3.73±0.23</td><td>9.62±1.40</td></tr><tr><td>w/o Context-conditioned</td><td>55.98±0.51</td><td>4.48±0.19</td><td>0.64±0.08</td></tr><tr><td>w/o On-road Projection</td><td>52.90±0.54</td><td>3.59±0.20</td><td>11.33±2.37</td></tr><tr><td>w/o LQR</td><td>61.68±0.96</td><td>3.54±0.16</td><td>0.47±0.07</td></tr></table>
+
+RAIL [5]: we learn the model as PS-GAIL but with additional displacement, off-road and terminal rewards.
+
+We train and evaluate each model five times to obtain the mean and standard deviation (std) of various metrics. Note that we do not apply on-road projection and LQR for baselines. We evaluate both short-term and long-term performance, as shown in Tab. 1 and Tab. 2, respectively. Our method achieves better results than all baselines in terms of position and velocity RMSE, road density and speed RMSE, with minor off-road rate.
+
+# 5.4. Ablation Study
+
+We conducted a series of ablation experiments to assess the individual contributions of crucial components in our approach, whose results are presented in Tab. 1 and Tab. 2.
+
+Augmentation: By removing our VAE module and directly learning the original expert state and action, we analyze the importance of our data augmentation technique. The results demonstrate that augmentation plays a vital role in improving both short-term and long-term simulation performance by mitigating covariate shift.
+
+Context-conditioned VAE: To emphasize the significance of modeling the context-conditioned trajectory distribution rather than the whole state distribution, we replaced our context-conditioned VAE with a naive VAE that directly
+
+models the expert and learner state distribution. The observed drop in performance demonstrates the challenges in reconstructing the context distribution.
+
+On-road projection: Our ablation study on the on-road projection module aims to show its impact on reducing the off-road rate. The results show that the on-road projection module leads to a notable decrease in the off-road rate and moderate improvements in other performance metrics.
+
+LQR: Removing LQR module allows us to evaluate its effectiveness. While LQR led to a higher short-term off-road rate due to more constrained movement (driving off-road due to inertia), its removal deteriorates other short-term and long-term metrics, because LQR can smooth the trajectory, thus leads to more realistic simulations.
+
+# 5.5. Qualitative Result
+
+In Fig. 2, we present the mean road density and speed for real-world data, SUMO simulation, and our proposed method over all time steps. The results demonstrate that our proposed method surpasses the capabilities of the SUMO simulator at replicating long-term macroscopic traffic patterns due to our model's enhanced ability to replicate the typical microscopic driving behaviors over a long period.
+
+![](images/7fe78b129460e56077e2dacba9ddc2df6714e3b7076b387f2f8e7ad5ec3de2b5.jpg)  
+Figure 2. Mean density and speed on each road over all time steps in the long-term evaluation. Our method's density and speed hot-maps have a more similar color to the ground-truth one compared with the SUMO's.
+
+# 6. Conclusion
+
+In conclusion, we have addressed the challenge of creating a realistic traffic simulator that accurately models human driving behaviors in various traffic conditions. Traditional imitation learning-based simulators often fail to deliver accurate long-term simulations due to the covariate shift problem in multi-agent imitation learning. To tackle this issue, we proposed a learner-aware supervised imitation learning method, which leverages a context-conditioned VAE to generate learner-aware augmented expert states. We leverage a context-conditioned VAE to simultaneously reconstruct the expert and learner state. This approach enables the reproduction of long-term stable microscopic traffic simulations, marking a significant advancement in the field of urban
+
+traffic simulation. Our method has demonstrated superior performance over existing state-of-the-art simulators when evaluated on the real-world dataset pNEUMA, achieving better short-term microscopic and long-term macroscopic similarity to real-world data than state-of-the-art baselines.
+
+# 7. Acknowledgements
+
+This research project is partially supported by the Innovation and Technology Commission of the HKSAR Government under the InnoHK initiative, Hong Kong General Research Fund (11202119 and 11208718), Innovation and Technology Commission (GHP/126/21GD), and Guangdong, Hong Kong and Macao Joint Innovation Project (2023A0505010016).
+
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+        "text": "LASO: Language-guided Affordance Segmentation on 3D Object",
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+        "text": "Yicong Li $^{1}$ , Na Zhao $^{2*}$ , Junbin Xiao $^{1}$ , Chun Feng $^{3}$ , Xiang Wang $^{3*†}$ , Tat-seng Chua $^{1}$ ,",
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+        "text": "$^{1}$ National University of Singapore,  $^{2}$ Singapore University of Technology and Design,  $^{3}$ University of Science and Technology of China,",
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+        "text": "liyicong@u.nus.edu,na_zhao@sutd.edu.sg,junbin@comp.nus.edu.sg",
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+        "text": "fengchun3364@mail.ustc.edu.cn,xiangwangl223@gmail.com,dcstsc@nus.edu.sg",
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+        "type": "text",
+        "text": "Abstract",
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+        "text": "Segmenting affordance in 3D data is key for bridging perception and action in robots. Existing efforts mostly focus on the visual side and overlook the affordance knowledge from a semantic aspect. This oversight not only limits their generalization to unseen objects, but more importantly, hinders their synergy with large language models (LLMs) which are excellent task planners that can decompose an overarching command into agent-actionable instructions. With this regard, we propose a novel task, Language-guided Affordance Segmentation on 3D Object (LASO), which challenges a model to segment a 3D object's part relevant to a given affordance question. To facilitate the task, we contribute a dataset comprising 19,751 point-question pairs, covering 8434 object shapes and 870 expert-crafted questions. As a pioneer solution, we further propose PointRefer, which highlights an adaptive fusion module to identify target affordance regions at different scales. To ensure a text-aware segmentation, we adopt a set of affordance queries conditioned on linguistic cues to generate dynamic kernels. These kernels are further used to convolute with point features and generate a segmentation mask. Comprehensive experiments and analyses validate PointRefer's effectiveness. With these efforts, We hope that LASO can steer the direction of 3D affordance, guiding it towards enhanced integration with the evolving capabilities of LLMs. Code and data are available at https://github.com/y13800/LASO.",
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+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "Affordance describes specific regions on an object that enable or facilitate certain human interactions. In this context,",
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+        "image_caption": [
+            "Figure 1. Illustration of LASO, language-guided affordance segmentation on 3D object. Given an object point cloud and a question, the model is expected to segment the functional part delineated in question."
+        ],
+        "image_footnote": [],
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+        "text": "the task of 3D affordance segmentation is raised to identify parts of 3D objects that imply a certain function. It has been deemed as a critical step in bridging perception and operation in the physical world for an embodied agent, thus has shown substantial impact on practical applications such as robotic manipulation [10, 14, 31].",
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+        "text": "Recently, the advancement of Large Language Models (LLMs) has enabled their deployment as task planners, breaking down an intricate instruction into a sequence of affordance-aware, robot-executable instructions [12, 35, 36]. This equips intelligent agents with the capability to undertake complex tasks. For example, the overarching command \"Pass me the mug in the microwave\" can be systematically deconstructed into a series of affordance-aware inquiries: Q1) \"How to get to the microwave?\", Q2) \"How to open the microwave\", Q3) \"How to grab the mug?\", and Q4) \"How to return to the user?\" Ideally, each query would correspond to a predefined subtask that effectively translates language instructions into actionable steps. While Q1 and Q4 are related to language-conditioned path planning [42] and navigation [37], Q2 and Q3, which involve the 'open microwave' and 'grab the mug' actions, ex",
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+        "text": "CVF",
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+        "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
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+        "text": "*Corresponding author.",
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+        "text": "$\\dagger$  Xiang Wang is also affiliated with Institute of Artificial Intelligence,",
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+        "text": "Institute of Dataspace, Hefei Comprehensive National Science Center.",
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+        "type": "text",
+        "text": "pose a gap — to the best of our knowledge, currently understanding affordance via language cues remains unexplored.",
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+        "text": "Leaving language cues untouched, current 3D affordance segmentation focuses primarily on the visual aspect. It associates the specific geo-structure with either explicit affordance categories [7] or implicit affordance information from the 2D showcase [44]. Such visual-only settings make the segmentation models confined to visually predefined affordance types, thus impeding integration with language-based instructions from LLMs. As a result, fulfilling the aforementioned user's request becomes challenging, due to this inability to address Q2 and Q3.",
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+        "text": "Towards these limitations, we introduce a novel task: Language-guided Affordance Segmentation on 3D Object (LASO), where 3D objects are paired with natural language questions that probe specific affordance parts. As a cornerstone task, LASO can provide an agent with affordance knowledge to answer the aforementioned Q2 and Q3 raised by LLM. For instance, the first two rows in Fig. 1 demonstrate how LASO imparts knowledge that enables an agent to interpret the semantic instructions \"open the microwave\" and \"grasp the mug\" in a 3D context, which are sufficient to execute Q2 and Q3, respectively. In LASO, questions are crafted to reflect diverse real-world scenarios, translating various affordance types into a range of semantic contexts. By learning from different contexts, we expect the agent not to memorize predefined affordance types but rather to abstract generalizable affordance knowledge within a broader semantic context. Notably, the diverse scales and shapes of affordance parts pose a significant perceptual challenge for the model. For instance, in the third row of Fig. 1, the target backrest of a chair occupies a large portion and has a significantly different shape compared to the small knob on a door in the last row.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "To facilitate the study, we develop the 1st question-affordance dataset comprising 19,751 point cloud-question pairs. The questions, originally crafted by experts, are further diversified using GPT-4 [33] under principles of contextual enrichment, concise phrasing, and structural diversity. These principles enable a deep and varied exploration of object affordances. Based on the dataset, we have developed a strong baseline model named PointRefer that is capable of adapting to varying scales and shapes of object parts, conditioned on the question. It consists of two modules: 1) an Adaptive Fusion Module (AFM) that integrates question semantics to point features at different scales, which caters to varied target regions with better point feature discriminativeness; and 2) a Referred Point Decoder (RPD) that generates a segmentation mask via conditioned affordance queries, which, after refinement, forms dynamic convolution kernels to capture point-wise affordance for mask prediction. In summary, our contributions are as follows:",
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+    },
+    {
+        "type": "text",
+        "text": "- We propose the task of Language-guided Affordance Seg",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/31b0b464e12a209949a0fe651ce2f3ee5cf847ceaeb881a076774d1035daa881.jpg",
+        "table_caption": [
+            "Table 1. Efforts on affordance learning. Part indicates whether the prediction specifies the object part (✓) or the whole object  $(\\times)$ ."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Domain</td><td>Studies</td><td>Vision</td><td>Text</td><td>Part</td></tr><tr><td rowspan=\"3\">2D</td><td>[1, 46]</td><td>Image</td><td>×</td><td>×</td></tr><tr><td>[9, 25, 32]</td><td>Image/Video</td><td>×</td><td>✓</td></tr><tr><td>[24, 29]</td><td>Image</td><td>✓</td><td>×</td></tr><tr><td rowspan=\"3\">3D</td><td>[7, 30, 30, 43]</td><td>Point Cloud</td><td>×</td><td>✓</td></tr><tr><td>[44]</td><td>Point Cloud &amp; Image</td><td>×</td><td>✓</td></tr><tr><td>Ours</td><td>Point Cloud</td><td>✓</td><td>✓</td></tr></table>",
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+    },
+    {
+        "type": "text",
+        "text": "mentation on 3D Objects (LASO), which helps AI agents derive affordance knowledge from textual cues, facilitating a crucial advancement for LLM integration.",
+        "bbox": [
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+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- We develop a dataset with 19,751 question-point affordance pairs which are meticulously curated via a collaborative effort of human experts and GPT-4, thereby establishing the 1st benchmark for evaluating LASO.",
+            "- We build a strong baseline PointRefer, which employs textual-conditioned affordance queries to isolate afforded segments and devises an adaptive fusion module to enhance the discriminability of point feature."
+        ],
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Affordance Learning. Originating from the image domain, initial efforts concentrate on detecting objects with affordances [1, 46]. Progressing from there, later studies [24, 29] incorporate linguistic descriptions to augment the process but still neglect the granularity of analysis, generally focusing on object-level affordances. Addressing this oversight, subsequent research [9, 25, 32] shift towards scrutinizing specific affordance parts, establishing a new norm for precision in the field.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "With the rise of embodied AI, the scope of affordance learning expands into the 3D realm. 3D AffordanceNet [7] introduces the first benchmark dataset for learning affordance from object point cloud geometry. Building on this, Yang et al. [44] propose a setting for learning 3D affordance parts guided by image demonstrations. Nonetheless, these approaches predominantly rely on a visual-only approach, tightly coupling geometric features with affordance labels and overlooking the semantic dimension. This limitation hinders the integration with Large Language Models (LLMs) that could otherwise substantiate affordance segmentation to real-world deployment. Moreover, the common practice of predicting affordance types as an auxiliary task [7, 44] may dilute the primary challenge of understanding affordance knowledge. In contrast, our work sidesteps auxiliary predictions, advocating for direct learning from the linguistic context, which aligns more closely with the innate capabilities of LLMs and their semantic richness.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Text-Point Cloud Cross-Modal Learning. The integration of vision and natural language has recently sparked increased interest [16-21, 41]. Such a tendency naturally extends to 3D vision due to its pivotal role in embodied AI. To",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "14252",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "image",
+        "img_path": "images/f02f4f367fd6504dc0599f11f0b7da47dce2cc5d8670c945bc01f637a759f629.jpg",
+        "image_caption": [
+            "Figure 2. Illustration of question augmentation principles."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "advance the 3D-language tasks, datasets like ScanRefer [5] and ReferIt3D [2] have been instrumental in benchmarking the grounding of natural language to 3D objects. Complementing this, Azuma et al. [3] introduce ScanQA for 3D question-answering, while Ma et al. [28] propose SQA3D for situated reasoning within 3D environments. In terms of models, a variety of efforts [3, 13, 45] have emerged from these benchmarks, with notable examples like 3D-SPS [26] and BUTD-DETR [13] employing cross-attention mechanisms and linguistic cues for object discovery. Others, such as 3DVG [45], and ViL3DRel [6], focus on 3D grounding by incorporating spatial relation cues, showcasing the evolving landscape of 3D-VL models. Unlike the existing work that focuses on grounding and QA that perform scene-level reasoning, we tackle a dense prediction task at object part level that bridges reasoning to operation. To the best of our knowledge, we are the first to introduce the 3D affordance problem as a language-guided segmentation task.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3. Dataset",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "To underpin our proposed task, we have meticulously compiled a question-point affordance dataset with 19,751 paired samples, featuring 8,434 distinct object shapes across 23 classes. Accompanying these are 870 expertly crafted questions, covering 17 affordance categories.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1. Annotation Details",
+        "text_level": 1,
+        "bbox": [
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+            659
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Point Cloud. Our dataset leverages the point cloud and affordance annotations from the 3D-AffordanceNet [7]. Specifically, the affordance annotation in [7] is multi-class, with each point on an object potentially supporting multiple affordance types. In our case, each question is tailored to a specific affordance type, while each sample can associate with several questions. Consequently, the same object can exhibit diverse affordance segmentation, depending on the specific question posed.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Question. To create the questions, we draw 58 object-affordance combinations from [7], and craft 15 unique questions for each of the 58 combinations, resulting in 870 tailored questions. Specifically, five manual questions per combination are initially composed to represent different scenarios. Subsequently, we employ GPT-4 [33] to diver",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "table",
+        "img_path": "images/d709bc24a5eff4cb6cad052fd9b1c2a9cf88f7a166ec0b98c98eed85d9db1c07.jpg",
+        "table_caption": [
+            "Table 2. Dataset Statistics"
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Task</td><td colspan=\"3\">Train</td><td colspan=\"3\">Val</td><td colspan=\"3\">Test</td></tr><tr><td>Shape</td><td>Qst</td><td>Inst</td><td>Shape</td><td>Qst</td><td>Inst</td><td>Shape</td><td>Qst</td><td>Inst</td></tr><tr><td>Seen</td><td>6883</td><td>638</td><td>16120</td><td rowspan=\"2\">516</td><td rowspan=\"2\">58</td><td rowspan=\"2\">1215</td><td rowspan=\"2\">1035</td><td rowspan=\"2\">174</td><td rowspan=\"2\">2416</td></tr><tr><td>Unseen</td><td>6160</td><td>458</td><td>11558</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/058b1cac9cc8965d2e5d05a665f8f8ce3c0ea0c2d9db887094e1c4c1334812c5.jpg",
+        "image_caption": [
+            "Figure 3. Landscape of our dataset."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            501,
+            174,
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+            315
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "sify the dataset with 10 additional questions for each combination, adhering to three key principles (as shown in Fig. 2): 1) Contextual Enrichment. Some questions were expanded to include additional context or details, fostering a more precise connection to the specified affordance of the target object. For instance, Q1 in Fig. 2 is reformed by a functional situation \"cutting paper\". 2) Concise Phrasing. In other cases, questions were distilled to their essence, making them succinct yet still meaningful. Q2 in Fig. 2 exemplifies this approach. 3) Structural Diversity. We employed a range of sentence structures, from questions to statements, to introduce natural linguistic variations and prevent model bias toward any specific phrasing or sentence length. A diversified example can be found in the Q3 of Fig. 2. All questions generated by GPT-4 undergo manual verification after this augmentation process.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "It's worth mentioning that the affordance type was only a tool for crafting the questions and pinpointing the correct segmentation areas. We refrain from using explicit affordance labels during both training and testing. This deliberate choice ensures that the learning process is driven by the semantic content of the questions, rather than by direct affordance label association.",
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.2. Statistics and Setting",
+        "text_level": 1,
+        "bbox": [
+            500,
+            695,
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+            710
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Dataset Settings. We show the statistical landscape of our dataset in Fig. 3. Specifically, it contains 17 affordance types and 23 object categories, composing 58 unique object-affordance combinations.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In the spirit of the work by [44], we offer two distinct dataset settings: Seen: The default configuration, where the training and testing phases share similar distributions of object classes and affordance types. Unseen: This configuration is purpose-built to test the model's ability to generalize affordance knowledge. Certain affordance types, when paired with specific object classes, are omitted from the training set but included in the test set. For instance, while",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "14253",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "the model may learn to grasp bags and mugs during training, it is expected to apply the concept of 'grasp' to earphones, which is an affordance-object pairing not encountered during training. For a comprehensive account of the unseen setting, please refer to Appendix Sec. 7.1.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Training and Evaluation Protocols. Notably, since questions are created based on a combination of object class and affordance type, one object class can have many shape instances. Thus, the design of our dataset accounts for the multiplicity of shapes within each object class, leading to a non-bijective pairing between shape instances and corresponding questions. To ensure comprehensive learning, during training, each shape instance is matched with a randomly selected question that aligns with its affordance type for every iteration. This random pairing exposes the model to a variety of semantic contexts, bolstering its ability to generalize. For the validation and test sets, question pairings are fixed to minimize variability and ensure consistent inference. These questions are unique to the evaluation phase and are not revealed during the training process to maintain the integrity of the evaluation.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4. Method",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "LASO Task Definition. Given a question  $Q_{raw}$  and an object point cloud  $\\mathbf{P}_{raw} \\in \\mathbb{R}^{N \\times 3}$  with  $N$  points, the goal of LASO is to predict a binary mask of  $\\mathbf{M} \\in \\mathbb{R}^N$  that segments the functional part related to the question.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Framework Overview. Due to the varying scale of target affordance region, LASO naturally challenges models adaptiveness at different scales. To address this, we devise a strong baseline, named PointRefer. As shown in Fig. 4, the object point cloud  $\\mathbf{P}_{raw}$  is first processed by a 3D backbone, which typically consists of the multi-stage encoding and decoding process. To adapt PointRefer to the point feature at multiple scales, we introduce an Adaptive Fusion Module (AFM) to the backbone's decoding process. It performs multi-scale cross-modal fusion by injecting text clues to point features at a different decoding stage, which progressively refine the point feature map in a top-down manner. Then, to predict the segmentation mask, we introduce a Referred Point Decoder (RPD) that leverages a set of learnable queries conditioned on the input question, termed affordance queries, as the input of the transformer decoder. These affordance queries are obligated to look at the referred points only and generate question-aware dynamic kernels. The final segmentation mask is obtained by convoluting these dynamic kernels with the AFM-enhanced point feature.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Feature Encoding. For the question, we prepend a \"[CLS]\" token to the question sequence before feeding them to a language model to capture the global language context. The encoded feature of the question is denoted by  $\\mathbf{X} \\in \\mathbb{R}^{L \\times d}$ , where  $L$  is the number of tokens and  $d$  is the feature di",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "mension. For the point cloud, PointRefer can adopt any off-the-shelf 3D segmentation backbone.<sup>1</sup> to transform the  $\\mathbf{P}_{raw}$  into the feature space. Note that a 3D backbone for segmentation typically consists of several encoding and decoding stages, and we take the point-wise feature map after the last decoding stage as the output of the backbone.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4.1. Adaptive Fusion Module",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "AFM is designed to enhance the point-wise features by incorporating question information. As illustrated in Fig. 4, we integrate AFM into different decoder layers to enhance its adaptiveness to target regions of various scales and shapes. Given the conventional downsampling operators in 3D backbones (e.g. PointNet++ [34]), the number of points varies across different encoder/decoder layers. Our AFM is designed to seamlessly adapt to the varying number of points.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "For simplification, we omit the notation for different decoder layers and use  $\\mathbf{P} \\in \\mathbb{R}^{T \\times d}$  to denote the point feature at a certain decoding layer, where  $T$  represents the number of points at that layer. As visualized in Fig. 4, AFM adopts a bottleneck architecture with three key steps: Grouping, Mixing, and Ungrouping. In the grouping step, the point features are grouped by text tokens, these grouped tokens are then thoroughly mixed via an MLP-Mixer [38]. Subsequently, the ungrouping step encapsulates the mixed features into individual point features, completing the AFM procedure by embedding valuable textual information into the point feature.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "To facilitate an efficient grouping process for our AFM, we employ a lightweight cross-attention module by omitting the transformation of both query and value. It takes the question feature  $\\mathbf{X}$  as query and the point feature  $\\mathbf{P}$  as key and value, then output grouped token  $\\mathbf{G} \\in \\mathbb{R}^{L \\times d}$ :",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {G} = \\operatorname {A t t e n t i o n} \\left(\\mathbf {X}, \\mathbf {W} _ {1} \\mathbf {P}, \\mathbf {P}\\right) + \\mathbf {X}, \\tag {1}\n$$\n",
+        "text_format": "latex",
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\operatorname {A t t e n t i o n} (\\mathbf {Q}, \\mathbf {K}, \\mathbf {V}) = \\operatorname {S o f t m a x} \\left(\\frac {\\mathbf {Q} \\mathbf {K} ^ {T}}{\\sqrt {d}}\\right) \\mathbf {V}, \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathbf{W}_1$  is a linear transformation.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "After attaining the grouped feature, we update them using an MLP-Mixer [38], which employs two consecutive multilayer perceptrons (MLPs), producing fused feature  $\\mathbf{F}$  by combining with two consecutive MLPs.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {G} ^ {\\prime} = \\mathbf {G} + \\operatorname {M L P} _ {1} \\left(\\mathbf {G} ^ {T}\\right) ^ {T}, \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {F} = \\mathbf {G} ^ {\\prime} + \\mathrm {M L P} _ {2} \\left(\\mathbf {G} ^ {\\prime}\\right), \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where,  $\\mathrm{MLP}_1$  and  $\\mathrm{MLP}_2$  are used to mix group-wise and channel-wise information, respectively, and  $T[\\cdot]$  denotes the transpose operation. Finally, we return the fused feature  $\\mathbf{F}$  to the point-space via the ungrouping process and",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "page_footnote",
+        "text": "1The impact of backbone choices can be observed in Tab. 5.",
+        "bbox": [
+            517,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "14254",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/e9b18ca47acf1010aba4b1a6f550693ca4313b08db5a15d713f522946cff3c15.jpg",
+        "image_caption": [
+            "(a) Overview of PointRefer."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            81,
+            88,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/d72ddcef34d4d0b43226e356b67b7c1342c77602abfa91c7a9b82df45cf402de.jpg",
+        "image_caption": [
+            "(b) Adaptive Fusion Module.",
+            "Figure 4. The overall framework of our proposed PointRefer (a), which contains an adaptive fusion modal (b) that can be injected in different stages of the backbone decoder. As a result, it takes the point-wise feature generated at the last decoder layer as the final output of the 3D backbone. Then, the Referred Point Decoder takes in a set of question-conditioned affordance queries and feeds it to a transformer decoder together with the fused point feature, where the output is then reformed to a set of dynamic kernels. Finally, these dynamic kernels are used as convolution kernels to filter out the segmentation mask from the fused point feature."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            678,
+            93,
+            893,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "acquire the fused point feature  $\\mathbf{P}^m$ . We implement the ungrouping process as a similar lightweight attention module as the grouping process. However, in this case, it takes  $\\mathbf{P}$  as query and  $\\mathbf{F}$  as key and value:",
+        "bbox": [
+            75,
+            446,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {P} ^ {m} = \\operatorname {A t t e n t i o n} (\\mathbf {P}, \\mathbf {W} _ {2} \\mathbf {F}, \\mathbf {F}) + \\mathbf {P}, \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            156,
+            518,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathbf{W}_2$  is a linear transformation. Lastly, the final output  $\\mathbf{P}^o$  is formed by adding residual connections to  $\\mathbf{P}^m$ . Notably, we take  $\\mathbf{P}^o$  after the last decoding stage as the output of the 3D backbone.",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.2. Referred Point Decoder",
+        "text_level": 1,
+        "bbox": [
+            76,
+            617,
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+            631
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Inspired by the success of learnable query-based methods in object detection [4] and segmentation [40], we introduce learnable affordance queries conditioned on the corresponding question of an object to decode the segmentation mask for the object. Specifically, we impose linguistic restrictions on all affordance queries, narrowing the model's focus to the relevant object parts and thereby facilitating convergence. These affordance queries, after being processed by a transformer decoder, are repurposed as dynamic kernels to deduce the segmentation mask from the point features, which are the final output of the 3D backbone.",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Question-Conditioned Affordance Query In the transformer decoder, it is well known that content and position embeddings are responsible for encoding instance-specific and spatial information, respectively. In PointRefer, we feed these two parts with the text feature and learnable query parameters, respectively, so that all the queries are",
+        "bbox": [
+            75,
+            810,
+            468,
+            901
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "shaped by the nuances of the linguistic input. Specifically, the affordance queries  $\\mathbf{A}$  are formed by adding question embedding  $\\mathbf{X}$  with learnable embeddings. Thus, the resulting  $\\mathbf{A} \\in \\mathbb{R}^{L \\times d}$  are the same length of the question.",
+        "bbox": [
+            498,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Reasoning and Mask Prediction. After forming the affordance query, we feed it to a transformer decoder [39] together with the fused point feature  $\\mathbf{P}_o$  from the 3D backbone. In this manner, all the queries will use the question context as guidance and target to aggregate the feature of the referred points from the object, resulting in  $\\mathbf{A}'$ :",
+        "bbox": [
+            498,
+            510,
+            890,
+            601
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {A} ^ {\\prime} = \\text {T r a n s f o r m e r - D e c o d e r} (\\mathbf {A}; \\mathbf {P} _ {o}). \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            576,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Subsequently, we perform dynamic convolution by applying a two-layer MLP on top of the transfer decoder to produce  $L$  dynamic kernels  $\\Omega = \\{\\omega_{i}\\}_{i = 1}^{L}$ , where each kernel  $\\omega_{i}$  is reshaped to a  $1\\times 1$  convolutional kernel with the channel number of  $d$ .",
+        "bbox": [
+            498,
+            642,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\Omega = \\operatorname {M L P} \\left(\\mathbf {A} ^ {\\prime}\\right). \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            642,
+            729,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Since the dynamic kernels have captured the question- information, we use them as convolution filters on the feature maps for mask decoding. Specifically, we use each dynamic kernel in  $\\Omega$  to convolute the point-wise feature map  $\\mathbf{P}_o$ , which returns  $L$  point masks  $\\mathbf{S} = \\{\\mathbf{s}_i\\}_{i=1}^L$ .",
+        "bbox": [
+            498,
+            758,
+            890,
+            834
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {S} _ {i} = \\left\\{\\mathbf {P} _ {o} * \\omega_ {i} \\right\\} _ {i = 1} ^ {L}. \\tag {8}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            625,
+            839,
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+            859
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Then, we apply mean pooling over all masks in  $\\mathbf{S}$  followed by a sigmoid activation to acquire the final segmentation",
+        "bbox": [
+            498,
+            869,
+            890,
+            900
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "14255",
+        "bbox": [
+            480,
+            944,
+            517,
+            955
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "mask  $\\mathbf{M}\\in \\mathbb{R}^N$  ..",
+        "bbox": [
+            76,
+            90,
+            181,
+            104
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {M} = \\sigma (\\operatorname {M a x - P o o l} ((\\mathbf {S}))), \\tag {9}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            187,
+            113,
+            468,
+            128
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where  $\\sigma (\\cdot)$  denote the sigmoid function.",
+        "bbox": [
+            76,
+            137,
+            344,
+            151
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Intuitively, each dynamic kernel is expected to capture one aspect of the referred object part according to conditioned the question token. By ensembling all generated point masks, the final segmentation mask can integrate different response regions, thus making the result more robust.",
+        "bbox": [
+            76,
+            152,
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+            227
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Objectives. Unlike [44], which relies on an auxiliary affordance label for prediction, our model seeks to forge a direct link between language context and object affordance. Thus, we solely employ Dice loss and Binary Cross-Entropy (BCE) loss to guide the segmentation mask prediction, bypassing the need for additional affordance labels.",
+        "bbox": [
+            76,
+            229,
+            468,
+            320
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {B C E} + \\mathcal {L} _ {D i c e} \\tag {10}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            200,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5. Experiment",
+        "text_level": 1,
+        "bbox": [
+            76,
+            332,
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+            349
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Evaluation Metrics. For a thorough assessment, we benchmark our dataset against leading studies in 3D affordance learning [7, 44], employing four evaluation metrics to ensure robust analysis. These include Area Under the Curve (AUC), Mean Intersection Over Union (mIoU), Similarity (SIM), and Mean Absolute Error (MAE). Appendix Sec. 7.2 provides detailed explanations for the evaluation protocols.",
+        "bbox": [
+            76,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Implementation Details. PointRefer employs PointNet++ as the default 3D backbone to align with the standards established in [7, 44]. For text encoding, we utilize a pretrained RoBERTa model [23] to process linguistic inputs. The feature dimension  $d$  is set to 512. During training, we use the Adam optimizer with a learning rate set to 1e-4.",
+        "bbox": [
+            76,
+            465,
+            468,
+            556
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Baseline Models. Since there is no prior work using paired question-point cloud data to segment object affordance. For a thorough comparison of our method, we adopt two 3D cross-modal works (3D-SPS [26] and IAGNet[44]) and two referred image segmentation works (ReferTrans [15] and RelA [22]) to LASO task. For the referred image segmentation models, we substitute their image backbones with a 3D counterpart, retaining their fusion mechanisms and mask decoding strategies. For the language-guided grounding model, 3D-SPS [26], we omit its bounding box prediction module while leveraging its inherent point selection scheme for our segmentation setting. The most related work is IAGNet [44], an affordance detection method that takes paired image-point cloud as input. To adapt IAGNet to our needs, we simply replace its image backbone with a language model, preserving the remainder of its architecture.",
+        "bbox": [
+            76,
+            559,
+            468,
+            800
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Next, we show the effectiveness of our PointRefer by answering the following questions:",
+        "bbox": [
+            76,
+            806,
+            468,
+            835
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- Q1: How is PointRefer compared to other baselines on the proposed dataset?",
+            "- Q2: How effective are the proposed components?",
+            "- Q3: What learning pattern does the PointRefer capture?"
+        ],
+        "bbox": [
+            76,
+            837,
+            467,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/37931b6d0726af191bd50a6c013764788cb4c8cb21bc1cd62b40c5eef736dbba.jpg",
+        "table_caption": [
+            "Table 3. Main Results. The overall results of all comparative methods, the best results are in bold. Seen and Unseen are two partitions of the dataset. AUC and aIOU are shown in percentage."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>Method</td><td>mIoU↑</td><td>AUC↑</td><td>SIM↑</td><td>MAE↓</td></tr><tr><td rowspan=\"5\">Steen</td><td>ReferTrans [15]</td><td>13.7</td><td>79.8</td><td>0.497</td><td>0.124</td></tr><tr><td>ReLA [22]</td><td>15.2</td><td>78.9</td><td>0.532</td><td>0.118</td></tr><tr><td>3D-SPS [26]</td><td>11.4</td><td>76.2</td><td>0.433</td><td>0.138</td></tr><tr><td>IAGNet [44]</td><td>17.8</td><td>82.3</td><td>0.561</td><td>0.109</td></tr><tr><td>PointRefer</td><td>20.8</td><td>87.3</td><td>0.629</td><td>0.093</td></tr><tr><td rowspan=\"5\">Unseen</td><td>ReferTrans [15]</td><td>10.2</td><td>69.1</td><td>0.432</td><td>0.145</td></tr><tr><td>ReLA [22]</td><td>10.7</td><td>69.7</td><td>0.429</td><td>0.144</td></tr><tr><td>3D-SPS [26]</td><td>7.9</td><td>68.8</td><td>0.402</td><td>0.158</td></tr><tr><td>IAGNet [44]</td><td>12.9</td><td>77.8</td><td>0.443</td><td>0.129</td></tr><tr><td>PointRefer</td><td>14.6</td><td>80.2</td><td>0.507</td><td>0.119</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5.1. Main Result (Q1)",
+        "text_level": 1,
+        "bbox": [
+            500,
+            309,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "In Table 3, PointRefer demonstrates superior performance across all evaluation metrics compared to the baseline methods. Our observations are as follows:",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "PointRefer vs. Other Models: IAGNet secures the second-best performance in both seen and unseen settings for all metrics. This is likely due to its specific design for object affordance segmentation, despite differences in input modality, making it a strong fit for our task with minimal adaptation. In contrast, 3D-SPS underperforms, potentially due to its progressive point selection mechanism. This approach involves a non-differentiable selection process, which may complicate the optimization within our task framework. Image-based methods, while showing decent performance, appear to be constrained by the modality gap. Originally trained on vast datasets of image-text pairs, where text is often a brief label, these methods now face fully formed, context-rich questions with a more limited training corpus.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Seen vs. Unseen Performance: A notable performance drop from seen to unseen settings is observed across all baselines. This discrepancy underscores the difficulty in learning affordance knowledge that generalizes well, corroborating the necessity of our task design. Current methods struggle to bridge this gap in knowledge transfer, suggesting an avenue for future research: utilizing the extensive commonsense knowledge embedded in LLMs could potentially mitigate this challenge.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5.2. In-Depth Study (Q2)",
+        "text_level": 1,
+        "bbox": [
+            500,
+            756,
+            694,
+            772
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Ablation Study. We show ablative results in Tab. 4. To verify that PointRefer prediction is based on the question, we conduct a blind test by training without questioning information, where the distinctive performance gap indicates that PointRefer has comprehended the question and can make a prediction based on it. Then, we study the effectiveness of PointRefer by removing both AFM and PRD (\"w/o AFM & PRD\"), which induces a severe performance",
+        "bbox": [
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+            779,
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+            900
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "14256",
+        "bbox": [
+            480,
+            944,
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+            955
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/fe6f55be7872c2c69349e23bbb6881cb74d1615b258bfa0c469c0f7c157b16f7.jpg",
+        "table_caption": [
+            "Table 4. Ablative Results."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Variants</td><td>mIoU↑</td><td>AUC↑</td><td>SIM↑</td><td>MAE↓</td></tr><tr><td>Blind</td><td>10.8</td><td>78.2</td><td>0.506</td><td>0.125</td></tr><tr><td>w/o AFM &amp; PRD</td><td>17.7</td><td>82.1</td><td>0.558</td><td>0.110</td></tr><tr><td>w/o AFM</td><td>19.8</td><td>83.9</td><td>0.592</td><td>0.104</td></tr><tr><td>w/o multi-scale</td><td>20.4</td><td>87.1</td><td>0.628</td><td>0.095</td></tr><tr><td>w/o PRD</td><td>18.7</td><td>85.6</td><td>0.619</td><td>0.098</td></tr><tr><td>w/o condition</td><td>19.2</td><td>86.9</td><td>0.590</td><td>0.100</td></tr><tr><td>w/o dynamic filter</td><td>19.5</td><td>87.1</td><td>0.623</td><td>0.096</td></tr><tr><td>PointRefer</td><td>20.8</td><td>87.3</td><td>0.629</td><td>0.093</td></tr></table>",
+        "bbox": [
+            86,
+            104,
+            464,
+            239
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/0059e5e9abed1c1735ec3c0c0de6edbfdc697c4b25e56f290503c2482f64a20a.jpg",
+        "image_caption": [
+            "Figure 5. The bar chart shows the training sample distribution over different question lengths, and the line chart shows the performance of PointRefer grouped by question length."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            109,
+            244,
+            433,
+            407
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "decline on every metric, thus, validating the overall effectiveness of our design. Then, we also verify the functionality of AFM via the performance drop when it is removed (\"w/o AFM). As a comparison, a relatively slighter declination is witnessed when we only apply AFM at the single scale (\"w/o multi-scale\"), which indicates the benefit of multi-scale cross-modal fusion. Then, we conduct some detailed breakdown tests to study PRD, we notice that when the affordance queries are not conditioned on the question (\"w/o condition\") the performance drops drastically, indicating that our affordance queries help to capture semantic clues in 3D space. Finally, we validate the superiority of the dynamic filtering strategy, because a declination is also observed when the dynamic filter is erased (\"w/o dynamic filter\"), and this variant adopts IAGNet's [44] mask prediction strategy as an alternative.",
+        "bbox": [
+            75,
+            469,
+            468,
+            712
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Effect of Question Length. In Fig. 5, we show the performance of PointRefer on different question lengths. Specifically, The bar plot reveals the distribution of question length in the training set. Meanwhile, the line chart illustrates PointRefer's performance on different question lengths. Here, the performances are normalizing against the average number under that metric, e.g. IoU for each question length mIoU. Notably, PointRefer excels with questions that are more prevalent in the training set and with those that are lengthier—exceeding 14 words—owing to the richer contextual information they provide, which is instrumental in discerning the object's affordance.",
+        "bbox": [
+            75,
+            719,
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+            900
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/078425933709c631814008e073540023c5abcd8fed7395bd4362e95c58c7e601.jpg",
+        "image_caption": [
+            "Figure 6. Illustration of how the percentage of omitted samples affect transferability of affordance knowledge (indicated by the difference between seen and unseen). For each affordance type, the bar shows a number of omitted samples from seen, i.e.  $\\frac{\\# \\text{Seen} - \\# \\text{Unseen}}{\\# \\text{Seen}} (\\%)$ , and the lines show the testing IoU of models trained on Seen and Unseen. Difference (IoU): Seen - Unseen."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            527,
+            89,
+            861,
+            266
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/ef69cb8a8a45baf52e0ce3e91993bedc4dd179df47f74081bb20faab5285d120.jpg",
+        "table_caption": [
+            "Table 5. Study of Backbones. PN:PointNet++; PM:PointMLP."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>3D</td><td>LM</td><td>mIoU↑</td><td>AUC↑</td><td>SIM↑</td><td>MAE↓</td></tr><tr><td rowspan=\"6\">Seen</td><td rowspan=\"3\">PM [27]</td><td>Bert [8]</td><td>18.2</td><td>85.5</td><td>0.618</td><td>0.099</td></tr><tr><td>Deberta [11]</td><td>19.3</td><td>86.5</td><td>0.621</td><td>0.096</td></tr><tr><td>Roberta [23]</td><td>19.6</td><td>86.4</td><td>62.3</td><td>0.097</td></tr><tr><td rowspan=\"3\">PN [34]</td><td>Bert [8]</td><td>20.1</td><td>86.4</td><td>0.615</td><td>0.101</td></tr><tr><td>Deberta [11]</td><td>20.4</td><td>87.0</td><td>0.624</td><td>0.095</td></tr><tr><td>Roberta [23]</td><td>20.8</td><td>87.3</td><td>0.629</td><td>0.093</td></tr><tr><td rowspan=\"6\">Unseen</td><td rowspan=\"3\">PM [27]</td><td>Bert [8]</td><td>11.5</td><td>76.3</td><td>0.43</td><td>0.128</td></tr><tr><td>Deberta [11]</td><td>12.3</td><td>76.8</td><td>0.435</td><td>0.133</td></tr><tr><td>Roberta [23]</td><td>12.1</td><td>76.8</td><td>0.434</td><td>0.136</td></tr><tr><td rowspan=\"3\">PN [34]</td><td>Bert [8]</td><td>14.1</td><td>78.1</td><td>0.47</td><td>0.122</td></tr><tr><td>Deberta [11]</td><td>14.5</td><td>78.9</td><td>0.50</td><td>0.114</td></tr><tr><td>Roberta [23]</td><td>14.6</td><td>80.2</td><td>0.507</td><td>0.119</td></tr></table>",
+        "bbox": [
+            517,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Seen vs. Unseen. Recall that to create the training set for the unseen setting, for an affordance type, we omit its combination with certain objects from seen. For example, the seen partition has \"grasp-mug\", and \"grasp-bag\" in its training, we create the unseen training set by removing the \"grasp-mug\" from the seen training set. In this case, the model is expected to learn the generalizable affordance knowledge of \"grasp\" and transfer it to an unseen object during testing. Note that seen and unseen setting shares the same validation and testing set. To investigate how PointRefer captures such transferability for each affordance type, The bar in Fig. 6 shows the percentage of samples that are omitted from seen under each affordance type. Then, the lines show the performance of the model trained with seen and unseen partitions for each affordance type, and their difference—the indicator of transferability of learned affordance knowledge. In general, we notice that the curve of seen and unseen follows a similar pattern, which indicates that PointRefer can capture a similar affordance knowledge even trained with far less object class. However, we also notice that the difference between seen and unseen enlarges as the omitted percentage grows, regardless of the absolution IoU. This is expected since the removed object can lead to under-diversified affordance representation.",
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+            "Figure 7. Case-Study of PointRefer's segmentation. Each showcase comes with one question and four shapes, showing the generalization ability of the affordance knowledge. The segmented affordance part is highlighted in red."
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+        "text": "Choice of Backbone. To S backbone, we investigate the I with some alternative backbone that, for both seen and unseen as a 3D backbone generally pr than PointMLP, thus, we set 1 3D backbone. As for the lamance of Roberta prevails Ber setting. Whereas in the unseen and Roberta brings no signifca PointRefer uses Roberta as th",
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+        "text": "5.3. Qualitative Results",
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+        "text": "Case Study. As shown in Fig. 1, the capacity to accurately co- given the question. It is noteworthy",
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+        "text": "with small affordance components, such as the microwa door handle, our model still exhibits decent ability.",
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+            "Figure 8. Failure cases due to non-comprehended text (left) and over-segmentation (right)."
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+        "text": "6. Conclusion",
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+        "text": "In this paper, we have introduced the pioneering task of Language-guided Affordance Segmentation on 3D Objects (LASO), which establishes a vital connection between AI agents and Large Language Models (LLMs) via textual cues. Our contributions include the development of an extensive dataset consisting of 19,751 question-point pairs and the creation of PointRefer, a baseline model that lays the groundwork for the LASO task. We envisage that LASO will steer the trajectory of the 3D affordance field towards better integration with the advancements in LLMs.",
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+        "text": "7. Acknowledgments",
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+        "text": "This work is supported by the National Natural Science Foundation of China (92270114), the Agency for Science, Technology and Research (A\\*STAR) under MTC Programmatic Funds (Grant No.M23L7b0021), and NExT center.",
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+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
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2024/LASO_ Language-guided Affordance Segmentation on 3D Object/4a958b96-aed8-4e26-96c9-3b681d296992_model.json

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+            "content": "LASO: Language-guided Affordance Segmentation on 3D Object"
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+            "content": "Yicong Li\\(^{1}\\), Na Zhao\\(^{2*}\\), Junbin Xiao\\(^{1}\\), Chun Feng\\(^{3}\\), Xiang Wang\\(^{3*†}\\), Tat-seng Chua\\(^{1}\\),"
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+            "content": "\\(^{1}\\)National University of Singapore, \\(^{2}\\)Singapore University of Technology and Design, \\(^{3}\\)University of Science and Technology of China,"
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+            "content": "liyicong@u.nus.edu,na_zhao@sutd.edu.sg,junbin@comp.nus.edu.sg"
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+            "content": "fengchun3364@mail.ustc.edu.cn,xiangwangl223@gmail.com,dcstsc@nus.edu.sg"
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+        {
+            "type": "title",
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+            "bbox": [
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+            "content": "Segmenting affordance in 3D data is key for bridging perception and action in robots. Existing efforts mostly focus on the visual side and overlook the affordance knowledge from a semantic aspect. This oversight not only limits their generalization to unseen objects, but more importantly, hinders their synergy with large language models (LLMs) which are excellent task planners that can decompose an overarching command into agent-actionable instructions. With this regard, we propose a novel task, Language-guided Affordance Segmentation on 3D Object (LASO), which challenges a model to segment a 3D object's part relevant to a given affordance question. To facilitate the task, we contribute a dataset comprising 19,751 point-question pairs, covering 8434 object shapes and 870 expert-crafted questions. As a pioneer solution, we further propose PointRefer, which highlights an adaptive fusion module to identify target affordance regions at different scales. To ensure a text-aware segmentation, we adopt a set of affordance queries conditioned on linguistic cues to generate dynamic kernels. These kernels are further used to convolute with point features and generate a segmentation mask. Comprehensive experiments and analyses validate PointRefer's effectiveness. With these efforts, We hope that LASO can steer the direction of 3D affordance, guiding it towards enhanced integration with the evolving capabilities of LLMs. Code and data are available at https://github.com/y13800/LASO."
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+            "content": "1. Introduction"
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+            "content": "Affordance describes specific regions on an object that enable or facilitate certain human interactions. In this context,"
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+            "content": "Figure 1. Illustration of LASO, language-guided affordance segmentation on 3D object. Given an object point cloud and a question, the model is expected to segment the functional part delineated in question."
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+            "content": "the task of 3D affordance segmentation is raised to identify parts of 3D objects that imply a certain function. It has been deemed as a critical step in bridging perception and operation in the physical world for an embodied agent, thus has shown substantial impact on practical applications such as robotic manipulation [10, 14, 31]."
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+            "content": "Recently, the advancement of Large Language Models (LLMs) has enabled their deployment as task planners, breaking down an intricate instruction into a sequence of affordance-aware, robot-executable instructions [12, 35, 36]. This equips intelligent agents with the capability to undertake complex tasks. For example, the overarching command \"Pass me the mug in the microwave\" can be systematically deconstructed into a series of affordance-aware inquiries: Q1) \"How to get to the microwave?\", Q2) \"How to open the microwave\", Q3) \"How to grab the mug?\", and Q4) \"How to return to the user?\" Ideally, each query would correspond to a predefined subtask that effectively translates language instructions into actionable steps. While Q1 and Q4 are related to language-conditioned path planning [42] and navigation [37], Q2 and Q3, which involve the 'open microwave' and 'grab the mug' actions, ex"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.096,
+                0.863,
+                0.223,
+                0.876
+            ],
+            "angle": 0,
+            "content": "*Corresponding author."
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.096,
+                0.876,
+                0.468,
+                0.889
+            ],
+            "angle": 0,
+            "content": "\\(\\dagger\\) Xiang Wang is also affiliated with Institute of Artificial Intelligence,"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.079,
+                0.889,
+                0.449,
+                0.9
+            ],
+            "angle": 0,
+            "content": "Institute of Dataspace, Hefei Comprehensive National Science Center."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.079,
+                0.863,
+                0.468,
+                0.9
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.518,
+                0.957
+            ],
+            "angle": 0,
+            "content": "14251"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.092,
+                0.468,
+                0.122
+            ],
+            "angle": 0,
+            "content": "pose a gap — to the best of our knowledge, currently understanding affordance via language cues remains unexplored."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.124,
+                0.468,
+                0.275
+            ],
+            "angle": 0,
+            "content": "Leaving language cues untouched, current 3D affordance segmentation focuses primarily on the visual aspect. It associates the specific geo-structure with either explicit affordance categories [7] or implicit affordance information from the 2D showcase [44]. Such visual-only settings make the segmentation models confined to visually predefined affordance types, thus impeding integration with language-based instructions from LLMs. As a result, fulfilling the aforementioned user's request becomes challenging, due to this inability to address Q2 and Q3."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.277,
+                0.47,
+                0.609
+            ],
+            "angle": 0,
+            "content": "Towards these limitations, we introduce a novel task: Language-guided Affordance Segmentation on 3D Object (LASO), where 3D objects are paired with natural language questions that probe specific affordance parts. As a cornerstone task, LASO can provide an agent with affordance knowledge to answer the aforementioned Q2 and Q3 raised by LLM. For instance, the first two rows in Fig. 1 demonstrate how LASO imparts knowledge that enables an agent to interpret the semantic instructions \"open the microwave\" and \"grasp the mug\" in a 3D context, which are sufficient to execute Q2 and Q3, respectively. In LASO, questions are crafted to reflect diverse real-world scenarios, translating various affordance types into a range of semantic contexts. By learning from different contexts, we expect the agent not to memorize predefined affordance types but rather to abstract generalizable affordance knowledge within a broader semantic context. Notably, the diverse scales and shapes of affordance parts pose a significant perceptual challenge for the model. For instance, in the third row of Fig. 1, the target backrest of a chair occupies a large portion and has a significantly different shape compared to the small knob on a door in the last row."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.612,
+                0.468,
+                0.883
+            ],
+            "angle": 0,
+            "content": "To facilitate the study, we develop the 1st question-affordance dataset comprising 19,751 point cloud-question pairs. The questions, originally crafted by experts, are further diversified using GPT-4 [33] under principles of contextual enrichment, concise phrasing, and structural diversity. These principles enable a deep and varied exploration of object affordances. Based on the dataset, we have developed a strong baseline model named PointRefer that is capable of adapting to varying scales and shapes of object parts, conditioned on the question. It consists of two modules: 1) an Adaptive Fusion Module (AFM) that integrates question semantics to point features at different scales, which caters to varied target regions with better point feature discriminativeness; and 2) a Referred Point Decoder (RPD) that generates a segmentation mask via conditioned affordance queries, which, after refinement, forms dynamic convolution kernels to capture point-wise affordance for mask prediction. In summary, our contributions are as follows:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.078,
+                0.886,
+                0.468,
+                0.902
+            ],
+            "angle": 0,
+            "content": "- We propose the task of Language-guided Affordance Seg"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.5,
+                0.09,
+                0.892,
+                0.118
+            ],
+            "angle": 0,
+            "content": "Table 1. Efforts on affordance learning. Part indicates whether the prediction specifies the object part (✓) or the whole object \\((\\times)\\)."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.521,
+                0.121,
+                0.876,
+                0.224
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Domain</td><td>Studies</td><td>Vision</td><td>Text</td><td>Part</td></tr><tr><td rowspan=\"3\">2D</td><td>[1, 46]</td><td>Image</td><td>×</td><td>×</td></tr><tr><td>[9, 25, 32]</td><td>Image/Video</td><td>×</td><td>✓</td></tr><tr><td>[24, 29]</td><td>Image</td><td>✓</td><td>×</td></tr><tr><td rowspan=\"3\">3D</td><td>[7, 30, 30, 43]</td><td>Point Cloud</td><td>×</td><td>✓</td></tr><tr><td>[44]</td><td>Point Cloud &amp; Image</td><td>×</td><td>✓</td></tr><tr><td>Ours</td><td>Point Cloud</td><td>✓</td><td>✓</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.233,
+                0.892,
+                0.278
+            ],
+            "angle": 0,
+            "content": "mentation on 3D Objects (LASO), which helps AI agents derive affordance knowledge from textual cues, facilitating a crucial advancement for LLM integration."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.279,
+                0.891,
+                0.338
+            ],
+            "angle": 0,
+            "content": "- We develop a dataset with 19,751 question-point affordance pairs which are meticulously curated via a collaborative effort of human experts and GPT-4, thereby establishing the 1st benchmark for evaluating LASO."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.339,
+                0.892,
+                0.399
+            ],
+            "angle": 0,
+            "content": "- We build a strong baseline PointRefer, which employs textual-conditioned affordance queries to isolate afforded segments and devises an adaptive fusion module to enhance the discriminability of point feature."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.5,
+                0.279,
+                0.892,
+                0.399
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.408,
+                0.642,
+                0.423
+            ],
+            "angle": 0,
+            "content": "2. Related Work"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.425,
+                0.892,
+                0.56
+            ],
+            "angle": 0,
+            "content": "Affordance Learning. Originating from the image domain, initial efforts concentrate on detecting objects with affordances [1, 46]. Progressing from there, later studies [24, 29] incorporate linguistic descriptions to augment the process but still neglect the granularity of analysis, generally focusing on object-level affordances. Addressing this oversight, subsequent research [9, 25, 32] shift towards scrutinizing specific affordance parts, establishing a new norm for precision in the field."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.563,
+                0.892,
+                0.835
+            ],
+            "angle": 0,
+            "content": "With the rise of embodied AI, the scope of affordance learning expands into the 3D realm. 3D AffordanceNet [7] introduces the first benchmark dataset for learning affordance from object point cloud geometry. Building on this, Yang et al. [44] propose a setting for learning 3D affordance parts guided by image demonstrations. Nonetheless, these approaches predominantly rely on a visual-only approach, tightly coupling geometric features with affordance labels and overlooking the semantic dimension. This limitation hinders the integration with Large Language Models (LLMs) that could otherwise substantiate affordance segmentation to real-world deployment. Moreover, the common practice of predicting affordance types as an auxiliary task [7, 44] may dilute the primary challenge of understanding affordance knowledge. In contrast, our work sidesteps auxiliary predictions, advocating for direct learning from the linguistic context, which aligns more closely with the innate capabilities of LLMs and their semantic richness."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.84,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Text-Point Cloud Cross-Modal Learning. The integration of vision and natural language has recently sparked increased interest [16-21, 41]. Such a tendency naturally extends to 3D vision due to its pivotal role in embodied AI. To"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
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+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "14252"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.1,
+                0.09,
+                0.447,
+                0.235
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.101,
+                0.241,
+                0.444,
+                0.255
+            ],
+            "angle": 0,
+            "content": "Figure 2. Illustration of question augmentation principles."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.263,
+                0.473,
+                0.536
+            ],
+            "angle": 0,
+            "content": "advance the 3D-language tasks, datasets like ScanRefer [5] and ReferIt3D [2] have been instrumental in benchmarking the grounding of natural language to 3D objects. Complementing this, Azuma et al. [3] introduce ScanQA for 3D question-answering, while Ma et al. [28] propose SQA3D for situated reasoning within 3D environments. In terms of models, a variety of efforts [3, 13, 45] have emerged from these benchmarks, with notable examples like 3D-SPS [26] and BUTD-DETR [13] employing cross-attention mechanisms and linguistic cues for object discovery. Others, such as 3DVG [45], and ViL3DRel [6], focus on 3D grounding by incorporating spatial relation cues, showcasing the evolving landscape of 3D-VL models. Unlike the existing work that focuses on grounding and QA that perform scene-level reasoning, we tackle a dense prediction task at object part level that bridges reasoning to operation. To the best of our knowledge, we are the first to introduce the 3D affordance problem as a language-guided segmentation task."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.544,
+                0.166,
+                0.558
+            ],
+            "angle": 0,
+            "content": "3. Dataset"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.561,
+                0.47,
+                0.637
+            ],
+            "angle": 0,
+            "content": "To underpin our proposed task, we have meticulously compiled a question-point affordance dataset with 19,751 paired samples, featuring 8,434 distinct object shapes across 23 classes. Accompanying these are 870 expertly crafted questions, covering 17 affordance categories."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.646,
+                0.258,
+                0.66
+            ],
+            "angle": 0,
+            "content": "3.1. Annotation Details"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.67,
+                0.47,
+                0.806
+            ],
+            "angle": 0,
+            "content": "Point Cloud. Our dataset leverages the point cloud and affordance annotations from the 3D-AffordanceNet [7]. Specifically, the affordance annotation in [7] is multi-class, with each point on an object potentially supporting multiple affordance types. In our case, each question is tailored to a specific affordance type, while each sample can associate with several questions. Consequently, the same object can exhibit diverse affordance segmentation, depending on the specific question posed."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.811,
+                0.471,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Question. To create the questions, we draw 58 object-affordance combinations from [7], and craft 15 unique questions for each of the 58 combinations, resulting in 870 tailored questions. Specifically, five manual questions per combination are initially composed to represent different scenarios. Subsequently, we employ GPT-4 [33] to diver"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.618,
+                0.09,
+                0.774,
+                0.102
+            ],
+            "angle": 0,
+            "content": "Table 2. Dataset Statistics"
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.507,
+                0.107,
+                0.89,
+                0.167
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Task</td><td colspan=\"3\">Train</td><td colspan=\"3\">Val</td><td colspan=\"3\">Test</td></tr><tr><td>Shape</td><td>Qst</td><td>Inst</td><td>Shape</td><td>Qst</td><td>Inst</td><td>Shape</td><td>Qst</td><td>Inst</td></tr><tr><td>Seen</td><td>6883</td><td>638</td><td>16120</td><td rowspan=\"2\">516</td><td rowspan=\"2\">58</td><td rowspan=\"2\">1215</td><td rowspan=\"2\">1035</td><td rowspan=\"2\">174</td><td rowspan=\"2\">2416</td></tr><tr><td>Unseen</td><td>6160</td><td>458</td><td>11558</td></tr></table>"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.503,
+                0.175,
+                0.889,
+                0.316
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.589,
+                0.318,
+                0.802,
+                0.332
+            ],
+            "angle": 0,
+            "content": "Figure 3. Landscape of our dataset."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.334,
+                0.892,
+                0.576
+            ],
+            "angle": 0,
+            "content": "sify the dataset with 10 additional questions for each combination, adhering to three key principles (as shown in Fig. 2): 1) Contextual Enrichment. Some questions were expanded to include additional context or details, fostering a more precise connection to the specified affordance of the target object. For instance, Q1 in Fig. 2 is reformed by a functional situation \"cutting paper\". 2) Concise Phrasing. In other cases, questions were distilled to their essence, making them succinct yet still meaningful. Q2 in Fig. 2 exemplifies this approach. 3) Structural Diversity. We employed a range of sentence structures, from questions to statements, to introduce natural linguistic variations and prevent model bias toward any specific phrasing or sentence length. A diversified example can be found in the Q3 of Fig. 2. All questions generated by GPT-4 undergo manual verification after this augmentation process."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.577,
+                0.892,
+                0.682
+            ],
+            "angle": 0,
+            "content": "It's worth mentioning that the affordance type was only a tool for crafting the questions and pinpointing the correct segmentation areas. We refrain from using explicit affordance labels during both training and testing. This deliberate choice ensures that the learning process is driven by the semantic content of the questions, rather than by direct affordance label association."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.696,
+                0.698,
+                0.712
+            ],
+            "angle": 0,
+            "content": "3.2. Statistics and Setting"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.72,
+                0.892,
+                0.779
+            ],
+            "angle": 0,
+            "content": "Dataset Settings. We show the statistical landscape of our dataset in Fig. 3. Specifically, it contains 17 affordance types and 23 object categories, composing 58 unique object-affordance combinations."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.781,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "In the spirit of the work by [44], we offer two distinct dataset settings: Seen: The default configuration, where the training and testing phases share similar distributions of object classes and affordance types. Unseen: This configuration is purpose-built to test the model's ability to generalize affordance knowledge. Certain affordance types, when paired with specific object classes, are omitted from the training set but included in the test set. For instance, while"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "14253"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.468,
+                0.167
+            ],
+            "angle": 0,
+            "content": "the model may learn to grasp bags and mugs during training, it is expected to apply the concept of 'grasp' to earphones, which is an affordance-object pairing not encountered during training. For a comprehensive account of the unseen setting, please refer to Appendix Sec. 7.1."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.168,
+                0.47,
+                0.409
+            ],
+            "angle": 0,
+            "content": "Training and Evaluation Protocols. Notably, since questions are created based on a combination of object class and affordance type, one object class can have many shape instances. Thus, the design of our dataset accounts for the multiplicity of shapes within each object class, leading to a non-bijective pairing between shape instances and corresponding questions. To ensure comprehensive learning, during training, each shape instance is matched with a randomly selected question that aligns with its affordance type for every iteration. This random pairing exposes the model to a variety of semantic contexts, bolstering its ability to generalize. For the validation and test sets, question pairings are fixed to minimize variability and ensure consistent inference. These questions are unique to the evaluation phase and are not revealed during the training process to maintain the integrity of the evaluation."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.411,
+                0.168,
+                0.426
+            ],
+            "angle": 0,
+            "content": "4. Method"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.437,
+                0.47,
+                0.498
+            ],
+            "angle": 0,
+            "content": "LASO Task Definition. Given a question \\( Q_{raw} \\) and an object point cloud \\( \\mathbf{P}_{raw} \\in \\mathbb{R}^{N \\times 3} \\) with \\( N \\) points, the goal of LASO is to predict a binary mask of \\( \\mathbf{M} \\in \\mathbb{R}^N \\) that segments the functional part related to the question."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.503,
+                0.47,
+                0.82
+            ],
+            "angle": 0,
+            "content": "Framework Overview. Due to the varying scale of target affordance region, LASO naturally challenges models adaptiveness at different scales. To address this, we devise a strong baseline, named PointRefer. As shown in Fig. 4, the object point cloud \\(\\mathbf{P}_{raw}\\) is first processed by a 3D backbone, which typically consists of the multi-stage encoding and decoding process. To adapt PointRefer to the point feature at multiple scales, we introduce an Adaptive Fusion Module (AFM) to the backbone's decoding process. It performs multi-scale cross-modal fusion by injecting text clues to point features at a different decoding stage, which progressively refine the point feature map in a top-down manner. Then, to predict the segmentation mask, we introduce a Referred Point Decoder (RPD) that leverages a set of learnable queries conditioned on the input question, termed affordance queries, as the input of the transformer decoder. These affordance queries are obligated to look at the referred points only and generate question-aware dynamic kernels. The final segmentation mask is obtained by convoluting these dynamic kernels with the AFM-enhanced point feature."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.825,
+                0.468,
+                0.9
+            ],
+            "angle": 0,
+            "content": "Feature Encoding. For the question, we prepend a \"[CLS]\" token to the question sequence before feeding them to a language model to capture the global language context. The encoded feature of the question is denoted by \\(\\mathbf{X} \\in \\mathbb{R}^{L \\times d}\\), where \\(L\\) is the number of tokens and \\(d\\) is the feature di"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.183
+            ],
+            "angle": 0,
+            "content": "mension. For the point cloud, PointRefer can adopt any off-the-shelf 3D segmentation backbone.<sup>1</sup> to transform the \\(\\mathbf{P}_{raw}\\) into the feature space. Note that a 3D backbone for segmentation typically consists of several encoding and decoding stages, and we take the point-wise feature map after the last decoding stage as the output of the backbone."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.192,
+                0.727,
+                0.208
+            ],
+            "angle": 0,
+            "content": "4.1. Adaptive Fusion Module"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.215,
+                0.892,
+                0.35
+            ],
+            "angle": 0,
+            "content": "AFM is designed to enhance the point-wise features by incorporating question information. As illustrated in Fig. 4, we integrate AFM into different decoder layers to enhance its adaptiveness to target regions of various scales and shapes. Given the conventional downsampling operators in 3D backbones (e.g. PointNet++ [34]), the number of points varies across different encoder/decoder layers. Our AFM is designed to seamlessly adapt to the varying number of points."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.351,
+                0.892,
+                0.532
+            ],
+            "angle": 0,
+            "content": "For simplification, we omit the notation for different decoder layers and use \\(\\mathbf{P} \\in \\mathbb{R}^{T \\times d}\\) to denote the point feature at a certain decoding layer, where \\(T\\) represents the number of points at that layer. As visualized in Fig. 4, AFM adopts a bottleneck architecture with three key steps: Grouping, Mixing, and Ungrouping. In the grouping step, the point features are grouped by text tokens, these grouped tokens are then thoroughly mixed via an MLP-Mixer [38]. Subsequently, the ungrouping step encapsulates the mixed features into individual point features, completing the AFM procedure by embedding valuable textual information into the point feature."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.532,
+                0.892,
+                0.607
+            ],
+            "angle": 0,
+            "content": "To facilitate an efficient grouping process for our AFM, we employ a lightweight cross-attention module by omitting the transformation of both query and value. It takes the question feature \\(\\mathbf{X}\\) as query and the point feature \\(\\mathbf{P}\\) as key and value, then output grouped token \\(\\mathbf{G} \\in \\mathbb{R}^{L \\times d}\\):"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.584,
+                0.619,
+                0.891,
+                0.636
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbf {G} = \\operatorname {A t t e n t i o n} \\left(\\mathbf {X}, \\mathbf {W} _ {1} \\mathbf {P}, \\mathbf {P}\\right) + \\mathbf {X}, \\tag {1}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.55,
+                0.639,
+                0.892,
+                0.674
+            ],
+            "angle": 0,
+            "content": "\\[\n\\operatorname {A t t e n t i o n} (\\mathbf {Q}, \\mathbf {K}, \\mathbf {V}) = \\operatorname {S o f t m a x} \\left(\\frac {\\mathbf {Q} \\mathbf {K} ^ {T}}{\\sqrt {d}}\\right) \\mathbf {V}, \\tag {2}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.684,
+                0.744,
+                0.698
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathbf{W}_1\\) is a linear transformation."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.699,
+                0.892,
+                0.759
+            ],
+            "angle": 0,
+            "content": "After attaining the grouped feature, we update them using an MLP-Mixer [38], which employs two consecutive multilayer perceptrons (MLPs), producing fused feature \\(\\mathbf{F}\\) by combining with two consecutive MLPs."
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.612,
+                0.769,
+                0.891,
+                0.787
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbf {G} ^ {\\prime} = \\mathbf {G} + \\operatorname {M L P} _ {1} \\left(\\mathbf {G} ^ {T}\\right) ^ {T}, \\tag {3}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.622,
+                0.789,
+                0.891,
+                0.807
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbf {F} = \\mathbf {G} ^ {\\prime} + \\mathrm {M L P} _ {2} \\left(\\mathbf {G} ^ {\\prime}\\right), \\tag {4}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.818,
+                0.892,
+                0.879
+            ],
+            "angle": 0,
+            "content": "where, \\(\\mathrm{MLP}_1\\) and \\(\\mathrm{MLP}_2\\) are used to mix group-wise and channel-wise information, respectively, and \\(T[\\cdot]\\) denotes the transpose operation. Finally, we return the fused feature \\(\\mathbf{F}\\) to the point-space via the ungrouping process and"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.518,
+                0.887,
+                0.836,
+                0.9
+            ],
+            "angle": 0,
+            "content": "1The impact of backbone choices can be observed in Tab. 5."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "14254"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.082,
+                0.089,
+                0.635,
+                0.354
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.274,
+                0.356,
+                0.438,
+                0.368
+            ],
+            "angle": 0,
+            "content": "(a) Overview of PointRefer."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.679,
+                0.094,
+                0.895,
+                0.35
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.678,
+                0.351,
+                0.848,
+                0.365
+            ],
+            "angle": 0,
+            "content": "(b) Adaptive Fusion Module."
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.075,
+                0.369,
+                0.892,
+                0.44
+            ],
+            "angle": 0,
+            "content": "Figure 4. The overall framework of our proposed PointRefer (a), which contains an adaptive fusion modal (b) that can be injected in different stages of the backbone decoder. As a result, it takes the point-wise feature generated at the last decoder layer as the final output of the 3D backbone. Then, the Referred Point Decoder takes in a set of question-conditioned affordance queries and feeds it to a transformer decoder together with the fused point feature, where the output is then reformed to a set of dynamic kernels. Finally, these dynamic kernels are used as convolution kernels to filter out the segmentation mask from the fused point feature."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.447,
+                0.47,
+                0.507
+            ],
+            "angle": 0,
+            "content": "acquire the fused point feature \\(\\mathbf{P}^m\\). We implement the ungrouping process as a similar lightweight attention module as the grouping process. However, in this case, it takes \\(\\mathbf{P}\\) as query and \\(\\mathbf{F}\\) as key and value:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.158,
+                0.519,
+                0.469,
+                0.535
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbf {P} ^ {m} = \\operatorname {A t t e n t i o n} (\\mathbf {P}, \\mathbf {W} _ {2} \\mathbf {F}, \\mathbf {F}) + \\mathbf {P}, \\tag {5}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.548,
+                0.469,
+                0.607
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathbf{W}_2\\) is a linear transformation. Lastly, the final output \\(\\mathbf{P}^o\\) is formed by adding residual connections to \\(\\mathbf{P}^m\\). Notably, we take \\(\\mathbf{P}^o\\) after the last decoding stage as the output of the 3D backbone."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.618,
+                0.295,
+                0.632
+            ],
+            "angle": 0,
+            "content": "4.2. Referred Point Decoder"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.64,
+                0.469,
+                0.806
+            ],
+            "angle": 0,
+            "content": "Inspired by the success of learnable query-based methods in object detection [4] and segmentation [40], we introduce learnable affordance queries conditioned on the corresponding question of an object to decode the segmentation mask for the object. Specifically, we impose linguistic restrictions on all affordance queries, narrowing the model's focus to the relevant object parts and thereby facilitating convergence. These affordance queries, after being processed by a transformer decoder, are repurposed as dynamic kernels to deduce the segmentation mask from the point features, which are the final output of the 3D backbone."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.811,
+                0.469,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Question-Conditioned Affordance Query In the transformer decoder, it is well known that content and position embeddings are responsible for encoding instance-specific and spatial information, respectively. In PointRefer, we feed these two parts with the text feature and learnable query parameters, respectively, so that all the queries are"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.447,
+                0.891,
+                0.507
+            ],
+            "angle": 0,
+            "content": "shaped by the nuances of the linguistic input. Specifically, the affordance queries \\(\\mathbf{A}\\) are formed by adding question embedding \\(\\mathbf{X}\\) with learnable embeddings. Thus, the resulting \\(\\mathbf{A} \\in \\mathbb{R}^{L \\times d}\\) are the same length of the question."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.511,
+                0.892,
+                0.602
+            ],
+            "angle": 0,
+            "content": "Reasoning and Mask Prediction. After forming the affordance query, we feed it to a transformer decoder [39] together with the fused point feature \\(\\mathbf{P}_o\\) from the 3D backbone. In this manner, all the queries will use the question context as guidance and target to aggregate the feature of the referred points from the object, resulting in \\(\\mathbf{A}'\\):"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.577,
+                0.614,
+                0.891,
+                0.631
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbf {A} ^ {\\prime} = \\text {T r a n s f o r m e r - D e c o d e r} (\\mathbf {A}; \\mathbf {P} _ {o}). \\tag {6}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.643,
+                0.891,
+                0.716
+            ],
+            "angle": 0,
+            "content": "Subsequently, we perform dynamic convolution by applying a two-layer MLP on top of the transfer decoder to produce \\(L\\) dynamic kernels \\(\\Omega = \\{\\omega_{i}\\}_{i = 1}^{L}\\), where each kernel \\(\\omega_{i}\\) is reshaped to a \\(1\\times 1\\) convolutional kernel with the channel number of \\(d\\)."
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.643,
+                0.73,
+                0.891,
+                0.746
+            ],
+            "angle": 0,
+            "content": "\\[\n\\Omega = \\operatorname {M L P} \\left(\\mathbf {A} ^ {\\prime}\\right). \\tag {7}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.759,
+                0.891,
+                0.835
+            ],
+            "angle": 0,
+            "content": "Since the dynamic kernels have captured the question- information, we use them as convolution filters on the feature maps for mask decoding. Specifically, we use each dynamic kernel in \\(\\Omega\\) to convolute the point-wise feature map \\(\\mathbf{P}_o\\), which returns \\(L\\) point masks \\(\\mathbf{S} = \\{\\mathbf{s}_i\\}_{i=1}^L\\)."
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.627,
+                0.84,
+                0.891,
+                0.86
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbf {S} _ {i} = \\left\\{\\mathbf {P} _ {o} * \\omega_ {i} \\right\\} _ {i = 1} ^ {L}. \\tag {8}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.871,
+                0.891,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Then, we apply mean pooling over all masks in \\(\\mathbf{S}\\) followed by a sigmoid activation to acquire the final segmentation"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.518,
+                0.957
+            ],
+            "angle": 0,
+            "content": "14255"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.078,
+                0.091,
+                0.182,
+                0.105
+            ],
+            "angle": 0,
+            "content": "mask \\(\\mathbf{M}\\in \\mathbb{R}^N\\) .."
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.188,
+                0.114,
+                0.469,
+                0.13
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbf {M} = \\sigma (\\operatorname {M a x - P o o l} ((\\mathbf {S}))), \\tag {9}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.078,
+                0.138,
+                0.345,
+                0.152
+            ],
+            "angle": 0,
+            "content": "where \\(\\sigma (\\cdot)\\) denote the sigmoid function."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.153,
+                0.469,
+                0.228
+            ],
+            "angle": 0,
+            "content": "Intuitively, each dynamic kernel is expected to capture one aspect of the referred object part according to conditioned the question token. By ensembling all generated point masks, the final segmentation mask can integrate different response regions, thus making the result more robust."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.23,
+                0.469,
+                0.321
+            ],
+            "angle": 0,
+            "content": "Objectives. Unlike [44], which relies on an auxiliary affordance label for prediction, our model seeks to forge a direct link between language context and object affordance. Thus, we solely employ Dice loss and Binary Cross-Entropy (BCE) loss to guide the segmentation mask prediction, bypassing the need for additional affordance labels."
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.202,
+                0.324,
+                0.469,
+                0.339
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {B C E} + \\mathcal {L} _ {D i c e} \\tag {10}\n\\]"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.333,
+                0.201,
+                0.35
+            ],
+            "angle": 0,
+            "content": "5. Experiment"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.358,
+                0.469,
+                0.464
+            ],
+            "angle": 0,
+            "content": "Evaluation Metrics. For a thorough assessment, we benchmark our dataset against leading studies in 3D affordance learning [7, 44], employing four evaluation metrics to ensure robust analysis. These include Area Under the Curve (AUC), Mean Intersection Over Union (mIoU), Similarity (SIM), and Mean Absolute Error (MAE). Appendix Sec. 7.2 provides detailed explanations for the evaluation protocols."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.466,
+                0.469,
+                0.557
+            ],
+            "angle": 0,
+            "content": "Implementation Details. PointRefer employs PointNet++ as the default 3D backbone to align with the standards established in [7, 44]. For text encoding, we utilize a pretrained RoBERTa model [23] to process linguistic inputs. The feature dimension \\( d \\) is set to 512. During training, we use the Adam optimizer with a learning rate set to 1e-4."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.56,
+                0.469,
+                0.801
+            ],
+            "angle": 0,
+            "content": "Baseline Models. Since there is no prior work using paired question-point cloud data to segment object affordance. For a thorough comparison of our method, we adopt two 3D cross-modal works (3D-SPS [26] and IAGNet[44]) and two referred image segmentation works (ReferTrans [15] and RelA [22]) to LASO task. For the referred image segmentation models, we substitute their image backbones with a 3D counterpart, retaining their fusion mechanisms and mask decoding strategies. For the language-guided grounding model, 3D-SPS [26], we omit its bounding box prediction module while leveraging its inherent point selection scheme for our segmentation setting. The most related work is IAGNet [44], an affordance detection method that takes paired image-point cloud as input. To adapt IAGNet to our needs, we simply replace its image backbone with a language model, preserving the remainder of its architecture."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.808,
+                0.469,
+                0.837
+            ],
+            "angle": 0,
+            "content": "Next, we show the effectiveness of our PointRefer by answering the following questions:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.078,
+                0.838,
+                0.468,
+                0.867
+            ],
+            "angle": 0,
+            "content": "- Q1: How is PointRefer compared to other baselines on the proposed dataset?"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.078,
+                0.868,
+                0.422,
+                0.883
+            ],
+            "angle": 0,
+            "content": "- Q2: How effective are the proposed components?"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.078,
+                0.884,
+                0.462,
+                0.898
+            ],
+            "angle": 0,
+            "content": "- Q3: What learning pattern does the PointRefer capture?"
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.078,
+                0.838,
+                0.468,
+                0.898
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.499,
+                0.09,
+                0.892,
+                0.132
+            ],
+            "angle": 0,
+            "content": "Table 3. Main Results. The overall results of all comparative methods, the best results are in bold. Seen and Unseen are two partitions of the dataset. AUC and aIOU are shown in percentage."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.518,
+                0.135,
+                0.88,
+                0.297
+            ],
+            "angle": 0,
+            "content": "<table><tr><td></td><td>Method</td><td>mIoU↑</td><td>AUC↑</td><td>SIM↑</td><td>MAE↓</td></tr><tr><td rowspan=\"5\">Steen</td><td>ReferTrans [15]</td><td>13.7</td><td>79.8</td><td>0.497</td><td>0.124</td></tr><tr><td>ReLA [22]</td><td>15.2</td><td>78.9</td><td>0.532</td><td>0.118</td></tr><tr><td>3D-SPS [26]</td><td>11.4</td><td>76.2</td><td>0.433</td><td>0.138</td></tr><tr><td>IAGNet [44]</td><td>17.8</td><td>82.3</td><td>0.561</td><td>0.109</td></tr><tr><td>PointRefer</td><td>20.8</td><td>87.3</td><td>0.629</td><td>0.093</td></tr><tr><td rowspan=\"5\">Unseen</td><td>ReferTrans [15]</td><td>10.2</td><td>69.1</td><td>0.432</td><td>0.145</td></tr><tr><td>ReLA [22]</td><td>10.7</td><td>69.7</td><td>0.429</td><td>0.144</td></tr><tr><td>3D-SPS [26]</td><td>7.9</td><td>68.8</td><td>0.402</td><td>0.158</td></tr><tr><td>IAGNet [44]</td><td>12.9</td><td>77.8</td><td>0.443</td><td>0.129</td></tr><tr><td>PointRefer</td><td>14.6</td><td>80.2</td><td>0.507</td><td>0.119</td></tr></table>"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.31,
+                0.671,
+                0.326
+            ],
+            "angle": 0,
+            "content": "5.1. Main Result (Q1)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.333,
+                0.892,
+                0.378
+            ],
+            "angle": 0,
+            "content": "In Table 3, PointRefer demonstrates superior performance across all evaluation metrics compared to the baseline methods. Our observations are as follows:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.382,
+                0.892,
+                0.609
+            ],
+            "angle": 0,
+            "content": "PointRefer vs. Other Models: IAGNet secures the second-best performance in both seen and unseen settings for all metrics. This is likely due to its specific design for object affordance segmentation, despite differences in input modality, making it a strong fit for our task with minimal adaptation. In contrast, 3D-SPS underperforms, potentially due to its progressive point selection mechanism. This approach involves a non-differentiable selection process, which may complicate the optimization within our task framework. Image-based methods, while showing decent performance, appear to be constrained by the modality gap. Originally trained on vast datasets of image-text pairs, where text is often a brief label, these methods now face fully formed, context-rich questions with a more limited training corpus."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.612,
+                0.892,
+                0.748
+            ],
+            "angle": 0,
+            "content": "Seen vs. Unseen Performance: A notable performance drop from seen to unseen settings is observed across all baselines. This discrepancy underscores the difficulty in learning affordance knowledge that generalizes well, corroborating the necessity of our task design. Current methods struggle to bridge this gap in knowledge transfer, suggesting an avenue for future research: utilizing the extensive commonsense knowledge embedded in LLMs could potentially mitigate this challenge."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.757,
+                0.695,
+                0.773
+            ],
+            "angle": 0,
+            "content": "5.2. In-Depth Study (Q2)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.78,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Ablation Study. We show ablative results in Tab. 4. To verify that PointRefer prediction is based on the question, we conduct a blind test by training without questioning information, where the distinctive performance gap indicates that PointRefer has comprehended the question and can make a prediction based on it. Then, we study the effectiveness of PointRefer by removing both AFM and PRD (\"w/o AFM & PRD\"), which induces a severe performance"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "14256"
+        }
+    ],
+    [
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.195,
+                0.09,
+                0.352,
+                0.102
+            ],
+            "angle": 0,
+            "content": "Table 4. Ablative Results."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.088,
+                0.106,
+                0.465,
+                0.24
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Variants</td><td>mIoU↑</td><td>AUC↑</td><td>SIM↑</td><td>MAE↓</td></tr><tr><td>Blind</td><td>10.8</td><td>78.2</td><td>0.506</td><td>0.125</td></tr><tr><td>w/o AFM &amp; PRD</td><td>17.7</td><td>82.1</td><td>0.558</td><td>0.110</td></tr><tr><td>w/o AFM</td><td>19.8</td><td>83.9</td><td>0.592</td><td>0.104</td></tr><tr><td>w/o multi-scale</td><td>20.4</td><td>87.1</td><td>0.628</td><td>0.095</td></tr><tr><td>w/o PRD</td><td>18.7</td><td>85.6</td><td>0.619</td><td>0.098</td></tr><tr><td>w/o condition</td><td>19.2</td><td>86.9</td><td>0.590</td><td>0.100</td></tr><tr><td>w/o dynamic filter</td><td>19.5</td><td>87.1</td><td>0.623</td><td>0.096</td></tr><tr><td>PointRefer</td><td>20.8</td><td>87.3</td><td>0.629</td><td>0.093</td></tr></table>"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.11,
+                0.246,
+                0.434,
+                0.408
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.416,
+                0.47,
+                0.459
+            ],
+            "angle": 0,
+            "content": "Figure 5. The bar chart shows the training sample distribution over different question lengths, and the line chart shows the performance of PointRefer grouped by question length."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.47,
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+            "angle": 0,
+            "content": "decline on every metric, thus, validating the overall effectiveness of our design. Then, we also verify the functionality of AFM via the performance drop when it is removed (\"w/o AFM). As a comparison, a relatively slighter declination is witnessed when we only apply AFM at the single scale (\"w/o multi-scale\"), which indicates the benefit of multi-scale cross-modal fusion. Then, we conduct some detailed breakdown tests to study PRD, we notice that when the affordance queries are not conditioned on the question (\"w/o condition\") the performance drops drastically, indicating that our affordance queries help to capture semantic clues in 3D space. Finally, we validate the superiority of the dynamic filtering strategy, because a declination is also observed when the dynamic filter is erased (\"w/o dynamic filter\"), and this variant adopts IAGNet's [44] mask prediction strategy as an alternative."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.72,
+                0.468,
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+            "angle": 0,
+            "content": "Effect of Question Length. In Fig. 5, we show the performance of PointRefer on different question lengths. Specifically, The bar plot reveals the distribution of question length in the training set. Meanwhile, the line chart illustrates PointRefer's performance on different question lengths. Here, the performances are normalizing against the average number under that metric, e.g. IoU for each question length mIoU. Notably, PointRefer excels with questions that are more prevalent in the training set and with those that are lengthier—exceeding 14 words—owing to the richer contextual information they provide, which is instrumental in discerning the object's affordance."
+        },
+        {
+            "type": "image",
+            "bbox": [
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+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
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+            "angle": 0,
+            "content": "Figure 6. Illustration of how the percentage of omitted samples affect transferability of affordance knowledge (indicated by the difference between seen and unseen). For each affordance type, the bar shows a number of omitted samples from seen, i.e. \\(\\frac{\\# \\text{Seen} - \\# \\text{Unseen}}{\\# \\text{Seen}} (\\%)\\), and the lines show the testing IoU of models trained on Seen and Unseen. Difference (IoU): Seen - Unseen."
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
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+            "angle": 0,
+            "content": "Table 5. Study of Backbones. PN:PointNet++; PM:PointMLP."
+        },
+        {
+            "type": "table",
+            "bbox": [
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+            "content": "<table><tr><td></td><td>3D</td><td>LM</td><td>mIoU↑</td><td>AUC↑</td><td>SIM↑</td><td>MAE↓</td></tr><tr><td rowspan=\"6\">Seen</td><td rowspan=\"3\">PM [27]</td><td>Bert [8]</td><td>18.2</td><td>85.5</td><td>0.618</td><td>0.099</td></tr><tr><td>Deberta [11]</td><td>19.3</td><td>86.5</td><td>0.621</td><td>0.096</td></tr><tr><td>Roberta [23]</td><td>19.6</td><td>86.4</td><td>62.3</td><td>0.097</td></tr><tr><td rowspan=\"3\">PN [34]</td><td>Bert [8]</td><td>20.1</td><td>86.4</td><td>0.615</td><td>0.101</td></tr><tr><td>Deberta [11]</td><td>20.4</td><td>87.0</td><td>0.624</td><td>0.095</td></tr><tr><td>Roberta [23]</td><td>20.8</td><td>87.3</td><td>0.629</td><td>0.093</td></tr><tr><td rowspan=\"6\">Unseen</td><td rowspan=\"3\">PM [27]</td><td>Bert [8]</td><td>11.5</td><td>76.3</td><td>0.43</td><td>0.128</td></tr><tr><td>Deberta [11]</td><td>12.3</td><td>76.8</td><td>0.435</td><td>0.133</td></tr><tr><td>Roberta [23]</td><td>12.1</td><td>76.8</td><td>0.434</td><td>0.136</td></tr><tr><td rowspan=\"3\">PN [34]</td><td>Bert [8]</td><td>14.1</td><td>78.1</td><td>0.47</td><td>0.122</td></tr><tr><td>Deberta [11]</td><td>14.5</td><td>78.9</td><td>0.50</td><td>0.114</td></tr><tr><td>Roberta [23]</td><td>14.6</td><td>80.2</td><td>0.507</td><td>0.119</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.539,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Seen vs. Unseen. Recall that to create the training set for the unseen setting, for an affordance type, we omit its combination with certain objects from seen. For example, the seen partition has \"grasp-mug\", and \"grasp-bag\" in its training, we create the unseen training set by removing the \"grasp-mug\" from the seen training set. In this case, the model is expected to learn the generalizable affordance knowledge of \"grasp\" and transfer it to an unseen object during testing. Note that seen and unseen setting shares the same validation and testing set. To investigate how PointRefer captures such transferability for each affordance type, The bar in Fig. 6 shows the percentage of samples that are omitted from seen under each affordance type. Then, the lines show the performance of the model trained with seen and unseen partitions for each affordance type, and their difference—the indicator of transferability of learned affordance knowledge. In general, we notice that the curve of seen and unseen follows a similar pattern, which indicates that PointRefer can capture a similar affordance knowledge even trained with far less object class. However, we also notice that the difference between seen and unseen enlarges as the omitted percentage grows, regardless of the absolution IoU. This is expected since the removed object can lead to under-diversified affordance representation."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
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+            "angle": 0,
+            "content": "14257"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.117,
+                0.063,
+                0.862,
+                0.429
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
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+            "angle": 0,
+            "content": "Figure 7. Case-Study of PointRefer's segmentation. Each showcase comes with one question and four shapes, showing the generalization ability of the affordance knowledge. The segmented affordance part is highlighted in red."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.466,
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+            ],
+            "angle": 0,
+            "content": "Choice of Backbone. To S backbone, we investigate the I with some alternative backbone that, for both seen and unseen as a 3D backbone generally pr than PointMLP, thus, we set 1 3D backbone. As for the lamance of Roberta prevails Ber setting. Whereas in the unseen and Roberta brings no signifca PointRefer uses Roberta as th"
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "angle": 0,
+            "content": "5.3. Qualitative Results"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
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+            "angle": 0,
+            "content": "Case Study. As shown in Fig. 1, the capacity to accurately co- given the question. It is noteworthy"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.72,
+                0.455,
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+            ],
+            "angle": 0,
+            "content": "with small affordance components, such as the microwa door handle, our model still exhibits decent ability."
+        },
+        {
+            "type": "image",
+            "bbox": [
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+                0.474,
+                0.391,
+                0.618
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
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+                0.547,
+                0.616
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+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.582,
+                0.472,
+                0.648,
+                0.483
+            ],
+            "angle": 0,
+            "content": "ting method?"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.58,
+                0.491,
+                0.692,
+                0.59
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.645,
+                0.592,
+                0.662,
+                0.601
+            ],
+            "angle": 0,
+            "content": "GT"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.707,
+                0.467,
+                0.865,
+                0.488
+            ],
+            "angle": 0,
+            "content": "When typing, which part should your fingers apply pressure to?"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.709,
+                0.492,
+                0.772,
+                0.59
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
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+                0.592,
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+            ],
+            "angle": 0,
+            "content": "Ours"
+        },
+        {
+            "type": "image",
+            "bbox": [
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+                0.494,
+                0.861,
+                0.592
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.815,
+                0.592,
+                0.831,
+                0.601
+            ],
+            "angle": 0,
+            "content": "GT"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.5,
+                0.602,
+                0.892,
+                0.631
+            ],
+            "angle": 0,
+            "content": "Figure 8. Failure cases due to non-comprehended text (left) and over-segmentation (right)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.501,
+                0.639,
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+            ],
+            "angle": 0,
+            "content": "6. Conclusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.656,
+                0.895,
+                0.807
+            ],
+            "angle": 0,
+            "content": "In this paper, we have introduced the pioneering task of Language-guided Affordance Segmentation on 3D Objects (LASO), which establishes a vital connection between AI agents and Large Language Models (LLMs) via textual cues. Our contributions include the development of an extensive dataset consisting of 19,751 question-point pairs and the creation of PointRefer, a baseline model that lays the groundwork for the LASO task. We envisage that LASO will steer the trajectory of the 3D affordance field towards better integration with the advancements in LLMs."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.823,
+                0.68,
+                0.84
+            ],
+            "angle": 0,
+            "content": "7. Acknowledgments"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.84,
+                0.893,
+                0.901
+            ],
+            "angle": 0,
+            "content": "This work is supported by the National Natural Science Foundation of China (92270114), the Agency for Science, Technology and Research (A\\*STAR) under MTC Programmatic Funds (Grant No.M23L7b0021), and NExT center."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
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+            "angle": 0,
+            "content": "14258"
+        }
+    ],
+    [
+        {
+            "type": "title",
+            "bbox": [
+                0.08,
+                0.09,
+                0.174,
+                0.106
+            ],
+            "angle": 0,
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2024/LASO_ Language-guided Affordance Segmentation on 3D Object/4a958b96-aed8-4e26-96c9-3b681d296992_origin.pdf

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2024/LASO_ Language-guided Affordance Segmentation on 3D Object/full.md

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+# LASO: Language-guided Affordance Segmentation on 3D Object
+
+Yicong Li $^{1}$ , Na Zhao $^{2*}$ , Junbin Xiao $^{1}$ , Chun Feng $^{3}$ , Xiang Wang $^{3*†}$ , Tat-seng Chua $^{1}$ ,
+
+$^{1}$ National University of Singapore,  $^{2}$ Singapore University of Technology and Design,  $^{3}$ University of Science and Technology of China,
+
+liyicong@u.nus.edu,na_zhao@sutd.edu.sg,junbin@comp.nus.edu.sg
+
+fengchun3364@mail.ustc.edu.cn,xiangwangl223@gmail.com,dcstsc@nus.edu.sg
+
+# Abstract
+
+Segmenting affordance in 3D data is key for bridging perception and action in robots. Existing efforts mostly focus on the visual side and overlook the affordance knowledge from a semantic aspect. This oversight not only limits their generalization to unseen objects, but more importantly, hinders their synergy with large language models (LLMs) which are excellent task planners that can decompose an overarching command into agent-actionable instructions. With this regard, we propose a novel task, Language-guided Affordance Segmentation on 3D Object (LASO), which challenges a model to segment a 3D object's part relevant to a given affordance question. To facilitate the task, we contribute a dataset comprising 19,751 point-question pairs, covering 8434 object shapes and 870 expert-crafted questions. As a pioneer solution, we further propose PointRefer, which highlights an adaptive fusion module to identify target affordance regions at different scales. To ensure a text-aware segmentation, we adopt a set of affordance queries conditioned on linguistic cues to generate dynamic kernels. These kernels are further used to convolute with point features and generate a segmentation mask. Comprehensive experiments and analyses validate PointRefer's effectiveness. With these efforts, We hope that LASO can steer the direction of 3D affordance, guiding it towards enhanced integration with the evolving capabilities of LLMs. Code and data are available at https://github.com/y13800/LASO.
+
+# 1. Introduction
+
+Affordance describes specific regions on an object that enable or facilitate certain human interactions. In this context,
+
+![](images/304263c7468019abd031dd459f80d845303ab370be9420da4a6eb9a7ffaed1e1.jpg)  
+Figure 1. Illustration of LASO, language-guided affordance segmentation on 3D object. Given an object point cloud and a question, the model is expected to segment the functional part delineated in question.
+
+the task of 3D affordance segmentation is raised to identify parts of 3D objects that imply a certain function. It has been deemed as a critical step in bridging perception and operation in the physical world for an embodied agent, thus has shown substantial impact on practical applications such as robotic manipulation [10, 14, 31].
+
+Recently, the advancement of Large Language Models (LLMs) has enabled their deployment as task planners, breaking down an intricate instruction into a sequence of affordance-aware, robot-executable instructions [12, 35, 36]. This equips intelligent agents with the capability to undertake complex tasks. For example, the overarching command "Pass me the mug in the microwave" can be systematically deconstructed into a series of affordance-aware inquiries: Q1) "How to get to the microwave?", Q2) "How to open the microwave", Q3) "How to grab the mug?", and Q4) "How to return to the user?" Ideally, each query would correspond to a predefined subtask that effectively translates language instructions into actionable steps. While Q1 and Q4 are related to language-conditioned path planning [42] and navigation [37], Q2 and Q3, which involve the 'open microwave' and 'grab the mug' actions, ex
+
+pose a gap — to the best of our knowledge, currently understanding affordance via language cues remains unexplored.
+
+Leaving language cues untouched, current 3D affordance segmentation focuses primarily on the visual aspect. It associates the specific geo-structure with either explicit affordance categories [7] or implicit affordance information from the 2D showcase [44]. Such visual-only settings make the segmentation models confined to visually predefined affordance types, thus impeding integration with language-based instructions from LLMs. As a result, fulfilling the aforementioned user's request becomes challenging, due to this inability to address Q2 and Q3.
+
+Towards these limitations, we introduce a novel task: Language-guided Affordance Segmentation on 3D Object (LASO), where 3D objects are paired with natural language questions that probe specific affordance parts. As a cornerstone task, LASO can provide an agent with affordance knowledge to answer the aforementioned Q2 and Q3 raised by LLM. For instance, the first two rows in Fig. 1 demonstrate how LASO imparts knowledge that enables an agent to interpret the semantic instructions "open the microwave" and "grasp the mug" in a 3D context, which are sufficient to execute Q2 and Q3, respectively. In LASO, questions are crafted to reflect diverse real-world scenarios, translating various affordance types into a range of semantic contexts. By learning from different contexts, we expect the agent not to memorize predefined affordance types but rather to abstract generalizable affordance knowledge within a broader semantic context. Notably, the diverse scales and shapes of affordance parts pose a significant perceptual challenge for the model. For instance, in the third row of Fig. 1, the target backrest of a chair occupies a large portion and has a significantly different shape compared to the small knob on a door in the last row.
+
+To facilitate the study, we develop the 1st question-affordance dataset comprising 19,751 point cloud-question pairs. The questions, originally crafted by experts, are further diversified using GPT-4 [33] under principles of contextual enrichment, concise phrasing, and structural diversity. These principles enable a deep and varied exploration of object affordances. Based on the dataset, we have developed a strong baseline model named PointRefer that is capable of adapting to varying scales and shapes of object parts, conditioned on the question. It consists of two modules: 1) an Adaptive Fusion Module (AFM) that integrates question semantics to point features at different scales, which caters to varied target regions with better point feature discriminativeness; and 2) a Referred Point Decoder (RPD) that generates a segmentation mask via conditioned affordance queries, which, after refinement, forms dynamic convolution kernels to capture point-wise affordance for mask prediction. In summary, our contributions are as follows:
+
+- We propose the task of Language-guided Affordance Seg
+
+Table 1. Efforts on affordance learning. Part indicates whether the prediction specifies the object part (✓) or the whole object  $(\times)$ .  
+
+<table><tr><td>Domain</td><td>Studies</td><td>Vision</td><td>Text</td><td>Part</td></tr><tr><td rowspan="3">2D</td><td>[1, 46]</td><td>Image</td><td>×</td><td>×</td></tr><tr><td>[9, 25, 32]</td><td>Image/Video</td><td>×</td><td>✓</td></tr><tr><td>[24, 29]</td><td>Image</td><td>✓</td><td>×</td></tr><tr><td rowspan="3">3D</td><td>[7, 30, 30, 43]</td><td>Point Cloud</td><td>×</td><td>✓</td></tr><tr><td>[44]</td><td>Point Cloud &amp; Image</td><td>×</td><td>✓</td></tr><tr><td>Ours</td><td>Point Cloud</td><td>✓</td><td>✓</td></tr></table>
+
+mentation on 3D Objects (LASO), which helps AI agents derive affordance knowledge from textual cues, facilitating a crucial advancement for LLM integration.
+
+- We develop a dataset with 19,751 question-point affordance pairs which are meticulously curated via a collaborative effort of human experts and GPT-4, thereby establishing the 1st benchmark for evaluating LASO.  
+- We build a strong baseline PointRefer, which employs textual-conditioned affordance queries to isolate afforded segments and devises an adaptive fusion module to enhance the discriminability of point feature.
+
+# 2. Related Work
+
+Affordance Learning. Originating from the image domain, initial efforts concentrate on detecting objects with affordances [1, 46]. Progressing from there, later studies [24, 29] incorporate linguistic descriptions to augment the process but still neglect the granularity of analysis, generally focusing on object-level affordances. Addressing this oversight, subsequent research [9, 25, 32] shift towards scrutinizing specific affordance parts, establishing a new norm for precision in the field.
+
+With the rise of embodied AI, the scope of affordance learning expands into the 3D realm. 3D AffordanceNet [7] introduces the first benchmark dataset for learning affordance from object point cloud geometry. Building on this, Yang et al. [44] propose a setting for learning 3D affordance parts guided by image demonstrations. Nonetheless, these approaches predominantly rely on a visual-only approach, tightly coupling geometric features with affordance labels and overlooking the semantic dimension. This limitation hinders the integration with Large Language Models (LLMs) that could otherwise substantiate affordance segmentation to real-world deployment. Moreover, the common practice of predicting affordance types as an auxiliary task [7, 44] may dilute the primary challenge of understanding affordance knowledge. In contrast, our work sidesteps auxiliary predictions, advocating for direct learning from the linguistic context, which aligns more closely with the innate capabilities of LLMs and their semantic richness.
+
+Text-Point Cloud Cross-Modal Learning. The integration of vision and natural language has recently sparked increased interest [16-21, 41]. Such a tendency naturally extends to 3D vision due to its pivotal role in embodied AI. To
+
+![](images/f02f4f367fd6504dc0599f11f0b7da47dce2cc5d8670c945bc01f637a759f629.jpg)  
+Figure 2. Illustration of question augmentation principles.
+
+advance the 3D-language tasks, datasets like ScanRefer [5] and ReferIt3D [2] have been instrumental in benchmarking the grounding of natural language to 3D objects. Complementing this, Azuma et al. [3] introduce ScanQA for 3D question-answering, while Ma et al. [28] propose SQA3D for situated reasoning within 3D environments. In terms of models, a variety of efforts [3, 13, 45] have emerged from these benchmarks, with notable examples like 3D-SPS [26] and BUTD-DETR [13] employing cross-attention mechanisms and linguistic cues for object discovery. Others, such as 3DVG [45], and ViL3DRel [6], focus on 3D grounding by incorporating spatial relation cues, showcasing the evolving landscape of 3D-VL models. Unlike the existing work that focuses on grounding and QA that perform scene-level reasoning, we tackle a dense prediction task at object part level that bridges reasoning to operation. To the best of our knowledge, we are the first to introduce the 3D affordance problem as a language-guided segmentation task.
+
+# 3. Dataset
+
+To underpin our proposed task, we have meticulously compiled a question-point affordance dataset with 19,751 paired samples, featuring 8,434 distinct object shapes across 23 classes. Accompanying these are 870 expertly crafted questions, covering 17 affordance categories.
+
+# 3.1. Annotation Details
+
+Point Cloud. Our dataset leverages the point cloud and affordance annotations from the 3D-AffordanceNet [7]. Specifically, the affordance annotation in [7] is multi-class, with each point on an object potentially supporting multiple affordance types. In our case, each question is tailored to a specific affordance type, while each sample can associate with several questions. Consequently, the same object can exhibit diverse affordance segmentation, depending on the specific question posed.
+
+Question. To create the questions, we draw 58 object-affordance combinations from [7], and craft 15 unique questions for each of the 58 combinations, resulting in 870 tailored questions. Specifically, five manual questions per combination are initially composed to represent different scenarios. Subsequently, we employ GPT-4 [33] to diver
+
+Table 2. Dataset Statistics  
+
+<table><tr><td rowspan="2">Task</td><td colspan="3">Train</td><td colspan="3">Val</td><td colspan="3">Test</td></tr><tr><td>Shape</td><td>Qst</td><td>Inst</td><td>Shape</td><td>Qst</td><td>Inst</td><td>Shape</td><td>Qst</td><td>Inst</td></tr><tr><td>Seen</td><td>6883</td><td>638</td><td>16120</td><td rowspan="2">516</td><td rowspan="2">58</td><td rowspan="2">1215</td><td rowspan="2">1035</td><td rowspan="2">174</td><td rowspan="2">2416</td></tr><tr><td>Unseen</td><td>6160</td><td>458</td><td>11558</td></tr></table>
+
+![](images/058b1cac9cc8965d2e5d05a665f8f8ce3c0ea0c2d9db887094e1c4c1334812c5.jpg)  
+Figure 3. Landscape of our dataset.
+
+sify the dataset with 10 additional questions for each combination, adhering to three key principles (as shown in Fig. 2): 1) Contextual Enrichment. Some questions were expanded to include additional context or details, fostering a more precise connection to the specified affordance of the target object. For instance, Q1 in Fig. 2 is reformed by a functional situation "cutting paper". 2) Concise Phrasing. In other cases, questions were distilled to their essence, making them succinct yet still meaningful. Q2 in Fig. 2 exemplifies this approach. 3) Structural Diversity. We employed a range of sentence structures, from questions to statements, to introduce natural linguistic variations and prevent model bias toward any specific phrasing or sentence length. A diversified example can be found in the Q3 of Fig. 2. All questions generated by GPT-4 undergo manual verification after this augmentation process.
+
+It's worth mentioning that the affordance type was only a tool for crafting the questions and pinpointing the correct segmentation areas. We refrain from using explicit affordance labels during both training and testing. This deliberate choice ensures that the learning process is driven by the semantic content of the questions, rather than by direct affordance label association.
+
+# 3.2. Statistics and Setting
+
+Dataset Settings. We show the statistical landscape of our dataset in Fig. 3. Specifically, it contains 17 affordance types and 23 object categories, composing 58 unique object-affordance combinations.
+
+In the spirit of the work by [44], we offer two distinct dataset settings: Seen: The default configuration, where the training and testing phases share similar distributions of object classes and affordance types. Unseen: This configuration is purpose-built to test the model's ability to generalize affordance knowledge. Certain affordance types, when paired with specific object classes, are omitted from the training set but included in the test set. For instance, while
+
+the model may learn to grasp bags and mugs during training, it is expected to apply the concept of 'grasp' to earphones, which is an affordance-object pairing not encountered during training. For a comprehensive account of the unseen setting, please refer to Appendix Sec. 7.1.
+
+Training and Evaluation Protocols. Notably, since questions are created based on a combination of object class and affordance type, one object class can have many shape instances. Thus, the design of our dataset accounts for the multiplicity of shapes within each object class, leading to a non-bijective pairing between shape instances and corresponding questions. To ensure comprehensive learning, during training, each shape instance is matched with a randomly selected question that aligns with its affordance type for every iteration. This random pairing exposes the model to a variety of semantic contexts, bolstering its ability to generalize. For the validation and test sets, question pairings are fixed to minimize variability and ensure consistent inference. These questions are unique to the evaluation phase and are not revealed during the training process to maintain the integrity of the evaluation.
+
+# 4. Method
+
+LASO Task Definition. Given a question  $Q_{raw}$  and an object point cloud  $\mathbf{P}_{raw} \in \mathbb{R}^{N \times 3}$  with  $N$  points, the goal of LASO is to predict a binary mask of  $\mathbf{M} \in \mathbb{R}^N$  that segments the functional part related to the question.
+
+Framework Overview. Due to the varying scale of target affordance region, LASO naturally challenges models adaptiveness at different scales. To address this, we devise a strong baseline, named PointRefer. As shown in Fig. 4, the object point cloud  $\mathbf{P}_{raw}$  is first processed by a 3D backbone, which typically consists of the multi-stage encoding and decoding process. To adapt PointRefer to the point feature at multiple scales, we introduce an Adaptive Fusion Module (AFM) to the backbone's decoding process. It performs multi-scale cross-modal fusion by injecting text clues to point features at a different decoding stage, which progressively refine the point feature map in a top-down manner. Then, to predict the segmentation mask, we introduce a Referred Point Decoder (RPD) that leverages a set of learnable queries conditioned on the input question, termed affordance queries, as the input of the transformer decoder. These affordance queries are obligated to look at the referred points only and generate question-aware dynamic kernels. The final segmentation mask is obtained by convoluting these dynamic kernels with the AFM-enhanced point feature.
+
+Feature Encoding. For the question, we prepend a "[CLS]" token to the question sequence before feeding them to a language model to capture the global language context. The encoded feature of the question is denoted by  $\mathbf{X} \in \mathbb{R}^{L \times d}$ , where  $L$  is the number of tokens and  $d$  is the feature di
+
+mension. For the point cloud, PointRefer can adopt any off-the-shelf 3D segmentation backbone.<sup>1</sup> to transform the  $\mathbf{P}_{raw}$  into the feature space. Note that a 3D backbone for segmentation typically consists of several encoding and decoding stages, and we take the point-wise feature map after the last decoding stage as the output of the backbone.
+
+# 4.1. Adaptive Fusion Module
+
+AFM is designed to enhance the point-wise features by incorporating question information. As illustrated in Fig. 4, we integrate AFM into different decoder layers to enhance its adaptiveness to target regions of various scales and shapes. Given the conventional downsampling operators in 3D backbones (e.g. PointNet++ [34]), the number of points varies across different encoder/decoder layers. Our AFM is designed to seamlessly adapt to the varying number of points.
+
+For simplification, we omit the notation for different decoder layers and use  $\mathbf{P} \in \mathbb{R}^{T \times d}$  to denote the point feature at a certain decoding layer, where  $T$  represents the number of points at that layer. As visualized in Fig. 4, AFM adopts a bottleneck architecture with three key steps: Grouping, Mixing, and Ungrouping. In the grouping step, the point features are grouped by text tokens, these grouped tokens are then thoroughly mixed via an MLP-Mixer [38]. Subsequently, the ungrouping step encapsulates the mixed features into individual point features, completing the AFM procedure by embedding valuable textual information into the point feature.
+
+To facilitate an efficient grouping process for our AFM, we employ a lightweight cross-attention module by omitting the transformation of both query and value. It takes the question feature  $\mathbf{X}$  as query and the point feature  $\mathbf{P}$  as key and value, then output grouped token  $\mathbf{G} \in \mathbb{R}^{L \times d}$ :
+
+$$
+\mathbf {G} = \operatorname {A t t e n t i o n} \left(\mathbf {X}, \mathbf {W} _ {1} \mathbf {P}, \mathbf {P}\right) + \mathbf {X}, \tag {1}
+$$
+
+$$
+\operatorname {A t t e n t i o n} (\mathbf {Q}, \mathbf {K}, \mathbf {V}) = \operatorname {S o f t m a x} \left(\frac {\mathbf {Q} \mathbf {K} ^ {T}}{\sqrt {d}}\right) \mathbf {V}, \tag {2}
+$$
+
+where  $\mathbf{W}_1$  is a linear transformation.
+
+After attaining the grouped feature, we update them using an MLP-Mixer [38], which employs two consecutive multilayer perceptrons (MLPs), producing fused feature  $\mathbf{F}$  by combining with two consecutive MLPs.
+
+$$
+\mathbf {G} ^ {\prime} = \mathbf {G} + \operatorname {M L P} _ {1} \left(\mathbf {G} ^ {T}\right) ^ {T}, \tag {3}
+$$
+
+$$
+\mathbf {F} = \mathbf {G} ^ {\prime} + \mathrm {M L P} _ {2} \left(\mathbf {G} ^ {\prime}\right), \tag {4}
+$$
+
+where,  $\mathrm{MLP}_1$  and  $\mathrm{MLP}_2$  are used to mix group-wise and channel-wise information, respectively, and  $T[\cdot]$  denotes the transpose operation. Finally, we return the fused feature  $\mathbf{F}$  to the point-space via the ungrouping process and
+
+![](images/e9b18ca47acf1010aba4b1a6f550693ca4313b08db5a15d713f522946cff3c15.jpg)  
+(a) Overview of PointRefer.
+
+![](images/d72ddcef34d4d0b43226e356b67b7c1342c77602abfa91c7a9b82df45cf402de.jpg)  
+(b) Adaptive Fusion Module.  
+Figure 4. The overall framework of our proposed PointRefer (a), which contains an adaptive fusion modal (b) that can be injected in different stages of the backbone decoder. As a result, it takes the point-wise feature generated at the last decoder layer as the final output of the 3D backbone. Then, the Referred Point Decoder takes in a set of question-conditioned affordance queries and feeds it to a transformer decoder together with the fused point feature, where the output is then reformed to a set of dynamic kernels. Finally, these dynamic kernels are used as convolution kernels to filter out the segmentation mask from the fused point feature.
+
+acquire the fused point feature  $\mathbf{P}^m$ . We implement the ungrouping process as a similar lightweight attention module as the grouping process. However, in this case, it takes  $\mathbf{P}$  as query and  $\mathbf{F}$  as key and value:
+
+$$
+\mathbf {P} ^ {m} = \operatorname {A t t e n t i o n} (\mathbf {P}, \mathbf {W} _ {2} \mathbf {F}, \mathbf {F}) + \mathbf {P}, \tag {5}
+$$
+
+where  $\mathbf{W}_2$  is a linear transformation. Lastly, the final output  $\mathbf{P}^o$  is formed by adding residual connections to  $\mathbf{P}^m$ . Notably, we take  $\mathbf{P}^o$  after the last decoding stage as the output of the 3D backbone.
+
+# 4.2. Referred Point Decoder
+
+Inspired by the success of learnable query-based methods in object detection [4] and segmentation [40], we introduce learnable affordance queries conditioned on the corresponding question of an object to decode the segmentation mask for the object. Specifically, we impose linguistic restrictions on all affordance queries, narrowing the model's focus to the relevant object parts and thereby facilitating convergence. These affordance queries, after being processed by a transformer decoder, are repurposed as dynamic kernels to deduce the segmentation mask from the point features, which are the final output of the 3D backbone.
+
+Question-Conditioned Affordance Query In the transformer decoder, it is well known that content and position embeddings are responsible for encoding instance-specific and spatial information, respectively. In PointRefer, we feed these two parts with the text feature and learnable query parameters, respectively, so that all the queries are
+
+shaped by the nuances of the linguistic input. Specifically, the affordance queries  $\mathbf{A}$  are formed by adding question embedding  $\mathbf{X}$  with learnable embeddings. Thus, the resulting  $\mathbf{A} \in \mathbb{R}^{L \times d}$  are the same length of the question.
+
+Reasoning and Mask Prediction. After forming the affordance query, we feed it to a transformer decoder [39] together with the fused point feature  $\mathbf{P}_o$  from the 3D backbone. In this manner, all the queries will use the question context as guidance and target to aggregate the feature of the referred points from the object, resulting in  $\mathbf{A}'$ :
+
+$$
+\mathbf {A} ^ {\prime} = \text {T r a n s f o r m e r - D e c o d e r} (\mathbf {A}; \mathbf {P} _ {o}). \tag {6}
+$$
+
+Subsequently, we perform dynamic convolution by applying a two-layer MLP on top of the transfer decoder to produce  $L$  dynamic kernels  $\Omega = \{\omega_{i}\}_{i = 1}^{L}$ , where each kernel  $\omega_{i}$  is reshaped to a  $1\times 1$  convolutional kernel with the channel number of  $d$ .
+
+$$
+\Omega = \operatorname {M L P} \left(\mathbf {A} ^ {\prime}\right). \tag {7}
+$$
+
+Since the dynamic kernels have captured the question- information, we use them as convolution filters on the feature maps for mask decoding. Specifically, we use each dynamic kernel in  $\Omega$  to convolute the point-wise feature map  $\mathbf{P}_o$ , which returns  $L$  point masks  $\mathbf{S} = \{\mathbf{s}_i\}_{i=1}^L$ .
+
+$$
+\mathbf {S} _ {i} = \left\{\mathbf {P} _ {o} * \omega_ {i} \right\} _ {i = 1} ^ {L}. \tag {8}
+$$
+
+Then, we apply mean pooling over all masks in  $\mathbf{S}$  followed by a sigmoid activation to acquire the final segmentation
+
+mask  $\mathbf{M}\in \mathbb{R}^N$  ..
+
+$$
+\mathbf {M} = \sigma (\operatorname {M a x - P o o l} ((\mathbf {S}))), \tag {9}
+$$
+
+where  $\sigma (\cdot)$  denote the sigmoid function.
+
+Intuitively, each dynamic kernel is expected to capture one aspect of the referred object part according to conditioned the question token. By ensembling all generated point masks, the final segmentation mask can integrate different response regions, thus making the result more robust.
+
+Objectives. Unlike [44], which relies on an auxiliary affordance label for prediction, our model seeks to forge a direct link between language context and object affordance. Thus, we solely employ Dice loss and Binary Cross-Entropy (BCE) loss to guide the segmentation mask prediction, bypassing the need for additional affordance labels.
+
+$$
+\mathcal {L} = \mathcal {L} _ {B C E} + \mathcal {L} _ {D i c e} \tag {10}
+$$
+
+# 5. Experiment
+
+Evaluation Metrics. For a thorough assessment, we benchmark our dataset against leading studies in 3D affordance learning [7, 44], employing four evaluation metrics to ensure robust analysis. These include Area Under the Curve (AUC), Mean Intersection Over Union (mIoU), Similarity (SIM), and Mean Absolute Error (MAE). Appendix Sec. 7.2 provides detailed explanations for the evaluation protocols.
+
+Implementation Details. PointRefer employs PointNet++ as the default 3D backbone to align with the standards established in [7, 44]. For text encoding, we utilize a pretrained RoBERTa model [23] to process linguistic inputs. The feature dimension  $d$  is set to 512. During training, we use the Adam optimizer with a learning rate set to 1e-4.
+
+Baseline Models. Since there is no prior work using paired question-point cloud data to segment object affordance. For a thorough comparison of our method, we adopt two 3D cross-modal works (3D-SPS [26] and IAGNet[44]) and two referred image segmentation works (ReferTrans [15] and RelA [22]) to LASO task. For the referred image segmentation models, we substitute their image backbones with a 3D counterpart, retaining their fusion mechanisms and mask decoding strategies. For the language-guided grounding model, 3D-SPS [26], we omit its bounding box prediction module while leveraging its inherent point selection scheme for our segmentation setting. The most related work is IAGNet [44], an affordance detection method that takes paired image-point cloud as input. To adapt IAGNet to our needs, we simply replace its image backbone with a language model, preserving the remainder of its architecture.
+
+Next, we show the effectiveness of our PointRefer by answering the following questions:
+
+- Q1: How is PointRefer compared to other baselines on the proposed dataset?  
+- Q2: How effective are the proposed components?  
+- Q3: What learning pattern does the PointRefer capture?
+
+Table 3. Main Results. The overall results of all comparative methods, the best results are in bold. Seen and Unseen are two partitions of the dataset. AUC and aIOU are shown in percentage.  
+
+<table><tr><td></td><td>Method</td><td>mIoU↑</td><td>AUC↑</td><td>SIM↑</td><td>MAE↓</td></tr><tr><td rowspan="5">Steen</td><td>ReferTrans [15]</td><td>13.7</td><td>79.8</td><td>0.497</td><td>0.124</td></tr><tr><td>ReLA [22]</td><td>15.2</td><td>78.9</td><td>0.532</td><td>0.118</td></tr><tr><td>3D-SPS [26]</td><td>11.4</td><td>76.2</td><td>0.433</td><td>0.138</td></tr><tr><td>IAGNet [44]</td><td>17.8</td><td>82.3</td><td>0.561</td><td>0.109</td></tr><tr><td>PointRefer</td><td>20.8</td><td>87.3</td><td>0.629</td><td>0.093</td></tr><tr><td rowspan="5">Unseen</td><td>ReferTrans [15]</td><td>10.2</td><td>69.1</td><td>0.432</td><td>0.145</td></tr><tr><td>ReLA [22]</td><td>10.7</td><td>69.7</td><td>0.429</td><td>0.144</td></tr><tr><td>3D-SPS [26]</td><td>7.9</td><td>68.8</td><td>0.402</td><td>0.158</td></tr><tr><td>IAGNet [44]</td><td>12.9</td><td>77.8</td><td>0.443</td><td>0.129</td></tr><tr><td>PointRefer</td><td>14.6</td><td>80.2</td><td>0.507</td><td>0.119</td></tr></table>
+
+# 5.1. Main Result (Q1)
+
+In Table 3, PointRefer demonstrates superior performance across all evaluation metrics compared to the baseline methods. Our observations are as follows:
+
+PointRefer vs. Other Models: IAGNet secures the second-best performance in both seen and unseen settings for all metrics. This is likely due to its specific design for object affordance segmentation, despite differences in input modality, making it a strong fit for our task with minimal adaptation. In contrast, 3D-SPS underperforms, potentially due to its progressive point selection mechanism. This approach involves a non-differentiable selection process, which may complicate the optimization within our task framework. Image-based methods, while showing decent performance, appear to be constrained by the modality gap. Originally trained on vast datasets of image-text pairs, where text is often a brief label, these methods now face fully formed, context-rich questions with a more limited training corpus.
+
+Seen vs. Unseen Performance: A notable performance drop from seen to unseen settings is observed across all baselines. This discrepancy underscores the difficulty in learning affordance knowledge that generalizes well, corroborating the necessity of our task design. Current methods struggle to bridge this gap in knowledge transfer, suggesting an avenue for future research: utilizing the extensive commonsense knowledge embedded in LLMs could potentially mitigate this challenge.
+
+# 5.2. In-Depth Study (Q2)
+
+Ablation Study. We show ablative results in Tab. 4. To verify that PointRefer prediction is based on the question, we conduct a blind test by training without questioning information, where the distinctive performance gap indicates that PointRefer has comprehended the question and can make a prediction based on it. Then, we study the effectiveness of PointRefer by removing both AFM and PRD ("w/o AFM & PRD"), which induces a severe performance
+
+Table 4. Ablative Results.  
+
+<table><tr><td>Variants</td><td>mIoU↑</td><td>AUC↑</td><td>SIM↑</td><td>MAE↓</td></tr><tr><td>Blind</td><td>10.8</td><td>78.2</td><td>0.506</td><td>0.125</td></tr><tr><td>w/o AFM &amp; PRD</td><td>17.7</td><td>82.1</td><td>0.558</td><td>0.110</td></tr><tr><td>w/o AFM</td><td>19.8</td><td>83.9</td><td>0.592</td><td>0.104</td></tr><tr><td>w/o multi-scale</td><td>20.4</td><td>87.1</td><td>0.628</td><td>0.095</td></tr><tr><td>w/o PRD</td><td>18.7</td><td>85.6</td><td>0.619</td><td>0.098</td></tr><tr><td>w/o condition</td><td>19.2</td><td>86.9</td><td>0.590</td><td>0.100</td></tr><tr><td>w/o dynamic filter</td><td>19.5</td><td>87.1</td><td>0.623</td><td>0.096</td></tr><tr><td>PointRefer</td><td>20.8</td><td>87.3</td><td>0.629</td><td>0.093</td></tr></table>
+
+![](images/0059e5e9abed1c1735ec3c0c0de6edbfdc697c4b25e56f290503c2482f64a20a.jpg)  
+Figure 5. The bar chart shows the training sample distribution over different question lengths, and the line chart shows the performance of PointRefer grouped by question length.
+
+decline on every metric, thus, validating the overall effectiveness of our design. Then, we also verify the functionality of AFM via the performance drop when it is removed ("w/o AFM). As a comparison, a relatively slighter declination is witnessed when we only apply AFM at the single scale ("w/o multi-scale"), which indicates the benefit of multi-scale cross-modal fusion. Then, we conduct some detailed breakdown tests to study PRD, we notice that when the affordance queries are not conditioned on the question ("w/o condition") the performance drops drastically, indicating that our affordance queries help to capture semantic clues in 3D space. Finally, we validate the superiority of the dynamic filtering strategy, because a declination is also observed when the dynamic filter is erased ("w/o dynamic filter"), and this variant adopts IAGNet's [44] mask prediction strategy as an alternative.
+
+Effect of Question Length. In Fig. 5, we show the performance of PointRefer on different question lengths. Specifically, The bar plot reveals the distribution of question length in the training set. Meanwhile, the line chart illustrates PointRefer's performance on different question lengths. Here, the performances are normalizing against the average number under that metric, e.g. IoU for each question length mIoU. Notably, PointRefer excels with questions that are more prevalent in the training set and with those that are lengthier—exceeding 14 words—owing to the richer contextual information they provide, which is instrumental in discerning the object's affordance.
+
+![](images/078425933709c631814008e073540023c5abcd8fed7395bd4362e95c58c7e601.jpg)  
+Figure 6. Illustration of how the percentage of omitted samples affect transferability of affordance knowledge (indicated by the difference between seen and unseen). For each affordance type, the bar shows a number of omitted samples from seen, i.e.  $\frac{\# \text{Seen} - \# \text{Unseen}}{\# \text{Seen}} (\%)$ , and the lines show the testing IoU of models trained on Seen and Unseen. Difference (IoU): Seen - Unseen.
+
+Table 5. Study of Backbones. PN:PointNet++; PM:PointMLP.  
+
+<table><tr><td></td><td>3D</td><td>LM</td><td>mIoU↑</td><td>AUC↑</td><td>SIM↑</td><td>MAE↓</td></tr><tr><td rowspan="6">Seen</td><td rowspan="3">PM [27]</td><td>Bert [8]</td><td>18.2</td><td>85.5</td><td>0.618</td><td>0.099</td></tr><tr><td>Deberta [11]</td><td>19.3</td><td>86.5</td><td>0.621</td><td>0.096</td></tr><tr><td>Roberta [23]</td><td>19.6</td><td>86.4</td><td>62.3</td><td>0.097</td></tr><tr><td rowspan="3">PN [34]</td><td>Bert [8]</td><td>20.1</td><td>86.4</td><td>0.615</td><td>0.101</td></tr><tr><td>Deberta [11]</td><td>20.4</td><td>87.0</td><td>0.624</td><td>0.095</td></tr><tr><td>Roberta [23]</td><td>20.8</td><td>87.3</td><td>0.629</td><td>0.093</td></tr><tr><td rowspan="6">Unseen</td><td rowspan="3">PM [27]</td><td>Bert [8]</td><td>11.5</td><td>76.3</td><td>0.43</td><td>0.128</td></tr><tr><td>Deberta [11]</td><td>12.3</td><td>76.8</td><td>0.435</td><td>0.133</td></tr><tr><td>Roberta [23]</td><td>12.1</td><td>76.8</td><td>0.434</td><td>0.136</td></tr><tr><td rowspan="3">PN [34]</td><td>Bert [8]</td><td>14.1</td><td>78.1</td><td>0.47</td><td>0.122</td></tr><tr><td>Deberta [11]</td><td>14.5</td><td>78.9</td><td>0.50</td><td>0.114</td></tr><tr><td>Roberta [23]</td><td>14.6</td><td>80.2</td><td>0.507</td><td>0.119</td></tr></table>
+
+Seen vs. Unseen. Recall that to create the training set for the unseen setting, for an affordance type, we omit its combination with certain objects from seen. For example, the seen partition has "grasp-mug", and "grasp-bag" in its training, we create the unseen training set by removing the "grasp-mug" from the seen training set. In this case, the model is expected to learn the generalizable affordance knowledge of "grasp" and transfer it to an unseen object during testing. Note that seen and unseen setting shares the same validation and testing set. To investigate how PointRefer captures such transferability for each affordance type, The bar in Fig. 6 shows the percentage of samples that are omitted from seen under each affordance type. Then, the lines show the performance of the model trained with seen and unseen partitions for each affordance type, and their difference—the indicator of transferability of learned affordance knowledge. In general, we notice that the curve of seen and unseen follows a similar pattern, which indicates that PointRefer can capture a similar affordance knowledge even trained with far less object class. However, we also notice that the difference between seen and unseen enlarges as the omitted percentage grows, regardless of the absolution IoU. This is expected since the removed object can lead to under-diversified affordance representation.
+
+![](images/1a89c80a6010d4952cc87e409c97820c74b8006f06ac5bac7b3fa9b3a5973077.jpg)  
+Figure 7. Case-Study of PointRefer's segmentation. Each showcase comes with one question and four shapes, showing the generalization ability of the affordance knowledge. The segmented affordance part is highlighted in red.
+
+Choice of Backbone. To S backbone, we investigate the I with some alternative backbone that, for both seen and unseen as a 3D backbone generally pr than PointMLP, thus, we set 1 3D backbone. As for the lamance of Roberta prevails Ber setting. Whereas in the unseen and Roberta brings no signifca PointRefer uses Roberta as th
+
+# 5.3. Qualitative Results
+
+Case Study. As shown in Fig. 1, the capacity to accurately co- given the question. It is noteworthy
+
+with small affordance components, such as the microwa door handle, our model still exhibits decent ability.
+
+![](images/3686ed50d26f28d574a77a62645f5c7782411961bc27d699591f15dd37a068ab.jpg)
+
+![](images/8763725ac8de1fd0427376685dcdc04c002dc725bdaa0231d50732676b7f6020.jpg)  
+Figure 8. Failure cases due to non-comprehended text (left) and over-segmentation (right).
+
+![](images/abd0418a56bb2f9c13e6c5d1c927312e02379f0beed5ed531f9d912515668230.jpg)  
+ting method?  
+GT
+
+![](images/497b81f755dcd97666eaf92c21d335e3f8d279880f2ea1e3f3ae7dd2bb2c8a1a.jpg)  
+When typing, which part should your fingers apply pressure to?  
+Ours
+
+![](images/481523d71a83bf7a67cf3b76e1f144cd04b017631c98ec86bd741d511284af78.jpg)  
+GT
+
+# 6. Conclusion
+
+In this paper, we have introduced the pioneering task of Language-guided Affordance Segmentation on 3D Objects (LASO), which establishes a vital connection between AI agents and Large Language Models (LLMs) via textual cues. Our contributions include the development of an extensive dataset consisting of 19,751 question-point pairs and the creation of PointRefer, a baseline model that lays the groundwork for the LASO task. We envisage that LASO will steer the trajectory of the 3D affordance field towards better integration with the advancements in LLMs.
+
+# 7. Acknowledgments
+
+This work is supported by the National Natural Science Foundation of China (92270114), the Agency for Science, Technology and Research (A\*STAR) under MTC Programmatic Funds (Grant No.M23L7b0021), and NExT center.
+
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+        "text": "LDP: Language-driven Dual-Pixel Image Defocus Deblurring Network",
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+        "text": "Hao Yang $^{1}$ , Liyuan Pan $^{1\\dagger}$ , Yan Yang $^{2}$ , Richard Hartley $^{2}$ , and Miaomiao Liu $^{2}$ $^{1}$ Beijing Institute of Technology  \n $^{2}$ Australian National University",
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+        "text": "{hao.yang, liyuan.pan}@bit.edu.cn, {yan.yang, richard.hartley, miaomiao.liu}@anu.edu.au",
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+        "text": "Abstract",
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+        "text": "Recovering sharp images from dual-pixel (DP) pairs with disparity-dependent blur is a challenging task. Existing blur map-based deblurring methods have demonstrated promising results. In this paper, we propose, to the best of our knowledge, the first framework that introduces the contrastive language-image pre-training framework (CLIP) to accurately estimate the blur map from a DP pair unsupervisedly. To achieve this, we first carefully design text prompts to enable CLIP to understand blur-related geometric prior knowledge from the DP pair. Then, we propose a format to input a stereo DP pair to CLIP without any fine-tuning, despite the fact that CLIP is pre-trained on monocular images. Given the estimated blur map, we introduce a blur-prior attention block, a blur-weighting loss, and a blur-aware loss to recover the all-in-focus image. Our method achieves state-of-the-art performance in extensive experiments (see Fig. 1).",
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+        "text": "1. Introduction",
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+        "text": "Defocus deblurring from a single image is an ill-posed problem [19, 28, 29, 33]. Compared to methods that restore an all-in-focus image directly [1, 2], blur map-based deblurring methods have demonstrated promising results [16, 26]. To simplify the blur removal process, several works [20, 34, 38] have utilized recent innovative dual-pixel (DP) sensors [6] to estimate blur maps, since the DP sensor captures a two-view image pair (a DP pair) in a single shot. The DP pair can be treated as images from a two-sample light field camera or a stereo system [24] with a tiny baseline [27, 34], which is beneficial for disparity estimation [1, 14, 23, 42]. Based on the DP image pair formation process, the disparity is geometrically related to the blur map, i.e., the degree of defocus blur proportional to disparity magnitudes [9].",
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+        "type": "text",
+        "text": "For estimating the blur map (defocus map or disparity",
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+        "image_caption": [
+            "Figure 1. Comparison of performance in terms of PSNR and Inference time. Our small and large models are respectively denoted by the Blue and Red cycles. The Green triangles represent previous state-of-the-art methods, and each of them is annotated with the method name, publication venue, and year. This figure is best viewed in color on the screen."
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+        "type": "text",
+        "text": "map), previous works either require extra data [3, 26], such as synthetic data, for supervision signals, or pre-calibrated blur kernels [34]. To avoid using extra information, several works explored unsupervised blur map estimation frameworks [16, 20]. Lee et al. [16] implicitly estimate the disparity of the left/right views using a spatial transformer, yet only in feature space, as well as Yang et al. [38]. Liang et al. [20] use fixed network branches for layer-wise defocus map estimation and deblurring, where the limited network branch number restricts the potential of its accuracy.",
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+        "text": "Recently, the contrastive language-image pre-training framework (CLIP) [30] has accomplished extraordinary success for vision tasks, such as semantic segmentation [31, 37], object detection [32], and point cloud understanding [40]. Therefore, a question naturally arises, can we avoid the cost of collecting data and model designing, to estimate the blur map unsupervisedly by using CLIP? Unfortunately, using semantic knowledge from CLIP to handle low-level vision tasks is underexplored.",
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+        "type": "text",
+        "text": "In this paper, for the first time, we explore the relationship between language and blur map estimation by applying CLIP. Note that CLIP is trained to match a monocular image with its corresponding language descriptions. Given a blurred image, it is intuitive to match it with a corre",
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+        "text": "CVF",
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+    {
+        "type": "header",
+        "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
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+        "type": "page_footnote",
+        "text": "† Corresponding author.",
+        "bbox": [
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+    },
+    {
+        "type": "page_number",
+        "text": "24078",
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+    {
+        "type": "text",
+        "text": "sponding text [A blurry image.], which allows the language model to find the blurred regions in an image. However, it is hard to quantize the blur level of an image without knowing its associated latent sharp one [25].",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Fortunately, we can leverage the capabilities of DP sensors. With DP pairs, blur quantization becomes possible without the need for its associated sharp image. The formation of DP ensures no disparity between left/right views for pixels in sharp regions, while a noticeable disparity exists for pixels in blurred regions. In essence, the detectable differences (disparities) in left/right views of a DP pair directly indicate the degree of defocus blurs. Consequently, we can quantify the variation between the left and right views, treating it as a valuable cue for estimating a blur map.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "However, CLIP still finds it challenging to simultaneously explore stereo DP pairs with left/right view images. To address this issue, we propose to explore the DP pair and design an 'image and text' format to better capture the blurs in the image. Specifically, we propose to create a new image from the DP pair and translate the description about the 'blurriness' of the image to measure the 'symmetry' of the newly formed image, which is based on the DP image formation process. The freshly designed image-text format allows the CLIP to estimate the blur map easily (see Sec. 3.1).",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Given the estimated blur map, we then restore the all-in-focus image from the DP pair. By observing that the attention map of the self-attention mechanism [8] can be used in the dynamic DP deblurring process, we introduce a blur prior attention (BPA) that modulates the attention map with the estimated blur map which provides prior knowledge of deblurring kernels (see Sec. 3.2).",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "To regulate the restoration, we specifically design two losses that are based on CLIP. Considering the network should focus more on heavily blurred regions, we propose a blur-weighting loss that imposes an adaptive penalty proportional to the blur degrees provided by the estimated blur map from CLIP. Then, to guarantee the restored image is sharp, we use CLIP to re-check the restored image and formulate a blur-aware loss (see Sec. 3.3).",
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+    {
+        "type": "text",
+        "text": "Our contributions are summarised as follows:",
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+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- We propose a Language-driven DP (LDP) defocus deblurring framework, by exploring the potential of CLIP in the low-level vision task.",
+            "- We design an image-text format for blur map estimation based on the geometric relationship between the blur and disparity of the DP pair.",
+            "- We propose a blur prior attention (BPA) block, a blur-weighting loss, and a blur-aware loss to encourage sharp restorations of the DP pair."
+        ],
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "We evaluate the proposed framework extensively on standard benchmark datasets. Though using the largescale foundation model, CLIP, for blur map estimation, our method achieves Pareto-optimality between deblurring performance and inference speed (refer to Fig. 1 for an",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "overview of the comparison).",
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "DP Defocus Deblurring. DP-based deblurring methods can be divided into single- and multi-task manners. For single-task based deblurring [1-3], methods apply different kernels at different regions of the DP pair to handle the spatially varying defocus deblur. This can usually be achieved by using parallel atrous convolutions [33], attention mechanisms [39], or deformable convolutions [17]. For multi-task deblurring methods, the blur/defocus/disparity map is auxiliarily estimated to benefit DP defocus deblurring. Pan et al. [26] and Xin et al. [34] use the estimated DP disparity to regularise the restoration through reblurring; however, with extra data or pre-calibrate kernel. Several works explored unsupervised defocus map (or disparity) estimation. Lee et al. [16] and Yang et al. [38] estimate defocus disparity only in feature space without explicitly showing a defocus map. Liang et al. [20] optimize a multi-channel defocus map based on [27]. However, hyperparameters, such as the defocus threshold and the number of channels, are preset, limiting blur map estimation accuracy. Unlike past works, by transferring the blur-related geometric prior knowledge into semantic prompts, we unsupervisedly estimate the blur map from CLIP to benefit defocus deblurring.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Language-driven Vision. Common objectives in visual-language learning are aligning the text with a paired image in the embedding space [21, 30, 35]. The CLIP, one of the milestone achievement in the area, demonstrate that language-independent computer vision tasks can be substantially benefited from visual-language learning, by achieving SOTA zero-shot classification performance in the ImageNet-1K benchmark [7]. Successive works have extended the zero-shot learning capability of CLIP to semantic segmentation [31, 44], monocular depth estimation [4, 10, 41], and point clouds [11, 40]. However, none of the existing works explores the zero-shot learning capability of CLIP in stereo/DP pairs. This paper proposes the first approach to use the monocular image-trained CLIP in zero-shot blur map segmentation of DP pairs.",
+        "bbox": [
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "3. Method",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Let us now introduce our language-driven dual-pixel image defocus deblurring framework. Given a defocus blurred DP pair  $(\\mathbf{B}_{\\mathrm{L}},\\mathbf{B}_{\\mathrm{R}})$ , we aim to restore an all-in-focus image  $\\mathbf{I}$  where  $\\mathbf{B}_{\\mathrm{L}}$  and  $\\mathbf{B}_{\\mathrm{R}}$  are the left and right view of a DP pair and  $\\mathbf{B}_{\\mathrm{L}},\\mathbf{B}_{\\mathrm{R}},\\mathbf{I}\\in \\mathbb{R}^{h\\times w\\times 3}$ . Here,  $h$  and  $w$  define the image height and width, respectively.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "We first design a DP-aware prompt to adapt CLIP to output a blur map,  $\\mathbf{M} \\in \\mathbb{R}^{h \\times w \\times 1}$ , which quantizes disparity unsupervisedly between  $\\mathbf{B}_{\\mathrm{L}}$  and  $\\mathbf{B}_{\\mathrm{R}}$ . Then, we propose a BPA block based network which employs the blur",
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+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "24079",
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+    {
+        "type": "image",
+        "img_path": "images/990fe983387e39d2f8b277fcf1f9eba3549aaf603c220bf2942e5ea3d19158d0.jpg",
+        "image_caption": [
+            "Figure 2. Overall architecture. Given a DP pair  $(\\mathbf{B}_{\\mathrm{L}},\\mathbf{B}_{\\mathrm{R}})$ , we first generate a blur map  $\\mathbf{M}$  by using our unsupervised blur map estimation strategy which is based on the CLIP with assembling format. We then forward the DP pair  $(\\mathbf{B}_{\\mathrm{L}},\\mathbf{B}_{\\mathrm{R}})$  to our deblurring backbone composed of an encoder and a decoder. Meanwhile, we have multiple BPA blocks, using the blur map  $\\mathbf{M}$  as deblurring kernel prior to refine the intermediate backbone feature embeddings. In the following, we have the restoration  $\\hat{\\mathbf{I}}$ . The deblurring network is optimized with three losses, charbonnier loss  $\\mathcal{L}_{char}$ , blur weighting loss  $\\mathcal{L}_{bwl}$ , and blur aware loss  $\\mathcal{L}_{bal}$ .  $\\mathcal{L}_{char}$  penalizes deviations from  $\\mathbf{I}$  in the resorption  $\\hat{\\mathbf{I}}$ .  $\\mathcal{L}_{bwl}$  and  $\\mathcal{L}_{bal}$  regularize the restoration by imposing an adaptive penalty on the blurred regions of the DP pair, and leveraging unsupervised blur map estimation strategy to encourage the restoration to be sharp, i.e., the blur map  $\\hat{\\mathbf{M}}$  for the restoration  $\\hat{\\mathbf{I}}$  is zero value filled."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "map  $\\mathbf{M}$  as deblurring priors to restore a sharp image  $\\hat{\\mathbf{I}}$  from  $(\\mathbf{B}_{\\mathrm{L}},\\mathbf{B}_{\\mathrm{R}})$ . To regularize the restoration of  $\\hat{\\mathbf{I}}$ , a blur-weighting loss  $\\mathcal{L}_{\\mathrm{bwl}}$  and a blur-aware loss  $\\mathcal{L}_{\\mathrm{bal}}$  are also introduced that were underpinned by our unsupervised blur map estimation strategy. The overall framework is shown in Fig. 2. Details are presented below.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1. Unsupervised Blur Map Estimation",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "Preliminary. CLIP respectively embeds an image and a text description into a common semantic space of dimension  $c$  with an image encoder and a text encoder, obtaining image embedding  $\\mathbf{f} \\in \\mathbb{R}^c$  and text embedding  $\\mathbf{t} \\in \\mathbb{R}^c$ . By optimizing a contrastive loss, the embeddings of the aligned image and text pair,  $\\Omega_a$ , stay similar, i.e., maximizing the semantic similarity by  $\\max_{\\mathbf{f}, \\mathbf{t} \\in \\Omega_a} \\sin(\\mathbf{f}, \\mathbf{t})$ , where  $\\sin(\\cdot, \\cdot)$  is the cosine similarity metric. Meanwhile, the semantics of misaligned pairs,  $\\Omega_{na}$  are pushed away from each other, i.e.,  $\\min_{\\mathbf{f}, \\mathbf{t} \\in \\Omega_{na}} \\sin(\\mathbf{f}, \\mathbf{t})$ . With comprehensive training data, CLIP can be leveraged to align images with pre-defined prompt templates composed of open-world text descriptions for zero-shot learning [30].",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "For a DP pair, the disparity  $d$  for a pixel in the left view is defined by its location  $(i,j)$  and that of its corresponding pixel at  $(i,k)$  in the right view.",
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "In the literature, this DP disparity [27] is defined as",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nd = j - k = A (r (z)) \\cdot B (z), \\mathbf {B} _ {\\mathrm {L}} (i, j) = \\mathbf {B} _ {\\mathrm {R}} (i, k), \\tag {1}\n$$\n",
+        "text_format": "latex",
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+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathbf{B}_{\\mathrm{L}}(i,j)$  and  $\\mathbf{B}_{\\mathrm{R}}(i,k)$  are the intensity of the two matching points,  $r(\\cdot)$  is a function of the radius of the circle of confusion,  $z$  is the point depth, and  $A(r(z))$  and  $B(z)$  are lens-dependent constants [2, 9, 26, 34].",
+        "bbox": [
+            75,
+            779,
+            468,
+            840
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Analysis. Leveraging the CLIP, zero-shot blur map estimation can be generally divided into three steps. i) Image Encoding. Considering the image encoder of the CLIP is trained with monocular RGB images, a function  $\\eta (\\cdot ,\\cdot)$  is",
+        "bbox": [
+            75,
+            839,
+            468,
+            901
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "required to create a new monocular image from the DP image pair  $(\\mathbf{B}_{\\mathrm{L}},\\mathbf{B}_{\\mathrm{R}})$ . To obtain the dense embedding for the blur map estimation task, we follow [41] to pop out the final pooling layer from the image encoder, yielding an embedding matrix  $\\mathbf{F}\\in \\mathbb{R}^{h_s\\times w_s\\times c}$ , where  $h_s$  and  $w_{s}$  are the height and width for embedding of the newly created image, respectively. Mathematically, we have",
+        "bbox": [
+            496,
+            363,
+            890,
+            470
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {F} = \\operatorname {I m a g e E n c o d e r} \\left(\\eta \\left(\\mathbf {B} _ {\\mathrm {L}}, \\mathbf {B} _ {\\mathrm {R}}\\right)\\right). \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            578,
+            484,
+            890,
+            502
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Each pixel of  $\\mathbf{F}$  has encoded the local semantic information for a corresponding region in  $\\eta (\\mathbf{B}_{\\mathrm{L}},\\mathbf{B}_{\\mathrm{R}})$ . ii) Text Encoding. A text encoder is used to embed the semantics of a prompt p describing the blur into the text embedding,",
+        "bbox": [
+            496,
+            516,
+            893,
+            578
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {t} = \\operatorname {T e x t E n c o d e r} (\\mathfrak {p}). \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            620,
+            593,
+            890,
+            609
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "iii) Blur map estimation. Let  $\\mathbf{F}(i,j)$  be a c-dimensional embedding at position  $(i,j)$  of  $\\mathbf{F}$ ,  $i\\in \\{1,\\dots ,\\mathrm{h}_{\\mathrm{s}}\\}$ , and  $j\\in \\{1,\\dots ,\\mathrm{w}_{\\mathrm{s}}\\}$ . The embedding  $\\mathbf{F}(i,j)$  and the blur semantic-based text embedding  $\\mathbf{t}$  are expected to be similar if the pixel at  $(i,j)$  is blurred. Therefore, the blur mask  $\\mathbf{M}_{\\mathbf{F}}$  of  $\\eta (\\mathbf{B}_{\\mathrm{L}},\\mathbf{B}_{\\mathrm{R}})$  is obtained by",
+        "bbox": [
+            496,
+            625,
+            893,
+            717
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {M} _ {\\mathbf {F}} (i, j) = \\sigma (\\operatorname {s i m} (\\mathbf {F} (i, j), \\mathbf {t})) . \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            583,
+            729,
+            890,
+            750
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Note,  $\\sigma (\\cdot)$  normalizes the cosine similarity  $\\mathfrak{sim}(\\cdot ,\\cdot)$  output to a probability space, to reflect the degree of blur at the position. Here,  $\\mathbf{M}_{\\mathbf{F}}$  is sampled to have the same resolution as  $\\mathbf{B}_{\\mathrm{L}}$  or  $\\mathbf{B}_{\\mathrm{R}}$ , returning  $\\mathbf{M}\\in \\mathbb{R}^{h\\times w\\times 1}$ .",
+        "bbox": [
+            496,
+            762,
+            890,
+            823
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Given the analysis above, our goal is to develop text prompts  $\\mathfrak{p}$ , while adapting the function  $\\eta(\\cdot, \\cdot)$ , to enable the use of semantic information from CLIP to generate the blur map  $\\mathbf{M}$  in an unsupervised manner. In particular, we explore the blur-aware, DP-aware, and ensembling formats with detailed presented below.",
+        "bbox": [
+            496,
+            824,
+            890,
+            915
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "24080",
+        "bbox": [
+            478,
+            944,
+            519,
+            955
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/18d45b8a20b3eaa4186ec61cbe6d094c70506c392e53a5046bae28f16976d1a4.jpg",
+        "image_caption": [
+            "Figure 3. The pipeline of our DP-aware format for obtaining the blur map  $\\mathbf{M}$ . Given a DP pair  $(\\mathbf{B}_{\\mathrm{L}},\\mathbf{B}_{\\mathrm{R}})$ , the function  $\\eta (\\mathbf{B}_{\\mathrm{L}},\\mathbf{B}_{\\mathrm{R}}^{h})$  concatenates the left view  $\\mathbf{B}_{\\mathrm{L}}$  and with horizontally flipped right view  $\\mathbf{B}_{\\mathrm{R}}^{h}$  for obtaining the  $\\mathbf{F}$  from the CLIP image encoder. We then apply  $\\alpha (F)$  to averagely pool the feature map according to the transformation imposed on the input DP pair, resulting in a new feature embedding with the same aspect ratio of the input DP pair. Meanwhile, we set the prompts  $\\mathfrak{p}$  to describe the symmetry of  $\\eta (\\mathbf{B}_{\\mathrm{L}},\\mathbf{B}_{\\mathrm{R}}^{h})$ , obtaining text embedding  $\\mathbf{t}$ . We finally have the blur map  $\\mathbf{M}$  by computing Eq. 6 and performing sampling."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            83,
+            90,
+            462,
+            272
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Blur-aware Format. An intuitive approach is setting a prompt  $\\mathbf{p}$  that describes the blur to query a blur map  $\\mathbf{M}$ , e.g.,  $\\mathbf{p} = [\\mathrm{A~blurry~image}.]$ . The  $\\eta(\\cdot, \\cdot)$  is then defined to synthesize a center view of the DP pair by averaging the left view  $\\mathbf{B}_{\\mathrm{L}}$  and right view  $\\mathbf{B}_{\\mathrm{R}}$ , as the average of two sub-images is equivalent to the image captured by a regular sensor [3, 27]. However, the disparity information among the DP pair is neglected, resulting in a sub-optimal blur map. Refer to Fig. 4 for comparisons.",
+        "bbox": [
+            75,
+            444,
+            468,
+            580
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "DP-aware Format. Based on the DP image formation process, the disparity is proportional to the degree of blur exhibited in the DP view [1]. We thus propose to guide CLIP to understand the disparity exhibited between  $\\mathbf{B}_{\\mathrm{L}}$  and  $\\mathbf{B}_{\\mathrm{R}}$  which eventually leads to better mask (M) generation. To this end, we first formulate the disparity in the DP pair and then study the disparity-aware prompt and function  $\\eta (\\cdot ,\\cdot)$  designing. Such design leads us to query degrees of displacement between the left and right view from the CLIP, without any fine-tuning, to obtain the blur map M.",
+        "bbox": [
+            75,
+            584,
+            468,
+            734
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Note that the CLIP is the vision-text alignment model trained with monocular image input. To extract the displacement between left/right views of the DP pair, we explore several input-prompt formats: i) Concatenating the left and right views horizontally, and prompting their difference, e.g., [The left and right of the image are different.]; ii) Prompting the horizontal symmetry between the left and right views, e.g., [A horizontally symmetric image.] (Fig. 3).",
+        "bbox": [
+            75,
+            736,
+            468,
+            872
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Empirically, we achieve the best performance with the second prompt format. When describing the symmetry in",
+        "bbox": [
+            76,
+            872,
+            468,
+            901
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/36370877f7d879fc524e4ff8f9994de1b61705a140a2a3adf717c1156d906117.jpg",
+        "image_caption": [
+            "(a)"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            501,
+            88,
+            596,
+            186
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/2adfbde67b3773aad6a74b04d1253cf65b912abc73088b937b9bfadbd6a43017.jpg",
+        "image_caption": [
+            "(b)"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            598,
+            88,
+            694,
+            186
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/b0872cd650385ca4ec8a5634d760a6ffa4998117d1739009563c34e8098ffa4a.jpg",
+        "image_caption": [
+            "(c)",
+            "Figure 4. Example of blur map estimation (the darker, the sharper). (a) The left view of the DP image. (b) and (c) Blur maps obtained with prompts of the blur-aware and DP-aware formats. (d) The blur maps obtained with the ensembling-based format, i.e., all eight blur-aware and DP-aware prompts are used (please refer to Tab. 4 for details)."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            694,
+            88,
+            790,
+            186
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/3b01f240f5b9ae389abd9aee3a971c85e3eec945b179276d04374353f0970329.jpg",
+        "image_caption": [
+            "(d)"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            790,
+            88,
+            887,
+            186
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "the prompt  $\\mathfrak{p}$ , we concatenate the left view  $\\mathbf{B}_{\\mathrm{L}}$  with a horizontally flipped right view  $\\mathbf{B}_{\\mathrm{R}}^{h} = \\mathrm{Flip}(\\mathbf{B}_{\\mathrm{R}})$  along the width axial in the  $\\eta (\\cdot ,\\cdot)$ . We then obtained image features  $\\mathbf{F} = \\mathrm{ImageEncoder}\\bigl (\\eta (\\mathbf{B}_{\\mathrm{L}},\\mathbf{B}_{\\mathrm{R}}^{h})\\bigr)$ . To transform  $\\mathbf{F}$  to the same aspect ratio of  $\\mathbf{B}_{\\mathrm{L}}$  and  $\\mathbf{B}_{\\mathrm{R}}$ , we average the corresponding pixel-wise features based on the transformation in  $\\eta (\\mathbf{B}_{\\mathrm{L}},\\mathbf{B}_{\\mathrm{R}}^{h})$  and have  $\\alpha (\\mathbf{F})$ . For  $i\\in \\{1,\\dots ,\\mathsf{h}_{\\mathsf{w}}\\}$  and  $j\\in \\{1,\\dots ,\\lfloor \\frac{1}{2}\\mathsf{w_s}\\rfloor \\}$ , we define",
+        "bbox": [
+            496,
+            300,
+            890,
+            417
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\alpha (\\mathbf {F}) (i, j) = \\frac {1}{2} \\mathbf {F} (i, j) + \\frac {1}{2} \\mathbf {F} (i, w _ {s} - j). \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            568,
+            429,
+            890,
+            455
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Back to the left-hand side of Eq. 4, we have",
+        "bbox": [
+            500,
+            468,
+            792,
+            484
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {M} _ {\\mathbf {F}} (i, j) = 1 - \\mathbf {M} _ {\\mathbf {F}} ^ {s} (i, j) = 1 - \\sigma \\left(\\operatorname {s i m} (\\alpha (\\mathbf {F}) (i, j), \\mathbf {t} ^ {s})\\right). \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            514,
+            494,
+            890,
+            525
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Here,  $\\mathbf{t}^s$  is the text embedding of the prompt describing symmetry. Note that the high similarity value, i.e.  $\\mathbf{M}_{\\mathbf{F}}^{s}(i,j) = \\sigma \\big(\\mathrm{sim}(\\alpha (\\mathbf{F})(i,j),\\mathbf{t}^{s})\\big)$  indicates pixels in sharp regions. Therefore the blur map is derived as  $1 - \\mathbf{M}_{\\mathbf{F}}^{s}(i,j)$  in Eq. 6. Similarly, the  $\\mathbf{M}_{\\mathbf{F}}$  is sampled to the same resolution of the DP pair, returning M. For this blur map estimation strategy, we conclude the lemma below,",
+        "bbox": [
+            496,
+            539,
+            890,
+            645
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Lemma 3.1. A pixel is sharp if and only if it is horizontally symmetric in the left view and the horizontally flipped right view, otherwise, the pixel is blurred.",
+        "bbox": [
+            496,
+            648,
+            893,
+            695
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Proof. Following Eq. (1), we have  $\\mathbf{B}_{\\mathrm{L}}(i,j)$  being sharp, given  $\\mathbf{B}_{\\mathrm{L}}(i,j) = \\mathrm{Flip}(\\mathbf{B}_{\\mathrm{R}})(i,\\mathsf{w} - j)$ . In other words, we have  $\\eta (\\mathbf{B}_{\\mathrm{L}},\\mathbf{B}_{\\mathrm{R}}^{h})(i,j) = \\eta (\\mathbf{B}_{\\mathrm{L}},\\mathbf{B}_{\\mathrm{R}}^{h})(i,\\mathsf{w}_{\\mathsf{s}} - j)$ , demonstrating the horizontal symmetry. Reversely, the horizontal symmetry breaks once the disparity/blur occurs.",
+        "bbox": [
+            496,
+            715,
+            890,
+            791
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Ensembling format. Given the analysis that the degradations in the DP pair can be described by both the blurriness and symmetricity, we thus propose to obtain the mask by assembling the blur-aware and DP-aware formats jointly. Please refer to Tab. 4 for details of the 8 prompts designed from blur-aware and DP-aware formats.",
+        "bbox": [
+            496,
+            809,
+            893,
+            898
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "24081",
+        "bbox": [
+            478,
+            944,
+            517,
+            955
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2. Network",
+        "text_level": 1,
+        "bbox": [
+            76,
+            90,
+            179,
+            104
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We train an encoder-decoder based deblurring network for restoring the DP pair  $(\\mathbf{B}_{\\mathrm{L}},\\mathbf{B}_{\\mathrm{R}})$  into a sharp image  $\\hat{\\mathbf{I}}$  with the derived blur map  $\\mathbf{M}$ . Our network consists of a backbone network based on [5] and a BPA block to interleave with the backbone network layers. In particular, the BPA block uses the obtained blur map  $\\mathbf{M}$  as deblur kernel prior to help the restoration of  $(\\mathbf{B}_{\\mathrm{L}},\\mathbf{B}_{\\mathrm{R}})$  on the fly.",
+        "bbox": [
+            75,
+            113,
+            468,
+            219
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Self-attention. The self-attention (SA) mechanism is widely used in the image restoration tasks [18, 36, 39]. We first briefly review it. Let  $\\mathbf{X} \\in \\mathbb{R}^{h_x \\times w_x \\times c_x}$  be the intermediate feature embedding of a blur image from the backbone encoder, where  $h_x$ ,  $w_x$ ,  $c_x$  are height, width, and channel of the feature. The self-attention is input with query  $\\mathbf{Q}$ , key  $\\mathbf{K}$ , and value  $\\mathbf{V}$  that are linearly projected from  $\\mathbf{X}$ , and then calculate an attention map between  $\\mathbf{Q}$  and  $\\mathbf{K}$  for adaptively aggregating  $\\mathbf{V}$ . This process is defined as follows,",
+        "bbox": [
+            75,
+            220,
+            470,
+            357
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {Q} = \\mathbf {X} \\mathbf {W} _ {\\mathbf {Q}}, \\quad \\mathbf {K} = \\mathbf {X} \\mathbf {W} _ {\\mathbf {K}}, \\quad \\mathbf {V} = \\mathbf {X} \\mathbf {W} _ {\\mathbf {V}}, \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            114,
+            369,
+            468,
+            387
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Attention  $(\\mathbf{Q},\\mathbf{K},\\mathbf{V}) = \\mathrm{Softmax}(\\mathbf{Q}\\mathbf{K}^{\\top} / \\beta)\\mathbf{V}$  (8)",
+        "bbox": [
+            114,
+            388,
+            468,
+            407
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathbf{W}_{\\mathbf{Q}}, \\mathbf{W}_{\\mathbf{K}}, \\mathbf{W}_{\\mathbf{V}} \\in \\mathbb{R}^{h_{\\mathbf{x}} \\times w_{\\mathbf{x}} \\times c_{\\mathbf{x}}}$  are learnable weight matrices,  $\\beta$  is a normalization factor that is typically set to the square root of the latent dimension, and  $\\operatorname{Softmax}(\\mathbf{Q}\\mathbf{K}^{\\top} / \\beta) \\in \\mathbb{R}^{(h_{\\mathbf{x}} \\times w_{\\mathbf{x}}) \\times (h_{\\mathbf{x}} \\times w_{\\mathbf{x}})}$  is attention map.",
+        "bbox": [
+            75,
+            420,
+            468,
+            482
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "BPA Block. The attention map can be considered as an adaptive deblur kernel prior for restoring the DP pair in the feature space. We are motivated to modulate the attention map by supplying the blur map  $\\mathbf{M}$ , utilizing blur-related prior knowledge to additionally assign a  $\\mathbf{q} \\times \\mathbf{q}$  deblur kernel for each region in  $\\mathbf{X}$  to aggregate a sharp feature embedding from its neighboring regions. We re-write the Eq. 8 as",
+        "bbox": [
+            75,
+            484,
+            468,
+            589
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Attention  $(\\mathbf{Q},\\mathbf{K},\\mathbf{V}) = \\mathrm{Softmax}(\\mathbf{Q}\\mathbf{K}^{\\top} / \\beta +\\mathbf{O})\\mathbf{V}$  (9)",
+        "bbox": [
+            91,
+            601,
+            468,
+            618
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {O} = \\operatorname {P a d} \\left(\\operatorname {F F N} _ {\\operatorname {C o n v}} \\left(\\sigma^ {- 1} (\\mathbf {M})\\right)\\right), \\tag {10}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            91,
+            621,
+            468,
+            638
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "and show that the restoration result is further improved in Fig. 5, where  $\\mathrm{FFN}_{\\mathrm{Conv}}(\\cdot)$  is a convolution-based feed forward layer that is used to learn a  $q \\times q$  deblur kernel for each region of  $\\mathbf{X}$  from the unnormalized blur map  $\\sigma^{-1}(\\mathbf{M})$ , resulting in  $\\mathrm{FFN}_{\\mathrm{Conv}}(\\sigma^{-1}(\\mathbf{M})) \\in \\mathbb{R}^{h_x \\times w_x \\times q^2}$ . The Pad( $\\cdot$ ) function reshapes  $\\mathrm{FFN}_{\\mathrm{Conv}}(\\sigma^{-1}(\\mathbf{M}))$  into  $\\mathbb{R}^{h_x \\times w_x \\times q \\times q}$ , and pads the reshaped  $\\mathrm{FFN}_{\\mathrm{Conv}}(\\sigma^{-1}(\\mathbf{M}))$  to  $\\mathbb{R}^{(h_x \\times w_x) \\times (h_x \\times w_x)}$ , for shape alignment issue.",
+        "bbox": [
+            75,
+            651,
+            468,
+            773
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.3. Network Training",
+        "text_level": 1,
+        "bbox": [
+            76,
+            784,
+            251,
+            800
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We optimize our deblurring network with the widely used Charbonnier loss. Moreover, we propose a blur-aware loss and a blur weighting loss to penalize the blurred regions in the restoration  $\\hat{\\mathbf{I}}$ .",
+        "bbox": [
+            75,
+            806,
+            468,
+            867
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Charbonnier loss. We encourage the restoration to be close to the ground truth by using Charbonnier loss [12, 43].",
+        "bbox": [
+            75,
+            869,
+            468,
+            900
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/480aad7501ee7e8b7fcb54754c39b4d78d088b346ac26c3d6c0e4798592d9d0c.jpg",
+        "image_caption": [
+            "(a)"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            501,
+            88,
+            570,
+            142
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/df89236f0ba3d0a983886e86e0fac8dc150f9b76ee15aaf584879ba6aa82d718.jpg",
+        "image_caption": [
+            "(b)"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            571,
+            88,
+            692,
+            142
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/8838b231c703c986bc4d3b093dad7eb2534b56e2645f464ec2a5a15cd603a2de.jpg",
+        "image_caption": [
+            "(c)",
+            "Figure 5. Example of deblurring with the blur map projected deblur kernel  $\\mathbf{O}$ . (a) and (b) are the left view of the DP pair and the ground truth sharp image. (c) and (d) are deblurred images with and without using  $\\mathbf{O}$ . Zoom in for better quality."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            694,
+            88,
+            761,
+            142
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/53c8c1fc807ced4c5c6267718200456ec40493e492d5f7a61f420f3dd08a2a77.jpg",
+        "image_caption": [
+            "(d)"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We empirically set  $\\varepsilon$  to  $10^{-4}$ , and define",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\text {c h a r}} = \\sqrt {\\| \\mathbf {I} (i , j) - \\hat {\\mathbf {I}} (i , j) \\| ^ {2} + \\varepsilon^ {2}}. \\tag {11}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Blur Weighting Loss. We impose an adaptive penalty on the blurred regions of the DP pair  $(\\mathbf{B}_{\\mathrm{L}},\\mathbf{B}_{\\mathrm{R}})$ , considering the degree of blur measured by CLIP. It encourages the network to focus on the restoration of heavily blurred regions. We first normalize the deviations between  $\\hat{\\mathbf{I}}$  and  $\\mathbf{I}$  by the deviations between  $(\\mathbf{B}_{\\mathrm{L}},\\mathbf{B}_{\\mathrm{R}})$  and  $\\mathbf{I}$ , and then re-use the blur map to select blurred regions residing in the DP pair.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\mathrm {b w l}} = \\frac {\\left\\| \\mathbf {I} (i , j) - \\hat {\\mathbf {I}} (i , j) \\right\\| ^ {2}}{\\left\\| \\hat {\\mathbf {I}} (i , j) - \\frac {1}{2} \\left(\\mathbf {B} _ {\\mathrm {L}} (i , j) + \\mathbf {B} _ {\\mathrm {R}} (i , j)\\right) \\right\\| ^ {2}} \\cdot \\mathbf {M} (i, j), \\tag {12}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            508,
+            407,
+            890,
+            460
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where we use the blur map  $\\mathbf{M}$  (with soft logits) to reflect the blur levels detected by CLIP.",
+        "bbox": [
+            498,
+            470,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Blur-aware Loss. We encourage  $\\hat{\\mathbf{I}}$  to be sharp by leveraging the versatile knowledge contained in the CLIP. We generate the blur map  $\\hat{\\mathbf{M}}$  by the blur-aware format for the restoration, and penalize the blur exhibited in  $\\hat{\\mathbf{I}}$ . Similar to  $\\mathcal{L}_{\\mathrm{bw1}}$ , we use the unnormalized version of the blur map,",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\text {b a l}} = \\hat {\\mathbf {M}} (i, j). \\tag {13}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            638,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "This encourages  $\\hat{\\mathbf{M}}$  to be zero, i.e., no blur exists in the restoration.",
+        "bbox": [
+            498,
+            617,
+            888,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Total Loss. Our network is optimized by minimizing the following loss function",
+        "bbox": [
+            498,
+            648,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\text {t o t a l}} = \\frac {1}{| \\Omega |} \\sum_ {(i, j) \\in \\Omega} \\left(\\mathcal {L} _ {\\text {c h a r}} + \\lambda_ {1} \\mathcal {L} _ {\\text {b a l}} + \\lambda_ {2} \\mathcal {L} _ {\\text {b w l}}\\right), \\tag {14}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            522,
+            688,
+            890,
+            726
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\frac{1}{|\\Omega|}$  is a normalization factor determined by the image domain size  $|\\Omega|$ , and  $\\lambda_{1}$  and  $\\lambda_{2}$  are hyperparameters to balance losses.",
+        "bbox": [
+            498,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4. Experiments and Analysis",
+        "text_level": 1,
+        "bbox": [
+            500,
+            800,
+            743,
+            816
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Implementation Details. We implement our model under the PyTorch framework. We use the pre-trained and ViT-B/32 [8] architecture-based CLIP [30] for our blur map estimation strategy. We train the deblurring network in two stages for  $6 \\times 10^{6}$  steps in total with the Adam optimizer.",
+        "bbox": [
+            498,
+            825,
+            890,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "24082",
+        "bbox": [
+            478,
+            944,
+            517,
+            955
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/e6eb4fa16d9dee32b9d8049eeb7788574651949f1c84b8e2ebcaa4d8e7feefee.jpg",
+        "table_caption": [
+            "Table 1. Quantitative comparisons on the DPD-blur dataset [1] composed of 37 indoor and 39 outdoor scenes. We respectively color the best and the second-best performance in red and blue."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"4\">Outdoor Scenes</td><td colspan=\"4\">Indoor Scenes</td><td colspan=\"4\">Average</td><td></td></tr><tr><td>PSNR↑</td><td>SSIM↑</td><td>MAE↓</td><td>RMSE rel↓</td><td>PSNR↑</td><td>SSIM↑</td><td>MAE↓</td><td>RMSE rel↓</td><td>PSNR↑</td><td>SSIM↑</td><td>MAE↓</td><td>RMSE rel↓</td><td>LPIPS↓</td></tr><tr><td>EBDB</td><td>25.77</td><td>0.772</td><td>0.040</td><td>0.051</td><td>21.25</td><td>0.599</td><td>0.058</td><td>0.086</td><td>23.45</td><td>0.683</td><td>0.049</td><td>0.067</td><td>0.336</td></tr><tr><td>DMENet</td><td>25.50</td><td>0.788</td><td>0.038</td><td>0.053</td><td>21.43</td><td>0.644</td><td>0.063</td><td>0.084</td><td>23.41</td><td>0.714</td><td>0.051</td><td>0.067</td><td>0.349</td></tr><tr><td>DPDNet</td><td>27.48</td><td>0.849</td><td>0.029</td><td>0.042</td><td>22.90</td><td>0.726</td><td>0.052</td><td>0.071</td><td>25.13</td><td>0.786</td><td>0.041</td><td>0.055</td><td>0.223</td></tr><tr><td>RDPD</td><td>28.10</td><td>0.843</td><td>0.027</td><td>0.039</td><td>22.82</td><td>0.704</td><td>0.053</td><td>0.072</td><td>25.39</td><td>0.772</td><td>0.040</td><td>0.053</td><td>0.255</td></tr><tr><td>DDDNet</td><td>27.57</td><td>0.833</td><td>0.030</td><td>0.041</td><td>23.28</td><td>0.708</td><td>0.050</td><td>0.068</td><td>25.36</td><td>0.768</td><td>0.041</td><td>0.054</td><td>0.197</td></tr><tr><td>IFAN</td><td>28.66</td><td>0.868</td><td>0.025</td><td>0.037</td><td>23.46</td><td>0.743</td><td>0.049</td><td>0.067</td><td>25.99</td><td>0.804</td><td>0.037</td><td>0.050</td><td>0.207</td></tr><tr><td>BAMBNet</td><td>28.60</td><td>0.872</td><td>0.026</td><td>0.037</td><td>24.30</td><td>0.772</td><td>0.045</td><td>0.060</td><td>26.40</td><td>0.821</td><td>0.036</td><td>0.047</td><td>0.141</td></tr><tr><td>DeepRFT</td><td>28.48</td><td>0.870</td><td>0.025</td><td>0.038</td><td>23.09</td><td>0.736</td><td>0.051</td><td>0.070</td><td>25.71</td><td>0.801</td><td>0.037</td><td>0.051</td><td>0.217</td></tr><tr><td>Restormer</td><td>29.48</td><td>0.895</td><td>0.023</td><td>0.034</td><td>23.97</td><td>0.773</td><td>0.047</td><td>0.063</td><td>26.66</td><td>0.833</td><td>0.035</td><td>0.046</td><td>0.155</td></tr><tr><td>K3DN</td><td>29.87</td><td>0.890</td><td>0.022</td><td>0.032</td><td>24.37</td><td>0.780</td><td>0.046</td><td>0.060</td><td>27.06</td><td>0.835</td><td>0.034</td><td>0.044</td><td>0.187</td></tr><tr><td>Ours (Small)</td><td>29.55</td><td>0.893</td><td>0.021</td><td>0.033</td><td>24.38</td><td>0.773</td><td>0.043</td><td>0.065</td><td>26.91</td><td>0.831</td><td>0.032</td><td>0.045</td><td>0.185</td></tr><tr><td>Ours (Large)</td><td>29.88</td><td>0.896</td><td>0.020</td><td>0.032</td><td>24.73</td><td>0.786</td><td>0.037</td><td>0.059</td><td>27.24</td><td>0.840</td><td>0.028</td><td>0.043</td><td>0.168</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/af59d58c1dfebd5a9ce8d718ea1d57d049685ba95a85e899be9a487dd5dbf731.jpg",
+        "table_caption": [
+            "Table 2. Quantitative comparisons on DDD-syn dataset."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>PSNR↑</td><td>SSIM↑</td><td>MAE↓</td><td>RMSE_rel↓</td></tr><tr><td>EBDB</td><td>26.48</td><td>0.683</td><td>0.036</td><td>0.047</td></tr><tr><td>DMENet</td><td>30.14</td><td>0.939</td><td>0.017</td><td>0.031</td></tr><tr><td>DPDNet</td><td>31.45</td><td>0.926</td><td>0.016</td><td>0.027</td></tr><tr><td>RDPD</td><td>32.42</td><td>0.912</td><td>0.016</td><td>0.024</td></tr><tr><td>DDDNet</td><td>33.21</td><td>0.956</td><td>0.010</td><td>0.022</td></tr><tr><td>IFAN</td><td>34.18</td><td>0.929</td><td>0.012</td><td>0.020</td></tr><tr><td>BAMBNet</td><td>35.90</td><td>0.954</td><td>0.012</td><td>0.016</td></tr><tr><td>DeepRFT</td><td>36.52</td><td>0.952</td><td>0.010</td><td>0.015</td></tr><tr><td>Restormer</td><td>36.44</td><td>0.957</td><td>0.010</td><td>0.015</td></tr><tr><td>K3DN</td><td>38.23</td><td>0.965</td><td>0.008</td><td>0.012</td></tr><tr><td>Ours (Small)</td><td>37.27</td><td>0.959</td><td>0.010</td><td>0.014</td></tr><tr><td>Ours (Large)</td><td>38.62</td><td>0.971</td><td>0.008</td><td>0.012</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "In each stage, the learning rate is decayed from  $2 \\times 10^{-4}$  to  $10^{-6}$  by a cosine annealing strategy. In the first stage, we train the network for  $5 \\times 10^{6}$  steps, and only use the Charbonnier loss  $\\mathcal{L}_{\\mathrm{char}}$ . In the second stage, the network is finetuned for  $1 \\times 10^{6}$  steps with  $\\mathcal{L}_{\\mathrm{total}}$ , where we have  $\\lambda_{1} = 10^{-1}$  and  $\\lambda_{2} = 2 \\times 10^{-1}$ . Code, results, and more details are given in our project page.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Datasets. Our method is evaluated on two real-world DP defocus deblurring datasets, DPD-blur dataset [1] and DPD-disp dataset [27]. We follow [1] on the training and testing splits. For the DPD-disp dataset, we use it for testing only, re-using the checkpoints trained from the DPD-blur dataset as they do not provide ground-truth (GT) data or with limited dataset size. Moreover, two synthetic datasets, DDD-syn [26] and RDPD [2], are also used for evaluations.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Evaluation Metrics. We use peak signal-to-noise ratio (PSNR), structural similarity (SSIM), mean absolute error (MAE), and root mean squared relative error (RMSE_ref) as our evaluation metrics.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Baseline Methods. We compare with SOTA DP defocus deblurring methods, i.e., EBDB [13], DMENet [15],",
+        "bbox": [
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+            468,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/0b0fcfdd19a74488061f44a8fa8e94ab12cff7720ace3d1c6d48eeffabd63eff.jpg",
+        "table_caption": [
+            "Table 3. Quantitative comparisons on RDPD dataset."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>PSNR↑</td><td>SSIM↑</td><td>MAE↓</td><td>RMSE rel↓</td></tr><tr><td>EBDB</td><td>24.23</td><td>0.637</td><td>0.031</td><td>0.054</td></tr><tr><td>DMENet</td><td>25.17</td><td>0.731</td><td>0.036</td><td>0.061</td></tr><tr><td>DPDNet</td><td>29.84</td><td>0.828</td><td>0.032</td><td>0.055</td></tr><tr><td>RDPD</td><td>31.09</td><td>0.861</td><td>0.025</td><td>0.028</td></tr><tr><td>DDDNet</td><td>30.14</td><td>0.840</td><td>0.016</td><td>0.031</td></tr><tr><td>IFAN</td><td>31.12</td><td>0.865</td><td>0.023</td><td>0.028</td></tr><tr><td>BAMBNet</td><td>31.78</td><td>0.867</td><td>0.016</td><td>0.026</td></tr><tr><td>DeepRFT</td><td>31.71</td><td>0.879</td><td>0.016</td><td>0.024</td></tr><tr><td>Restormer</td><td>32.27</td><td>0.871</td><td>0.016</td><td>0.024</td></tr><tr><td>K3DN</td><td>32.84</td><td>0.905</td><td>0.014</td><td>0.023</td></tr><tr><td>Ours (Small)</td><td>32.98</td><td>0.895</td><td>0.014</td><td>0.022</td></tr><tr><td>Ours (Large)</td><td>33.44</td><td>0.907</td><td>0.013</td><td>0.021</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "DPDNet [1], RDPD [2], DDDNet [26], IFAN [16], BAMBNet [20], DeepRFT [22], Restormer [39], and K3DN [38].",
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.1. Comparisons with State-of-the-Art",
+        "text_level": 1,
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "Quantitative Comparison. We compare with the SOTA methods on the DPD-blur, DDD-syn, and RDPD datasets in Tab. 1, Tab. 2, and Tab. 3, respectively. Our observations are as follows: i) With our model (Small), we achieve similar restoration results with Restormer and K3DN, the third-best and second-best method, in all datasets. ii) When scaling to the large model, we consistently outperform all methods on all evaluation metrics. For example, our method, K3DN, and Restormer respectively achieve 27.24/27.06/26.66, 38.62/38.23/36.44, and 33.44/32.84/32.27 PSNR (dB) in the DPD-blur, DDD-syn, and RDPD datasets. Meanwhile, on a single RTX 4090 GPU, we remain to have a lower Infer. time (including CLIP) which is 0.042s and 0.054s for our small and large models, while K3DN/Restormer takes 0.198s/0.255s.",
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Qualitative Comparison. We compare with state-of-the-art methods on the DPD-blur dataset (Fig. 6). As shown, our",
+        "bbox": [
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+        "image_caption": [
+            "Blurry Image"
+        ],
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+            "GT Image"
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+            "IFAN [16]"
+        ],
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/a38e83a781b12c8e4eee01d3784d2ce81064db85b5dc3eb35f35492a454af57f.jpg",
+        "image_caption": [
+            "DeepRFT [22]",
+            "Blurry Image",
+            "DeepRFT [22]"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            166,
+            234,
+            401,
+            356
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/d00923ce4f24847248c6927585b5be800a6d3253de2729faa764a9b0ad1da0f9.jpg",
+        "image_caption": [
+            "GT Image"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            406,
+            234,
+            500,
+            284
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/10c56ea97f9d68316bbdc7475b929b6f2caba95210b120acf0a3e447d2f67f52.jpg",
+        "image_caption": [
+            "Restormer [39]",
+            "Blurry Image"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            504,
+            234,
+            599,
+            284
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/c1cba08fd1c437d5faf95cc4c61b001bbfec7982372d7fff8b5e1e2745bb5b7f.jpg",
+        "image_caption": [
+            "K3DN [38]",
+            "IFAN [16]"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            604,
+            234,
+            697,
+            284
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/3deff5e3099745779cb9d782a3227a6d95e4b9a3129e3a16d70ece208f2f3ad0.jpg",
+        "image_caption": [
+            "Ours",
+            "DDDNet [26]"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            702,
+            234,
+            797,
+            284
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/e6d883e27feceebacbcd4f766c2154c76680ba300f69277ab319b309a3c8e21d.jpg",
+        "image_caption": [
+            "Figure 6. Qualitative comparison on the DPD-blur dataset [1]. We present the blurry image  $(\\mathbf{B}_{\\mathrm{L}})$  in the first column, and the ground truth (GT) image of regions residing in the red bounding box is shown in the second column. The cropped blurred image of the red bounding box region is in the third column."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            406,
+            308,
+            500,
+            356
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/0e2e56ebeb48ea5db23dc965bdb40ba0b1498af169039040fd80561846390f0d.jpg",
+        "image_caption": [
+            "Restormer [39]"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            504,
+            308,
+            599,
+            356
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/a3ae7e7d550322b212db7574819d25fe9d264c840e13caffee136fba8e2865e6.jpg",
+        "image_caption": [
+            "K3DN [38]"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            604,
+            308,
+            697,
+            356
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/3fe1437ecf8035033a05d2376d9f62d1fd4e4038bc29755523e7b1a9b1a2cddc.jpg",
+        "image_caption": [
+            "Ours"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            702,
+            308,
+            797,
+            356
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "method performs sharper and clearer restorations of edges and texts. To further demonstrate the benefits of using CLIP to generate the blur mask unsupervisedly in our approach, we provide an example in Fig. 7, which preserves sharp regions (e.g., text 'University') in the input blur image effectively compared to the second-best baseline.",
+        "bbox": [
+            75,
+            434,
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+            525
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/49d024ddac1a93a08d0f3ae7a68f2ae2039e91b0ac1850f8d2dcdedd2fdd5610.jpg",
+        "image_caption": [
+            "(a) Input",
+            "Figure 7. An example of the restoration results on the sharp region of the input DP image (left view)."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            81,
+            529,
+            176,
+            569
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/e3c81256f7e09608a955ef70e91d56ce26e088b522210737345b94a264481924.jpg",
+        "image_caption": [
+            "(b) K3DN"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            179,
+            529,
+            272,
+            569
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/fbad7c91f69532a328961c39f21d686aa4cff8de248434c3a6ea5e0377a8515b.jpg",
+        "image_caption": [
+            "(c) Restormer"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            274,
+            529,
+            369,
+            569
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/7d412d6a06994209392d2827b7c200204608fe6290bf8376b7f031b3173930e4.jpg",
+        "image_caption": [
+            "(d) Ours"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            370,
+            529,
+            465,
+            569
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.2. Ablation Study",
+        "text_level": 1,
+        "bbox": [
+            76,
+            619,
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+            636
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We study model architecture, blur map estimation, and losses in this section. All experiments are performed in the DPD-blur dataset.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Ablation of Model Architecture. We study the effective usage of blur map as prior knowledge for DP defocus deblurring (Tab. 6). To show the benefits of using blur maps, we consider four baselines: i) NAFNet [5], the baseline model; ii) Concat, concatenating the blur map with the DP pair before feeding to the model; iii) SA, using the self-attention layer [8] in Eq. 8 to the model only; iv) Concat+SA, combines the Concat and SA settings; v) BPA block, using kernel priors from the blur map to assist deblurring. Our model consistently outperforms all baselines, which indicates the effectiveness of using the blur map.",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Ablation of Losses. We investigate the proposed blur weighting loss  $\\mathcal{L}_{\\mathrm{bw}}$  and blur-aware loss  $\\mathcal{L}_{\\mathrm{bal}}$  (Tab. 7) with a baseline as the  $\\mathcal{L}_{\\mathrm{char}}$  setting. We first use  $\\mathcal{L}_{\\mathrm{bw}}$  and  $\\mathcal{L}_{\\mathrm{bal}}$",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "to our baseline, NAFNet (i.e., not using our BPA block), that only uses  $\\mathcal{L}_{\\mathrm{char}}$ , having 0.32 PSNR (dB) improvements. Secondly, we train our model (backbone + BPA block) with Charbonnier loss, resulting in 26.71/0.825 higher PSNR (dB)/SSIM. By using the  $\\mathcal{L}_{\\mathrm{bwl}}$  or  $\\mathcal{L}_{\\mathrm{bal}}$ , we respectively achieve 0.05/0.003 or 0.10/0.004 higher PSNR (dB)/SSIM. Combining all losses, we have the best restoration performance at 26.91/0.831 for PSNR (dB)/SSIM. Moreover, we verify the generalization ability of our  $\\mathcal{L}_{\\mathrm{bwl}}$  and  $\\mathcal{L}_{\\mathrm{bal}}$  losses on state-of-the-art networks, improving PSNR of Restormer and DeepRFT by 0.25 and 0.41 PSNR (dB).",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Ablation of Blur Map Estimation. We ablate with different prompts used to generate the blur map. The blur-aware and DP-aware prompts are presented in Tab. 4, and we show their impact on model performance with Tab. 5. We then ensemble the groups of blur-aware prompt and disparity-aware prompt individually (Ens. $^1$ ), leading to  $26.80\\mathrm{dB} / 0.829$  and  $26.84 / 0.830$  PSNR (dB)/SSIM. By assembling all prompts (Ens. $^2$ ), we have  $26.91 / 0.831$  PSNR (dB)/SSIM, consistently outperforming other approaches of generating blur masks.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.3. Discussion and Limitation",
+        "text_level": 1,
+        "bbox": [
+            498,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Discussion. The reader may wonder about the performance of our unsupervised blur map estimation strategy. Therefore, we perform two qualitative evaluations on the DPD-disp dataset, where the GT disparity is included. We compare with BAMBNet [20] and DPD-disp [27].",
+        "bbox": [
+            496,
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+            869
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "First, we consider blur map estimation. To obtain the GT blur map, the pixel with disparity  $d$  that satisfies  $|d|\\leq 1$",
+        "bbox": [
+            498,
+            869,
+            890,
+            900
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "24084",
+        "bbox": [
+            478,
+            944,
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+            955
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/054057e6ea0ca3eda4da11297624db98f45cdf17840b5131bb678044b149f705.jpg",
+        "table_caption": [
+            "Table 4. Prompts used for blur map estimation."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>Blur-aware Prompt</td><td>DP-aware Prompt</td></tr><tr><td>p1</td><td>[A blurry image.]</td><td>[A symmetrical image.]</td></tr><tr><td>p2</td><td>[An obscured image.]</td><td>[A horizontally symmetrical image.]</td></tr><tr><td>p3</td><td>[An out of focus image.]</td><td>[A left-right symmetrical image.]</td></tr><tr><td>p4</td><td>[An image lacking sharpness.]</td><td>[A symmetrical image at the pixel level.]</td></tr></table>",
+        "bbox": [
+            81,
+            103,
+            883,
+            189
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/fd845bada4709046aa36c7bcda4835ebe18691ddb98faac64d34b125b6988318.jpg",
+        "table_caption": [
+            "Table 5. Restoration performance of our methods by using blur-aware or/and DP-aware prompts for blur map estimation. Ens.  ${}^{1}$  denotes ensembling the group of blue-aware prompts and DP-aware prompts individually, and Ens.  ${}^{2}$  ensembles all prompts."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\"></td><td colspan=\"4\">Blur-aware Prompt</td><td colspan=\"4\">DP-aware Prompt</td></tr><tr><td>PSNR↑</td><td>SSIM↑</td><td>MAE↓</td><td>RMSE_rel↓</td><td>PSNR↑</td><td>SSIM↑</td><td>MAE↓</td><td>RMSE_rel↓</td></tr><tr><td>p1</td><td>26.83</td><td>0.829</td><td>0.033</td><td>0.045</td><td>26.82</td><td>0.830</td><td>0.033</td><td>0.046</td></tr><tr><td>p2</td><td>26.81</td><td>0.829</td><td>0.033</td><td>0.046</td><td>26.83</td><td>0.830</td><td>0.032</td><td>0.046</td></tr><tr><td>p3</td><td>26.75</td><td>0.828</td><td>0.034</td><td>0.046</td><td>26.82</td><td>0.830</td><td>0.033</td><td>0.046</td></tr><tr><td>p4</td><td>26.77</td><td>0.829</td><td>0.033</td><td>0.046</td><td>26.85</td><td>0.830</td><td>0.032</td><td>0.045</td></tr><tr><td>Ens.1</td><td>26.80</td><td>0.829</td><td>0.033</td><td>0.046</td><td>26.84</td><td>0.830</td><td>0.032</td><td>0.046</td></tr><tr><td>Ens.2</td><td>26.91</td><td>0.831</td><td>0.032</td><td>0.045</td><td>26.91</td><td>0.831</td><td>0.032</td><td>0.045</td></tr></table>",
+        "bbox": [
+            78,
+            222,
+            892,
+            354
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/1304abdac5fba0c5de280780e68e59e9f90789abc3022ac3f19f817492955c6a.jpg",
+        "table_caption": [
+            "Table 6. Ablation of model components."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Setting</td><td>PSNR↑</td><td>SSIM↑</td><td>MAE↓</td><td>RMSE rel↓</td></tr><tr><td>i) NAFNet</td><td>26.21</td><td>0.817</td><td>0.038</td><td>0.049</td></tr><tr><td>ii) Concat</td><td>26.76</td><td>0.826</td><td>0.033</td><td>0.046</td></tr><tr><td>iii) SA</td><td>26.59</td><td>0.824</td><td>0.036</td><td>0.047</td></tr><tr><td>iv) Concat + SA</td><td>26.80</td><td>0.829</td><td>0.032</td><td>0.046</td></tr><tr><td>v) BPA block</td><td>26.91</td><td>0.831</td><td>0.032</td><td>0.045</td></tr></table>",
+        "bbox": [
+            78,
+            387,
+            488,
+            487
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/e3c0811b2d01731d6a2a8a170cbde36ffd7f4ea5ecea06901cbe448122af2fd0.jpg",
+        "table_caption": [
+            "Table 7. The effectiveness of losses."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>BPA block</td><td>Loss</td><td>PSNR↑</td><td>SSIM↑</td><td>MAE↓</td><td>RMSE rel↓</td></tr><tr><td>X</td><td>Lchar</td><td>26.21</td><td>0.817</td><td>0.038</td><td>0.049</td></tr><tr><td>X</td><td>Ltotal</td><td>26.53</td><td>0.822</td><td>0.036</td><td>0.047</td></tr><tr><td>✓</td><td>Lchar</td><td>26.71</td><td>0.825</td><td>0.034</td><td>0.046</td></tr><tr><td>✓</td><td>Lchar + Lbwl</td><td>26.76</td><td>0.828</td><td>0.033</td><td>0.046</td></tr><tr><td>✓</td><td>Lchar + Lbal</td><td>26.81</td><td>0.829</td><td>0.032</td><td>0.046</td></tr><tr><td>✓</td><td>Ltotal</td><td>26.91</td><td>0.831</td><td>0.032</td><td>0.045</td></tr></table>",
+        "bbox": [
+            78,
+            520,
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+            640
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "is used as the sharp pixel, reversely, it is a buried pixel. Our method, BAMBNet [20] and DPD-disp [27] respectively have  $89.8\\% / 70.2\\% / 88.3\\%$  accuracy (the higher, the better), showing the effectiveness of our method.",
+        "bbox": [
+            75,
+            656,
+            468,
+            717
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Second, we explore disparity estimation. The log-its of our unnormalized blurred map are potentially linearly correlated with the ground-truth disparity. Therefore, we compare with the state-of-the-art DP disparity estimation method, DPD-disp [27]. Following [9, 27], we use AI(1), AI(2), and  $1 - |\\rho_s|$  as the evaluation metrics (the lower, the better). The AI(1), AI(2), and  $1 - |\\rho_s|$  of our method, BAMBNet, and DPD-disp are 0.063/0.106/0.069, 0.130/0.184/0.096, 0.306/0.772/0.0159. Though our blur map is estimated with a single forward pass, we still achieve a reasonable performance in the disparity estimation. This potentially explains the high performance of our DP defo",
+        "bbox": [
+            75,
+            719,
+            472,
+            901
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "cus deblurring network, as obtaining the disparity prior benefits the defocus task.",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Limitation. As the image encoder of CLIP is trained under a classification-alike pre-training task, it will focus more on local details that help identify its scene class. Textureless regions would produce non-significant semantic reactions, e.g., large areas of wall, ceiling, or floor, and reduce the quality of the estimated blur map. It is possible to use a vision language framework that drives more sensitivity to regions with less texture.",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5. Conclusion and Broader Impact",
+        "text_level": 1,
+        "bbox": [
+            498,
+            553,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we study end-to-end defocus deblurring of DP images, leveraging the blur-related prior knowledge from the CLIP. We first estimate a blur map with an ensemble of blur-aware and DP-aware strategies, and then use the estimated blur map as the deblurring kernel prior to restoring the DP image. We also propose a blur-aware and blur-weighting loss to regularize the restorations of the DP images during training, by distilling the knowledge of blur from CLIP. In extensive experiments, our method outperforms past works by a large margin in quantitative and qualitative restoration performance.",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Broader Impact. The proposed DP-aware strategy is promising to apply and extend CLIP to diverse zero-shot stereo vision tasks. We hope it will motivate future work.",
+        "bbox": [
+            496,
+            755,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Acknowledgment. This work was supported in part by the Beijing Institute of Technology Research Fund Program for Young Scholars, BIT Special-Zone, and National Natural Science Foundation of China 62302045, and Miaomiao Liu was supported by the ARC fellowship and Discovery Project grant (DE180100628, DP200102274).",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "page_number",
+        "text": "24085",
+        "bbox": [
+            478,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
+            78,
+            89,
+            174,
+            106
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
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+            "[3] Abdullah Abuolaim, Mahmoud Affi, and Michael S Brown. Improving single-image defocus deblurring: How dual-pixel images help through multi-task learning. In Proceedings of the IEEE/CVF Winter Conference on Applications of Computer Vision, pages 1231–1239, 2022. 1, 2, 4",
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+            "[5] Liangyu Chen, Xiaojie Chu, Xiangyu Zhang, and Jian Sun. Simple baselines for image restoration. In Computer Vision-ECCV 2022: 17th European Conference, Tel Aviv, Israel, October 23-27, 2022, Proceedings, Part VII, pages 17-33. Springer, 2022. 5, 7",
+            "[6] Myungsub Choi, Hana Lee, and Hyong-euk Lee. Exploring positional characteristics of dual-pixel data for camera autofocus. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 13158-13168, 2023. 1",
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2024/LDP_ Language-driven Dual-Pixel Image Defocus Deblurring Network/2d70b048-ecc7-45e4-b194-27af8843d7f3_origin.pdf

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2024/LDP_ Language-driven Dual-Pixel Image Defocus Deblurring Network/full.md

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+# LDP: Language-driven Dual-Pixel Image Defocus Deblurring Network
+
+Hao Yang $^{1}$ , Liyuan Pan $^{1\dagger}$ , Yan Yang $^{2}$ , Richard Hartley $^{2}$ , and Miaomiao Liu $^{2}$ $^{1}$ Beijing Institute of Technology  
+ $^{2}$ Australian National University
+
+{hao.yang, liyuan.pan}@bit.edu.cn, {yan.yang, richard.hartley, miaomiao.liu}@anu.edu.au
+
+# Abstract
+
+Recovering sharp images from dual-pixel (DP) pairs with disparity-dependent blur is a challenging task. Existing blur map-based deblurring methods have demonstrated promising results. In this paper, we propose, to the best of our knowledge, the first framework that introduces the contrastive language-image pre-training framework (CLIP) to accurately estimate the blur map from a DP pair unsupervisedly. To achieve this, we first carefully design text prompts to enable CLIP to understand blur-related geometric prior knowledge from the DP pair. Then, we propose a format to input a stereo DP pair to CLIP without any fine-tuning, despite the fact that CLIP is pre-trained on monocular images. Given the estimated blur map, we introduce a blur-prior attention block, a blur-weighting loss, and a blur-aware loss to recover the all-in-focus image. Our method achieves state-of-the-art performance in extensive experiments (see Fig. 1).
+
+# 1. Introduction
+
+Defocus deblurring from a single image is an ill-posed problem [19, 28, 29, 33]. Compared to methods that restore an all-in-focus image directly [1, 2], blur map-based deblurring methods have demonstrated promising results [16, 26]. To simplify the blur removal process, several works [20, 34, 38] have utilized recent innovative dual-pixel (DP) sensors [6] to estimate blur maps, since the DP sensor captures a two-view image pair (a DP pair) in a single shot. The DP pair can be treated as images from a two-sample light field camera or a stereo system [24] with a tiny baseline [27, 34], which is beneficial for disparity estimation [1, 14, 23, 42]. Based on the DP image pair formation process, the disparity is geometrically related to the blur map, i.e., the degree of defocus blur proportional to disparity magnitudes [9].
+
+For estimating the blur map (defocus map or disparity
+
+![](images/4289276f10163e17c2dd9aa619e2d3d885516c5673317bc1d8f7f482698b7003.jpg)  
+Figure 1. Comparison of performance in terms of PSNR and Inference time. Our small and large models are respectively denoted by the Blue and Red cycles. The Green triangles represent previous state-of-the-art methods, and each of them is annotated with the method name, publication venue, and year. This figure is best viewed in color on the screen.
+
+map), previous works either require extra data [3, 26], such as synthetic data, for supervision signals, or pre-calibrated blur kernels [34]. To avoid using extra information, several works explored unsupervised blur map estimation frameworks [16, 20]. Lee et al. [16] implicitly estimate the disparity of the left/right views using a spatial transformer, yet only in feature space, as well as Yang et al. [38]. Liang et al. [20] use fixed network branches for layer-wise defocus map estimation and deblurring, where the limited network branch number restricts the potential of its accuracy.
+
+Recently, the contrastive language-image pre-training framework (CLIP) [30] has accomplished extraordinary success for vision tasks, such as semantic segmentation [31, 37], object detection [32], and point cloud understanding [40]. Therefore, a question naturally arises, can we avoid the cost of collecting data and model designing, to estimate the blur map unsupervisedly by using CLIP? Unfortunately, using semantic knowledge from CLIP to handle low-level vision tasks is underexplored.
+
+In this paper, for the first time, we explore the relationship between language and blur map estimation by applying CLIP. Note that CLIP is trained to match a monocular image with its corresponding language descriptions. Given a blurred image, it is intuitive to match it with a corre
+
+sponding text [A blurry image.], which allows the language model to find the blurred regions in an image. However, it is hard to quantize the blur level of an image without knowing its associated latent sharp one [25].
+
+Fortunately, we can leverage the capabilities of DP sensors. With DP pairs, blur quantization becomes possible without the need for its associated sharp image. The formation of DP ensures no disparity between left/right views for pixels in sharp regions, while a noticeable disparity exists for pixels in blurred regions. In essence, the detectable differences (disparities) in left/right views of a DP pair directly indicate the degree of defocus blurs. Consequently, we can quantify the variation between the left and right views, treating it as a valuable cue for estimating a blur map.
+
+However, CLIP still finds it challenging to simultaneously explore stereo DP pairs with left/right view images. To address this issue, we propose to explore the DP pair and design an 'image and text' format to better capture the blurs in the image. Specifically, we propose to create a new image from the DP pair and translate the description about the 'blurriness' of the image to measure the 'symmetry' of the newly formed image, which is based on the DP image formation process. The freshly designed image-text format allows the CLIP to estimate the blur map easily (see Sec. 3.1).
+
+Given the estimated blur map, we then restore the all-in-focus image from the DP pair. By observing that the attention map of the self-attention mechanism [8] can be used in the dynamic DP deblurring process, we introduce a blur prior attention (BPA) that modulates the attention map with the estimated blur map which provides prior knowledge of deblurring kernels (see Sec. 3.2).
+
+To regulate the restoration, we specifically design two losses that are based on CLIP. Considering the network should focus more on heavily blurred regions, we propose a blur-weighting loss that imposes an adaptive penalty proportional to the blur degrees provided by the estimated blur map from CLIP. Then, to guarantee the restored image is sharp, we use CLIP to re-check the restored image and formulate a blur-aware loss (see Sec. 3.3).
+
+Our contributions are summarised as follows:
+
+- We propose a Language-driven DP (LDP) defocus deblurring framework, by exploring the potential of CLIP in the low-level vision task.  
+- We design an image-text format for blur map estimation based on the geometric relationship between the blur and disparity of the DP pair.  
+- We propose a blur prior attention (BPA) block, a blur-weighting loss, and a blur-aware loss to encourage sharp restorations of the DP pair.
+
+We evaluate the proposed framework extensively on standard benchmark datasets. Though using the largescale foundation model, CLIP, for blur map estimation, our method achieves Pareto-optimality between deblurring performance and inference speed (refer to Fig. 1 for an
+
+overview of the comparison).
+
+# 2. Related Work
+
+DP Defocus Deblurring. DP-based deblurring methods can be divided into single- and multi-task manners. For single-task based deblurring [1-3], methods apply different kernels at different regions of the DP pair to handle the spatially varying defocus deblur. This can usually be achieved by using parallel atrous convolutions [33], attention mechanisms [39], or deformable convolutions [17]. For multi-task deblurring methods, the blur/defocus/disparity map is auxiliarily estimated to benefit DP defocus deblurring. Pan et al. [26] and Xin et al. [34] use the estimated DP disparity to regularise the restoration through reblurring; however, with extra data or pre-calibrate kernel. Several works explored unsupervised defocus map (or disparity) estimation. Lee et al. [16] and Yang et al. [38] estimate defocus disparity only in feature space without explicitly showing a defocus map. Liang et al. [20] optimize a multi-channel defocus map based on [27]. However, hyperparameters, such as the defocus threshold and the number of channels, are preset, limiting blur map estimation accuracy. Unlike past works, by transferring the blur-related geometric prior knowledge into semantic prompts, we unsupervisedly estimate the blur map from CLIP to benefit defocus deblurring.
+
+Language-driven Vision. Common objectives in visual-language learning are aligning the text with a paired image in the embedding space [21, 30, 35]. The CLIP, one of the milestone achievement in the area, demonstrate that language-independent computer vision tasks can be substantially benefited from visual-language learning, by achieving SOTA zero-shot classification performance in the ImageNet-1K benchmark [7]. Successive works have extended the zero-shot learning capability of CLIP to semantic segmentation [31, 44], monocular depth estimation [4, 10, 41], and point clouds [11, 40]. However, none of the existing works explores the zero-shot learning capability of CLIP in stereo/DP pairs. This paper proposes the first approach to use the monocular image-trained CLIP in zero-shot blur map segmentation of DP pairs.
+
+# 3. Method
+
+Let us now introduce our language-driven dual-pixel image defocus deblurring framework. Given a defocus blurred DP pair  $(\mathbf{B}_{\mathrm{L}},\mathbf{B}_{\mathrm{R}})$ , we aim to restore an all-in-focus image  $\mathbf{I}$  where  $\mathbf{B}_{\mathrm{L}}$  and  $\mathbf{B}_{\mathrm{R}}$  are the left and right view of a DP pair and  $\mathbf{B}_{\mathrm{L}},\mathbf{B}_{\mathrm{R}},\mathbf{I}\in \mathbb{R}^{h\times w\times 3}$ . Here,  $h$  and  $w$  define the image height and width, respectively.
+
+We first design a DP-aware prompt to adapt CLIP to output a blur map,  $\mathbf{M} \in \mathbb{R}^{h \times w \times 1}$ , which quantizes disparity unsupervisedly between  $\mathbf{B}_{\mathrm{L}}$  and  $\mathbf{B}_{\mathrm{R}}$ . Then, we propose a BPA block based network which employs the blur
+
+![](images/990fe983387e39d2f8b277fcf1f9eba3549aaf603c220bf2942e5ea3d19158d0.jpg)  
+Figure 2. Overall architecture. Given a DP pair  $(\mathbf{B}_{\mathrm{L}},\mathbf{B}_{\mathrm{R}})$ , we first generate a blur map  $\mathbf{M}$  by using our unsupervised blur map estimation strategy which is based on the CLIP with assembling format. We then forward the DP pair  $(\mathbf{B}_{\mathrm{L}},\mathbf{B}_{\mathrm{R}})$  to our deblurring backbone composed of an encoder and a decoder. Meanwhile, we have multiple BPA blocks, using the blur map  $\mathbf{M}$  as deblurring kernel prior to refine the intermediate backbone feature embeddings. In the following, we have the restoration  $\hat{\mathbf{I}}$ . The deblurring network is optimized with three losses, charbonnier loss  $\mathcal{L}_{char}$ , blur weighting loss  $\mathcal{L}_{bwl}$ , and blur aware loss  $\mathcal{L}_{bal}$ .  $\mathcal{L}_{char}$  penalizes deviations from  $\mathbf{I}$  in the resorption  $\hat{\mathbf{I}}$ .  $\mathcal{L}_{bwl}$  and  $\mathcal{L}_{bal}$  regularize the restoration by imposing an adaptive penalty on the blurred regions of the DP pair, and leveraging unsupervised blur map estimation strategy to encourage the restoration to be sharp, i.e., the blur map  $\hat{\mathbf{M}}$  for the restoration  $\hat{\mathbf{I}}$  is zero value filled.
+
+map  $\mathbf{M}$  as deblurring priors to restore a sharp image  $\hat{\mathbf{I}}$  from  $(\mathbf{B}_{\mathrm{L}},\mathbf{B}_{\mathrm{R}})$ . To regularize the restoration of  $\hat{\mathbf{I}}$ , a blur-weighting loss  $\mathcal{L}_{\mathrm{bwl}}$  and a blur-aware loss  $\mathcal{L}_{\mathrm{bal}}$  are also introduced that were underpinned by our unsupervised blur map estimation strategy. The overall framework is shown in Fig. 2. Details are presented below.
+
+# 3.1. Unsupervised Blur Map Estimation
+
+Preliminary. CLIP respectively embeds an image and a text description into a common semantic space of dimension  $c$  with an image encoder and a text encoder, obtaining image embedding  $\mathbf{f} \in \mathbb{R}^c$  and text embedding  $\mathbf{t} \in \mathbb{R}^c$ . By optimizing a contrastive loss, the embeddings of the aligned image and text pair,  $\Omega_a$ , stay similar, i.e., maximizing the semantic similarity by  $\max_{\mathbf{f}, \mathbf{t} \in \Omega_a} \sin(\mathbf{f}, \mathbf{t})$ , where  $\sin(\cdot, \cdot)$  is the cosine similarity metric. Meanwhile, the semantics of misaligned pairs,  $\Omega_{na}$  are pushed away from each other, i.e.,  $\min_{\mathbf{f}, \mathbf{t} \in \Omega_{na}} \sin(\mathbf{f}, \mathbf{t})$ . With comprehensive training data, CLIP can be leveraged to align images with pre-defined prompt templates composed of open-world text descriptions for zero-shot learning [30].
+
+For a DP pair, the disparity  $d$  for a pixel in the left view is defined by its location  $(i,j)$  and that of its corresponding pixel at  $(i,k)$  in the right view.
+
+In the literature, this DP disparity [27] is defined as
+
+$$
+d = j - k = A (r (z)) \cdot B (z), \mathbf {B} _ {\mathrm {L}} (i, j) = \mathbf {B} _ {\mathrm {R}} (i, k), \tag {1}
+$$
+
+where  $\mathbf{B}_{\mathrm{L}}(i,j)$  and  $\mathbf{B}_{\mathrm{R}}(i,k)$  are the intensity of the two matching points,  $r(\cdot)$  is a function of the radius of the circle of confusion,  $z$  is the point depth, and  $A(r(z))$  and  $B(z)$  are lens-dependent constants [2, 9, 26, 34].
+
+Analysis. Leveraging the CLIP, zero-shot blur map estimation can be generally divided into three steps. i) Image Encoding. Considering the image encoder of the CLIP is trained with monocular RGB images, a function  $\eta (\cdot ,\cdot)$  is
+
+required to create a new monocular image from the DP image pair  $(\mathbf{B}_{\mathrm{L}},\mathbf{B}_{\mathrm{R}})$ . To obtain the dense embedding for the blur map estimation task, we follow [41] to pop out the final pooling layer from the image encoder, yielding an embedding matrix  $\mathbf{F}\in \mathbb{R}^{h_s\times w_s\times c}$ , where  $h_s$  and  $w_{s}$  are the height and width for embedding of the newly created image, respectively. Mathematically, we have
+
+$$
+\mathbf {F} = \operatorname {I m a g e E n c o d e r} \left(\eta \left(\mathbf {B} _ {\mathrm {L}}, \mathbf {B} _ {\mathrm {R}}\right)\right). \tag {2}
+$$
+
+Each pixel of  $\mathbf{F}$  has encoded the local semantic information for a corresponding region in  $\eta (\mathbf{B}_{\mathrm{L}},\mathbf{B}_{\mathrm{R}})$ . ii) Text Encoding. A text encoder is used to embed the semantics of a prompt p describing the blur into the text embedding,
+
+$$
+\mathbf {t} = \operatorname {T e x t E n c o d e r} (\mathfrak {p}). \tag {3}
+$$
+
+iii) Blur map estimation. Let  $\mathbf{F}(i,j)$  be a c-dimensional embedding at position  $(i,j)$  of  $\mathbf{F}$ ,  $i\in \{1,\dots ,\mathrm{h}_{\mathrm{s}}\}$ , and  $j\in \{1,\dots ,\mathrm{w}_{\mathrm{s}}\}$ . The embedding  $\mathbf{F}(i,j)$  and the blur semantic-based text embedding  $\mathbf{t}$  are expected to be similar if the pixel at  $(i,j)$  is blurred. Therefore, the blur mask  $\mathbf{M}_{\mathbf{F}}$  of  $\eta (\mathbf{B}_{\mathrm{L}},\mathbf{B}_{\mathrm{R}})$  is obtained by
+
+$$
+\mathbf {M} _ {\mathbf {F}} (i, j) = \sigma (\operatorname {s i m} (\mathbf {F} (i, j), \mathbf {t})) . \tag {4}
+$$
+
+Note,  $\sigma (\cdot)$  normalizes the cosine similarity  $\mathfrak{sim}(\cdot ,\cdot)$  output to a probability space, to reflect the degree of blur at the position. Here,  $\mathbf{M}_{\mathbf{F}}$  is sampled to have the same resolution as  $\mathbf{B}_{\mathrm{L}}$  or  $\mathbf{B}_{\mathrm{R}}$ , returning  $\mathbf{M}\in \mathbb{R}^{h\times w\times 1}$ .
+
+Given the analysis above, our goal is to develop text prompts  $\mathfrak{p}$ , while adapting the function  $\eta(\cdot, \cdot)$ , to enable the use of semantic information from CLIP to generate the blur map  $\mathbf{M}$  in an unsupervised manner. In particular, we explore the blur-aware, DP-aware, and ensembling formats with detailed presented below.
+
+![](images/18d45b8a20b3eaa4186ec61cbe6d094c70506c392e53a5046bae28f16976d1a4.jpg)  
+Figure 3. The pipeline of our DP-aware format for obtaining the blur map  $\mathbf{M}$ . Given a DP pair  $(\mathbf{B}_{\mathrm{L}},\mathbf{B}_{\mathrm{R}})$ , the function  $\eta (\mathbf{B}_{\mathrm{L}},\mathbf{B}_{\mathrm{R}}^{h})$  concatenates the left view  $\mathbf{B}_{\mathrm{L}}$  and with horizontally flipped right view  $\mathbf{B}_{\mathrm{R}}^{h}$  for obtaining the  $\mathbf{F}$  from the CLIP image encoder. We then apply  $\alpha (F)$  to averagely pool the feature map according to the transformation imposed on the input DP pair, resulting in a new feature embedding with the same aspect ratio of the input DP pair. Meanwhile, we set the prompts  $\mathfrak{p}$  to describe the symmetry of  $\eta (\mathbf{B}_{\mathrm{L}},\mathbf{B}_{\mathrm{R}}^{h})$ , obtaining text embedding  $\mathbf{t}$ . We finally have the blur map  $\mathbf{M}$  by computing Eq. 6 and performing sampling.
+
+Blur-aware Format. An intuitive approach is setting a prompt  $\mathbf{p}$  that describes the blur to query a blur map  $\mathbf{M}$ , e.g.,  $\mathbf{p} = [\mathrm{A~blurry~image}.]$ . The  $\eta(\cdot, \cdot)$  is then defined to synthesize a center view of the DP pair by averaging the left view  $\mathbf{B}_{\mathrm{L}}$  and right view  $\mathbf{B}_{\mathrm{R}}$ , as the average of two sub-images is equivalent to the image captured by a regular sensor [3, 27]. However, the disparity information among the DP pair is neglected, resulting in a sub-optimal blur map. Refer to Fig. 4 for comparisons.
+
+DP-aware Format. Based on the DP image formation process, the disparity is proportional to the degree of blur exhibited in the DP view [1]. We thus propose to guide CLIP to understand the disparity exhibited between  $\mathbf{B}_{\mathrm{L}}$  and  $\mathbf{B}_{\mathrm{R}}$  which eventually leads to better mask (M) generation. To this end, we first formulate the disparity in the DP pair and then study the disparity-aware prompt and function  $\eta (\cdot ,\cdot)$  designing. Such design leads us to query degrees of displacement between the left and right view from the CLIP, without any fine-tuning, to obtain the blur map M.
+
+Note that the CLIP is the vision-text alignment model trained with monocular image input. To extract the displacement between left/right views of the DP pair, we explore several input-prompt formats: i) Concatenating the left and right views horizontally, and prompting their difference, e.g., [The left and right of the image are different.]; ii) Prompting the horizontal symmetry between the left and right views, e.g., [A horizontally symmetric image.] (Fig. 3).
+
+Empirically, we achieve the best performance with the second prompt format. When describing the symmetry in
+
+![](images/36370877f7d879fc524e4ff8f9994de1b61705a140a2a3adf717c1156d906117.jpg)  
+(a)
+
+![](images/2adfbde67b3773aad6a74b04d1253cf65b912abc73088b937b9bfadbd6a43017.jpg)  
+(b)
+
+![](images/b0872cd650385ca4ec8a5634d760a6ffa4998117d1739009563c34e8098ffa4a.jpg)  
+(c)  
+Figure 4. Example of blur map estimation (the darker, the sharper). (a) The left view of the DP image. (b) and (c) Blur maps obtained with prompts of the blur-aware and DP-aware formats. (d) The blur maps obtained with the ensembling-based format, i.e., all eight blur-aware and DP-aware prompts are used (please refer to Tab. 4 for details).
+
+![](images/3b01f240f5b9ae389abd9aee3a971c85e3eec945b179276d04374353f0970329.jpg)  
+(d)
+
+the prompt  $\mathfrak{p}$ , we concatenate the left view  $\mathbf{B}_{\mathrm{L}}$  with a horizontally flipped right view  $\mathbf{B}_{\mathrm{R}}^{h} = \mathrm{Flip}(\mathbf{B}_{\mathrm{R}})$  along the width axial in the  $\eta (\cdot ,\cdot)$ . We then obtained image features  $\mathbf{F} = \mathrm{ImageEncoder}\bigl (\eta (\mathbf{B}_{\mathrm{L}},\mathbf{B}_{\mathrm{R}}^{h})\bigr)$ . To transform  $\mathbf{F}$  to the same aspect ratio of  $\mathbf{B}_{\mathrm{L}}$  and  $\mathbf{B}_{\mathrm{R}}$ , we average the corresponding pixel-wise features based on the transformation in  $\eta (\mathbf{B}_{\mathrm{L}},\mathbf{B}_{\mathrm{R}}^{h})$  and have  $\alpha (\mathbf{F})$ . For  $i\in \{1,\dots ,\mathsf{h}_{\mathsf{w}}\}$  and  $j\in \{1,\dots ,\lfloor \frac{1}{2}\mathsf{w_s}\rfloor \}$ , we define
+
+$$
+\alpha (\mathbf {F}) (i, j) = \frac {1}{2} \mathbf {F} (i, j) + \frac {1}{2} \mathbf {F} (i, w _ {s} - j). \tag {5}
+$$
+
+Back to the left-hand side of Eq. 4, we have
+
+$$
+\mathbf {M} _ {\mathbf {F}} (i, j) = 1 - \mathbf {M} _ {\mathbf {F}} ^ {s} (i, j) = 1 - \sigma \left(\operatorname {s i m} (\alpha (\mathbf {F}) (i, j), \mathbf {t} ^ {s})\right). \tag {6}
+$$
+
+Here,  $\mathbf{t}^s$  is the text embedding of the prompt describing symmetry. Note that the high similarity value, i.e.  $\mathbf{M}_{\mathbf{F}}^{s}(i,j) = \sigma \big(\mathrm{sim}(\alpha (\mathbf{F})(i,j),\mathbf{t}^{s})\big)$  indicates pixels in sharp regions. Therefore the blur map is derived as  $1 - \mathbf{M}_{\mathbf{F}}^{s}(i,j)$  in Eq. 6. Similarly, the  $\mathbf{M}_{\mathbf{F}}$  is sampled to the same resolution of the DP pair, returning M. For this blur map estimation strategy, we conclude the lemma below,
+
+Lemma 3.1. A pixel is sharp if and only if it is horizontally symmetric in the left view and the horizontally flipped right view, otherwise, the pixel is blurred.
+
+Proof. Following Eq. (1), we have  $\mathbf{B}_{\mathrm{L}}(i,j)$  being sharp, given  $\mathbf{B}_{\mathrm{L}}(i,j) = \mathrm{Flip}(\mathbf{B}_{\mathrm{R}})(i,\mathsf{w} - j)$ . In other words, we have  $\eta (\mathbf{B}_{\mathrm{L}},\mathbf{B}_{\mathrm{R}}^{h})(i,j) = \eta (\mathbf{B}_{\mathrm{L}},\mathbf{B}_{\mathrm{R}}^{h})(i,\mathsf{w}_{\mathsf{s}} - j)$ , demonstrating the horizontal symmetry. Reversely, the horizontal symmetry breaks once the disparity/blur occurs.
+
+Ensembling format. Given the analysis that the degradations in the DP pair can be described by both the blurriness and symmetricity, we thus propose to obtain the mask by assembling the blur-aware and DP-aware formats jointly. Please refer to Tab. 4 for details of the 8 prompts designed from blur-aware and DP-aware formats.
+
+# 3.2. Network
+
+We train an encoder-decoder based deblurring network for restoring the DP pair  $(\mathbf{B}_{\mathrm{L}},\mathbf{B}_{\mathrm{R}})$  into a sharp image  $\hat{\mathbf{I}}$  with the derived blur map  $\mathbf{M}$ . Our network consists of a backbone network based on [5] and a BPA block to interleave with the backbone network layers. In particular, the BPA block uses the obtained blur map  $\mathbf{M}$  as deblur kernel prior to help the restoration of  $(\mathbf{B}_{\mathrm{L}},\mathbf{B}_{\mathrm{R}})$  on the fly.
+
+Self-attention. The self-attention (SA) mechanism is widely used in the image restoration tasks [18, 36, 39]. We first briefly review it. Let  $\mathbf{X} \in \mathbb{R}^{h_x \times w_x \times c_x}$  be the intermediate feature embedding of a blur image from the backbone encoder, where  $h_x$ ,  $w_x$ ,  $c_x$  are height, width, and channel of the feature. The self-attention is input with query  $\mathbf{Q}$ , key  $\mathbf{K}$ , and value  $\mathbf{V}$  that are linearly projected from  $\mathbf{X}$ , and then calculate an attention map between  $\mathbf{Q}$  and  $\mathbf{K}$  for adaptively aggregating  $\mathbf{V}$ . This process is defined as follows,
+
+$$
+\mathbf {Q} = \mathbf {X} \mathbf {W} _ {\mathbf {Q}}, \quad \mathbf {K} = \mathbf {X} \mathbf {W} _ {\mathbf {K}}, \quad \mathbf {V} = \mathbf {X} \mathbf {W} _ {\mathbf {V}}, \tag {7}
+$$
+
+Attention  $(\mathbf{Q},\mathbf{K},\mathbf{V}) = \mathrm{Softmax}(\mathbf{Q}\mathbf{K}^{\top} / \beta)\mathbf{V}$  (8)
+
+where  $\mathbf{W}_{\mathbf{Q}}, \mathbf{W}_{\mathbf{K}}, \mathbf{W}_{\mathbf{V}} \in \mathbb{R}^{h_{\mathbf{x}} \times w_{\mathbf{x}} \times c_{\mathbf{x}}}$  are learnable weight matrices,  $\beta$  is a normalization factor that is typically set to the square root of the latent dimension, and  $\operatorname{Softmax}(\mathbf{Q}\mathbf{K}^{\top} / \beta) \in \mathbb{R}^{(h_{\mathbf{x}} \times w_{\mathbf{x}}) \times (h_{\mathbf{x}} \times w_{\mathbf{x}})}$  is attention map.
+
+BPA Block. The attention map can be considered as an adaptive deblur kernel prior for restoring the DP pair in the feature space. We are motivated to modulate the attention map by supplying the blur map  $\mathbf{M}$ , utilizing blur-related prior knowledge to additionally assign a  $\mathbf{q} \times \mathbf{q}$  deblur kernel for each region in  $\mathbf{X}$  to aggregate a sharp feature embedding from its neighboring regions. We re-write the Eq. 8 as
+
+Attention  $(\mathbf{Q},\mathbf{K},\mathbf{V}) = \mathrm{Softmax}(\mathbf{Q}\mathbf{K}^{\top} / \beta +\mathbf{O})\mathbf{V}$  (9)
+
+$$
+\mathbf {O} = \operatorname {P a d} \left(\operatorname {F F N} _ {\operatorname {C o n v}} \left(\sigma^ {- 1} (\mathbf {M})\right)\right), \tag {10}
+$$
+
+and show that the restoration result is further improved in Fig. 5, where  $\mathrm{FFN}_{\mathrm{Conv}}(\cdot)$  is a convolution-based feed forward layer that is used to learn a  $q \times q$  deblur kernel for each region of  $\mathbf{X}$  from the unnormalized blur map  $\sigma^{-1}(\mathbf{M})$ , resulting in  $\mathrm{FFN}_{\mathrm{Conv}}(\sigma^{-1}(\mathbf{M})) \in \mathbb{R}^{h_x \times w_x \times q^2}$ . The Pad( $\cdot$ ) function reshapes  $\mathrm{FFN}_{\mathrm{Conv}}(\sigma^{-1}(\mathbf{M}))$  into  $\mathbb{R}^{h_x \times w_x \times q \times q}$ , and pads the reshaped  $\mathrm{FFN}_{\mathrm{Conv}}(\sigma^{-1}(\mathbf{M}))$  to  $\mathbb{R}^{(h_x \times w_x) \times (h_x \times w_x)}$ , for shape alignment issue.
+
+# 3.3. Network Training
+
+We optimize our deblurring network with the widely used Charbonnier loss. Moreover, we propose a blur-aware loss and a blur weighting loss to penalize the blurred regions in the restoration  $\hat{\mathbf{I}}$ .
+
+Charbonnier loss. We encourage the restoration to be close to the ground truth by using Charbonnier loss [12, 43].
+
+![](images/480aad7501ee7e8b7fcb54754c39b4d78d088b346ac26c3d6c0e4798592d9d0c.jpg)  
+(a)
+
+![](images/df89236f0ba3d0a983886e86e0fac8dc150f9b76ee15aaf584879ba6aa82d718.jpg)  
+(b)
+
+![](images/8838b231c703c986bc4d3b093dad7eb2534b56e2645f464ec2a5a15cd603a2de.jpg)  
+(c)  
+Figure 5. Example of deblurring with the blur map projected deblur kernel  $\mathbf{O}$ . (a) and (b) are the left view of the DP pair and the ground truth sharp image. (c) and (d) are deblurred images with and without using  $\mathbf{O}$ . Zoom in for better quality.
+
+![](images/53c8c1fc807ced4c5c6267718200456ec40493e492d5f7a61f420f3dd08a2a77.jpg)  
+(d)
+
+We empirically set  $\varepsilon$  to  $10^{-4}$ , and define
+
+$$
+\mathcal {L} _ {\text {c h a r}} = \sqrt {\| \mathbf {I} (i , j) - \hat {\mathbf {I}} (i , j) \| ^ {2} + \varepsilon^ {2}}. \tag {11}
+$$
+
+Blur Weighting Loss. We impose an adaptive penalty on the blurred regions of the DP pair  $(\mathbf{B}_{\mathrm{L}},\mathbf{B}_{\mathrm{R}})$ , considering the degree of blur measured by CLIP. It encourages the network to focus on the restoration of heavily blurred regions. We first normalize the deviations between  $\hat{\mathbf{I}}$  and  $\mathbf{I}$  by the deviations between  $(\mathbf{B}_{\mathrm{L}},\mathbf{B}_{\mathrm{R}})$  and  $\mathbf{I}$ , and then re-use the blur map to select blurred regions residing in the DP pair.
+
+$$
+\mathcal {L} _ {\mathrm {b w l}} = \frac {\left\| \mathbf {I} (i , j) - \hat {\mathbf {I}} (i , j) \right\| ^ {2}}{\left\| \hat {\mathbf {I}} (i , j) - \frac {1}{2} \left(\mathbf {B} _ {\mathrm {L}} (i , j) + \mathbf {B} _ {\mathrm {R}} (i , j)\right) \right\| ^ {2}} \cdot \mathbf {M} (i, j), \tag {12}
+$$
+
+where we use the blur map  $\mathbf{M}$  (with soft logits) to reflect the blur levels detected by CLIP.
+
+Blur-aware Loss. We encourage  $\hat{\mathbf{I}}$  to be sharp by leveraging the versatile knowledge contained in the CLIP. We generate the blur map  $\hat{\mathbf{M}}$  by the blur-aware format for the restoration, and penalize the blur exhibited in  $\hat{\mathbf{I}}$ . Similar to  $\mathcal{L}_{\mathrm{bw1}}$ , we use the unnormalized version of the blur map,
+
+$$
+\mathcal {L} _ {\text {b a l}} = \hat {\mathbf {M}} (i, j). \tag {13}
+$$
+
+This encourages  $\hat{\mathbf{M}}$  to be zero, i.e., no blur exists in the restoration.
+
+Total Loss. Our network is optimized by minimizing the following loss function
+
+$$
+\mathcal {L} _ {\text {t o t a l}} = \frac {1}{| \Omega |} \sum_ {(i, j) \in \Omega} \left(\mathcal {L} _ {\text {c h a r}} + \lambda_ {1} \mathcal {L} _ {\text {b a l}} + \lambda_ {2} \mathcal {L} _ {\text {b w l}}\right), \tag {14}
+$$
+
+where  $\frac{1}{|\Omega|}$  is a normalization factor determined by the image domain size  $|\Omega|$ , and  $\lambda_{1}$  and  $\lambda_{2}$  are hyperparameters to balance losses.
+
+# 4. Experiments and Analysis
+
+Implementation Details. We implement our model under the PyTorch framework. We use the pre-trained and ViT-B/32 [8] architecture-based CLIP [30] for our blur map estimation strategy. We train the deblurring network in two stages for  $6 \times 10^{6}$  steps in total with the Adam optimizer.
+
+Table 1. Quantitative comparisons on the DPD-blur dataset [1] composed of 37 indoor and 39 outdoor scenes. We respectively color the best and the second-best performance in red and blue.  
+
+<table><tr><td rowspan="2">Method</td><td colspan="4">Outdoor Scenes</td><td colspan="4">Indoor Scenes</td><td colspan="4">Average</td><td></td></tr><tr><td>PSNR↑</td><td>SSIM↑</td><td>MAE↓</td><td>RMSE rel↓</td><td>PSNR↑</td><td>SSIM↑</td><td>MAE↓</td><td>RMSE rel↓</td><td>PSNR↑</td><td>SSIM↑</td><td>MAE↓</td><td>RMSE rel↓</td><td>LPIPS↓</td></tr><tr><td>EBDB</td><td>25.77</td><td>0.772</td><td>0.040</td><td>0.051</td><td>21.25</td><td>0.599</td><td>0.058</td><td>0.086</td><td>23.45</td><td>0.683</td><td>0.049</td><td>0.067</td><td>0.336</td></tr><tr><td>DMENet</td><td>25.50</td><td>0.788</td><td>0.038</td><td>0.053</td><td>21.43</td><td>0.644</td><td>0.063</td><td>0.084</td><td>23.41</td><td>0.714</td><td>0.051</td><td>0.067</td><td>0.349</td></tr><tr><td>DPDNet</td><td>27.48</td><td>0.849</td><td>0.029</td><td>0.042</td><td>22.90</td><td>0.726</td><td>0.052</td><td>0.071</td><td>25.13</td><td>0.786</td><td>0.041</td><td>0.055</td><td>0.223</td></tr><tr><td>RDPD</td><td>28.10</td><td>0.843</td><td>0.027</td><td>0.039</td><td>22.82</td><td>0.704</td><td>0.053</td><td>0.072</td><td>25.39</td><td>0.772</td><td>0.040</td><td>0.053</td><td>0.255</td></tr><tr><td>DDDNet</td><td>27.57</td><td>0.833</td><td>0.030</td><td>0.041</td><td>23.28</td><td>0.708</td><td>0.050</td><td>0.068</td><td>25.36</td><td>0.768</td><td>0.041</td><td>0.054</td><td>0.197</td></tr><tr><td>IFAN</td><td>28.66</td><td>0.868</td><td>0.025</td><td>0.037</td><td>23.46</td><td>0.743</td><td>0.049</td><td>0.067</td><td>25.99</td><td>0.804</td><td>0.037</td><td>0.050</td><td>0.207</td></tr><tr><td>BAMBNet</td><td>28.60</td><td>0.872</td><td>0.026</td><td>0.037</td><td>24.30</td><td>0.772</td><td>0.045</td><td>0.060</td><td>26.40</td><td>0.821</td><td>0.036</td><td>0.047</td><td>0.141</td></tr><tr><td>DeepRFT</td><td>28.48</td><td>0.870</td><td>0.025</td><td>0.038</td><td>23.09</td><td>0.736</td><td>0.051</td><td>0.070</td><td>25.71</td><td>0.801</td><td>0.037</td><td>0.051</td><td>0.217</td></tr><tr><td>Restormer</td><td>29.48</td><td>0.895</td><td>0.023</td><td>0.034</td><td>23.97</td><td>0.773</td><td>0.047</td><td>0.063</td><td>26.66</td><td>0.833</td><td>0.035</td><td>0.046</td><td>0.155</td></tr><tr><td>K3DN</td><td>29.87</td><td>0.890</td><td>0.022</td><td>0.032</td><td>24.37</td><td>0.780</td><td>0.046</td><td>0.060</td><td>27.06</td><td>0.835</td><td>0.034</td><td>0.044</td><td>0.187</td></tr><tr><td>Ours (Small)</td><td>29.55</td><td>0.893</td><td>0.021</td><td>0.033</td><td>24.38</td><td>0.773</td><td>0.043</td><td>0.065</td><td>26.91</td><td>0.831</td><td>0.032</td><td>0.045</td><td>0.185</td></tr><tr><td>Ours (Large)</td><td>29.88</td><td>0.896</td><td>0.020</td><td>0.032</td><td>24.73</td><td>0.786</td><td>0.037</td><td>0.059</td><td>27.24</td><td>0.840</td><td>0.028</td><td>0.043</td><td>0.168</td></tr></table>
+
+Table 2. Quantitative comparisons on DDD-syn dataset.  
+
+<table><tr><td>Method</td><td>PSNR↑</td><td>SSIM↑</td><td>MAE↓</td><td>RMSE_rel↓</td></tr><tr><td>EBDB</td><td>26.48</td><td>0.683</td><td>0.036</td><td>0.047</td></tr><tr><td>DMENet</td><td>30.14</td><td>0.939</td><td>0.017</td><td>0.031</td></tr><tr><td>DPDNet</td><td>31.45</td><td>0.926</td><td>0.016</td><td>0.027</td></tr><tr><td>RDPD</td><td>32.42</td><td>0.912</td><td>0.016</td><td>0.024</td></tr><tr><td>DDDNet</td><td>33.21</td><td>0.956</td><td>0.010</td><td>0.022</td></tr><tr><td>IFAN</td><td>34.18</td><td>0.929</td><td>0.012</td><td>0.020</td></tr><tr><td>BAMBNet</td><td>35.90</td><td>0.954</td><td>0.012</td><td>0.016</td></tr><tr><td>DeepRFT</td><td>36.52</td><td>0.952</td><td>0.010</td><td>0.015</td></tr><tr><td>Restormer</td><td>36.44</td><td>0.957</td><td>0.010</td><td>0.015</td></tr><tr><td>K3DN</td><td>38.23</td><td>0.965</td><td>0.008</td><td>0.012</td></tr><tr><td>Ours (Small)</td><td>37.27</td><td>0.959</td><td>0.010</td><td>0.014</td></tr><tr><td>Ours (Large)</td><td>38.62</td><td>0.971</td><td>0.008</td><td>0.012</td></tr></table>
+
+In each stage, the learning rate is decayed from  $2 \times 10^{-4}$  to  $10^{-6}$  by a cosine annealing strategy. In the first stage, we train the network for  $5 \times 10^{6}$  steps, and only use the Charbonnier loss  $\mathcal{L}_{\mathrm{char}}$ . In the second stage, the network is finetuned for  $1 \times 10^{6}$  steps with  $\mathcal{L}_{\mathrm{total}}$ , where we have  $\lambda_{1} = 10^{-1}$  and  $\lambda_{2} = 2 \times 10^{-1}$ . Code, results, and more details are given in our project page.
+
+Datasets. Our method is evaluated on two real-world DP defocus deblurring datasets, DPD-blur dataset [1] and DPD-disp dataset [27]. We follow [1] on the training and testing splits. For the DPD-disp dataset, we use it for testing only, re-using the checkpoints trained from the DPD-blur dataset as they do not provide ground-truth (GT) data or with limited dataset size. Moreover, two synthetic datasets, DDD-syn [26] and RDPD [2], are also used for evaluations.
+
+Evaluation Metrics. We use peak signal-to-noise ratio (PSNR), structural similarity (SSIM), mean absolute error (MAE), and root mean squared relative error (RMSE_ref) as our evaluation metrics.
+
+Baseline Methods. We compare with SOTA DP defocus deblurring methods, i.e., EBDB [13], DMENet [15],
+
+Table 3. Quantitative comparisons on RDPD dataset.  
+
+<table><tr><td>Method</td><td>PSNR↑</td><td>SSIM↑</td><td>MAE↓</td><td>RMSE rel↓</td></tr><tr><td>EBDB</td><td>24.23</td><td>0.637</td><td>0.031</td><td>0.054</td></tr><tr><td>DMENet</td><td>25.17</td><td>0.731</td><td>0.036</td><td>0.061</td></tr><tr><td>DPDNet</td><td>29.84</td><td>0.828</td><td>0.032</td><td>0.055</td></tr><tr><td>RDPD</td><td>31.09</td><td>0.861</td><td>0.025</td><td>0.028</td></tr><tr><td>DDDNet</td><td>30.14</td><td>0.840</td><td>0.016</td><td>0.031</td></tr><tr><td>IFAN</td><td>31.12</td><td>0.865</td><td>0.023</td><td>0.028</td></tr><tr><td>BAMBNet</td><td>31.78</td><td>0.867</td><td>0.016</td><td>0.026</td></tr><tr><td>DeepRFT</td><td>31.71</td><td>0.879</td><td>0.016</td><td>0.024</td></tr><tr><td>Restormer</td><td>32.27</td><td>0.871</td><td>0.016</td><td>0.024</td></tr><tr><td>K3DN</td><td>32.84</td><td>0.905</td><td>0.014</td><td>0.023</td></tr><tr><td>Ours (Small)</td><td>32.98</td><td>0.895</td><td>0.014</td><td>0.022</td></tr><tr><td>Ours (Large)</td><td>33.44</td><td>0.907</td><td>0.013</td><td>0.021</td></tr></table>
+
+DPDNet [1], RDPD [2], DDDNet [26], IFAN [16], BAMBNet [20], DeepRFT [22], Restormer [39], and K3DN [38].
+
+# 4.1. Comparisons with State-of-the-Art
+
+Quantitative Comparison. We compare with the SOTA methods on the DPD-blur, DDD-syn, and RDPD datasets in Tab. 1, Tab. 2, and Tab. 3, respectively. Our observations are as follows: i) With our model (Small), we achieve similar restoration results with Restormer and K3DN, the third-best and second-best method, in all datasets. ii) When scaling to the large model, we consistently outperform all methods on all evaluation metrics. For example, our method, K3DN, and Restormer respectively achieve 27.24/27.06/26.66, 38.62/38.23/36.44, and 33.44/32.84/32.27 PSNR (dB) in the DPD-blur, DDD-syn, and RDPD datasets. Meanwhile, on a single RTX 4090 GPU, we remain to have a lower Infer. time (including CLIP) which is 0.042s and 0.054s for our small and large models, while K3DN/Restormer takes 0.198s/0.255s.
+
+Qualitative Comparison. We compare with state-of-the-art methods on the DPD-blur dataset (Fig. 6). As shown, our
+
+![](images/1a5e452037bfcf471d7ed6ed97b64d00f80d482743a1e3ad6d7b9d34937e419a.jpg)  
+Blurry Image
+
+![](images/1a577a1e892a8fb4e3e7924fa7e1e060664c57fcf2ca9b0ed80042cb1be77ba2.jpg)  
+GT Image
+
+![](images/4e95c219927e2e91924f97c7242859158592d75f84a6394d22288eba860ab7aa.jpg)
+
+![](images/e263042cb2f4553c514700a14933a30b450d50b806f7a7b80439df6f943c6067.jpg)  
+IFAN [16]
+
+![](images/ceb81e56acb118fae69918d30d66a3cef1c1de4338a9c09c30cab0d81d1ec79e.jpg)  
+DDDNet [26]
+
+![](images/593fa7f0cd33870b2370f7686d3d006831fff4436a047c349f44ed5ff953fbc2.jpg)  
+Blurry Image
+
+![](images/71419781ec3eb04f150dd9a5e0d695549ad8f71fac20fec5db2020fdef535aa2.jpg)
+
+![](images/1ab9e10670eae6a5762ffcdbd1f94d11fb463e0508bfb974ed139b904a3febde.jpg)
+
+![](images/415d9511d004b84ab0fbe979d1a9d97b307e976b9d99d47209ccbd86eda5a141.jpg)
+
+![](images/a38e83a781b12c8e4eee01d3784d2ce81064db85b5dc3eb35f35492a454af57f.jpg)  
+DeepRFT [22]  
+Blurry Image  
+DeepRFT [22]
+
+![](images/d00923ce4f24847248c6927585b5be800a6d3253de2729faa764a9b0ad1da0f9.jpg)  
+GT Image
+
+![](images/10c56ea97f9d68316bbdc7475b929b6f2caba95210b120acf0a3e447d2f67f52.jpg)  
+Restormer [39]  
+Blurry Image
+
+![](images/c1cba08fd1c437d5faf95cc4c61b001bbfec7982372d7fff8b5e1e2745bb5b7f.jpg)  
+K3DN [38]  
+IFAN [16]
+
+![](images/3deff5e3099745779cb9d782a3227a6d95e4b9a3129e3a16d70ece208f2f3ad0.jpg)  
+Ours  
+DDDNet [26]
+
+![](images/e6d883e27feceebacbcd4f766c2154c76680ba300f69277ab319b309a3c8e21d.jpg)  
+Figure 6. Qualitative comparison on the DPD-blur dataset [1]. We present the blurry image  $(\mathbf{B}_{\mathrm{L}})$  in the first column, and the ground truth (GT) image of regions residing in the red bounding box is shown in the second column. The cropped blurred image of the red bounding box region is in the third column.
+
+![](images/0e2e56ebeb48ea5db23dc965bdb40ba0b1498af169039040fd80561846390f0d.jpg)  
+Restormer [39]
+
+![](images/a3ae7e7d550322b212db7574819d25fe9d264c840e13caffee136fba8e2865e6.jpg)  
+K3DN [38]
+
+![](images/3fe1437ecf8035033a05d2376d9f62d1fd4e4038bc29755523e7b1a9b1a2cddc.jpg)  
+Ours
+
+method performs sharper and clearer restorations of edges and texts. To further demonstrate the benefits of using CLIP to generate the blur mask unsupervisedly in our approach, we provide an example in Fig. 7, which preserves sharp regions (e.g., text 'University') in the input blur image effectively compared to the second-best baseline.
+
+![](images/49d024ddac1a93a08d0f3ae7a68f2ae2039e91b0ac1850f8d2dcdedd2fdd5610.jpg)  
+(a) Input  
+Figure 7. An example of the restoration results on the sharp region of the input DP image (left view).
+
+![](images/e3c81256f7e09608a955ef70e91d56ce26e088b522210737345b94a264481924.jpg)  
+(b) K3DN
+
+![](images/fbad7c91f69532a328961c39f21d686aa4cff8de248434c3a6ea5e0377a8515b.jpg)  
+(c) Restormer
+
+![](images/7d412d6a06994209392d2827b7c200204608fe6290bf8376b7f031b3173930e4.jpg)  
+(d) Ours
+
+# 4.2. Ablation Study
+
+We study model architecture, blur map estimation, and losses in this section. All experiments are performed in the DPD-blur dataset.
+
+Ablation of Model Architecture. We study the effective usage of blur map as prior knowledge for DP defocus deblurring (Tab. 6). To show the benefits of using blur maps, we consider four baselines: i) NAFNet [5], the baseline model; ii) Concat, concatenating the blur map with the DP pair before feeding to the model; iii) SA, using the self-attention layer [8] in Eq. 8 to the model only; iv) Concat+SA, combines the Concat and SA settings; v) BPA block, using kernel priors from the blur map to assist deblurring. Our model consistently outperforms all baselines, which indicates the effectiveness of using the blur map.
+
+Ablation of Losses. We investigate the proposed blur weighting loss  $\mathcal{L}_{\mathrm{bw}}$  and blur-aware loss  $\mathcal{L}_{\mathrm{bal}}$  (Tab. 7) with a baseline as the  $\mathcal{L}_{\mathrm{char}}$  setting. We first use  $\mathcal{L}_{\mathrm{bw}}$  and  $\mathcal{L}_{\mathrm{bal}}$
+
+to our baseline, NAFNet (i.e., not using our BPA block), that only uses  $\mathcal{L}_{\mathrm{char}}$ , having 0.32 PSNR (dB) improvements. Secondly, we train our model (backbone + BPA block) with Charbonnier loss, resulting in 26.71/0.825 higher PSNR (dB)/SSIM. By using the  $\mathcal{L}_{\mathrm{bwl}}$  or  $\mathcal{L}_{\mathrm{bal}}$ , we respectively achieve 0.05/0.003 or 0.10/0.004 higher PSNR (dB)/SSIM. Combining all losses, we have the best restoration performance at 26.91/0.831 for PSNR (dB)/SSIM. Moreover, we verify the generalization ability of our  $\mathcal{L}_{\mathrm{bwl}}$  and  $\mathcal{L}_{\mathrm{bal}}$  losses on state-of-the-art networks, improving PSNR of Restormer and DeepRFT by 0.25 and 0.41 PSNR (dB).
+
+Ablation of Blur Map Estimation. We ablate with different prompts used to generate the blur map. The blur-aware and DP-aware prompts are presented in Tab. 4, and we show their impact on model performance with Tab. 5. We then ensemble the groups of blur-aware prompt and disparity-aware prompt individually (Ens. $^1$ ), leading to  $26.80\mathrm{dB} / 0.829$  and  $26.84 / 0.830$  PSNR (dB)/SSIM. By assembling all prompts (Ens. $^2$ ), we have  $26.91 / 0.831$  PSNR (dB)/SSIM, consistently outperforming other approaches of generating blur masks.
+
+# 4.3. Discussion and Limitation
+
+Discussion. The reader may wonder about the performance of our unsupervised blur map estimation strategy. Therefore, we perform two qualitative evaluations on the DPD-disp dataset, where the GT disparity is included. We compare with BAMBNet [20] and DPD-disp [27].
+
+First, we consider blur map estimation. To obtain the GT blur map, the pixel with disparity  $d$  that satisfies  $|d|\leq 1$
+
+Table 4. Prompts used for blur map estimation.  
+
+<table><tr><td></td><td>Blur-aware Prompt</td><td>DP-aware Prompt</td></tr><tr><td>p1</td><td>[A blurry image.]</td><td>[A symmetrical image.]</td></tr><tr><td>p2</td><td>[An obscured image.]</td><td>[A horizontally symmetrical image.]</td></tr><tr><td>p3</td><td>[An out of focus image.]</td><td>[A left-right symmetrical image.]</td></tr><tr><td>p4</td><td>[An image lacking sharpness.]</td><td>[A symmetrical image at the pixel level.]</td></tr></table>
+
+Table 5. Restoration performance of our methods by using blur-aware or/and DP-aware prompts for blur map estimation. Ens.  ${}^{1}$  denotes ensembling the group of blue-aware prompts and DP-aware prompts individually, and Ens.  ${}^{2}$  ensembles all prompts.  
+
+<table><tr><td rowspan="2"></td><td colspan="4">Blur-aware Prompt</td><td colspan="4">DP-aware Prompt</td></tr><tr><td>PSNR↑</td><td>SSIM↑</td><td>MAE↓</td><td>RMSE_rel↓</td><td>PSNR↑</td><td>SSIM↑</td><td>MAE↓</td><td>RMSE_rel↓</td></tr><tr><td>p1</td><td>26.83</td><td>0.829</td><td>0.033</td><td>0.045</td><td>26.82</td><td>0.830</td><td>0.033</td><td>0.046</td></tr><tr><td>p2</td><td>26.81</td><td>0.829</td><td>0.033</td><td>0.046</td><td>26.83</td><td>0.830</td><td>0.032</td><td>0.046</td></tr><tr><td>p3</td><td>26.75</td><td>0.828</td><td>0.034</td><td>0.046</td><td>26.82</td><td>0.830</td><td>0.033</td><td>0.046</td></tr><tr><td>p4</td><td>26.77</td><td>0.829</td><td>0.033</td><td>0.046</td><td>26.85</td><td>0.830</td><td>0.032</td><td>0.045</td></tr><tr><td>Ens.1</td><td>26.80</td><td>0.829</td><td>0.033</td><td>0.046</td><td>26.84</td><td>0.830</td><td>0.032</td><td>0.046</td></tr><tr><td>Ens.2</td><td>26.91</td><td>0.831</td><td>0.032</td><td>0.045</td><td>26.91</td><td>0.831</td><td>0.032</td><td>0.045</td></tr></table>
+
+Table 6. Ablation of model components.  
+
+<table><tr><td>Setting</td><td>PSNR↑</td><td>SSIM↑</td><td>MAE↓</td><td>RMSE rel↓</td></tr><tr><td>i) NAFNet</td><td>26.21</td><td>0.817</td><td>0.038</td><td>0.049</td></tr><tr><td>ii) Concat</td><td>26.76</td><td>0.826</td><td>0.033</td><td>0.046</td></tr><tr><td>iii) SA</td><td>26.59</td><td>0.824</td><td>0.036</td><td>0.047</td></tr><tr><td>iv) Concat + SA</td><td>26.80</td><td>0.829</td><td>0.032</td><td>0.046</td></tr><tr><td>v) BPA block</td><td>26.91</td><td>0.831</td><td>0.032</td><td>0.045</td></tr></table>
+
+Table 7. The effectiveness of losses.  
+
+<table><tr><td>BPA block</td><td>Loss</td><td>PSNR↑</td><td>SSIM↑</td><td>MAE↓</td><td>RMSE rel↓</td></tr><tr><td>X</td><td>Lchar</td><td>26.21</td><td>0.817</td><td>0.038</td><td>0.049</td></tr><tr><td>X</td><td>Ltotal</td><td>26.53</td><td>0.822</td><td>0.036</td><td>0.047</td></tr><tr><td>✓</td><td>Lchar</td><td>26.71</td><td>0.825</td><td>0.034</td><td>0.046</td></tr><tr><td>✓</td><td>Lchar + Lbwl</td><td>26.76</td><td>0.828</td><td>0.033</td><td>0.046</td></tr><tr><td>✓</td><td>Lchar + Lbal</td><td>26.81</td><td>0.829</td><td>0.032</td><td>0.046</td></tr><tr><td>✓</td><td>Ltotal</td><td>26.91</td><td>0.831</td><td>0.032</td><td>0.045</td></tr></table>
+
+is used as the sharp pixel, reversely, it is a buried pixel. Our method, BAMBNet [20] and DPD-disp [27] respectively have  $89.8\% / 70.2\% / 88.3\%$  accuracy (the higher, the better), showing the effectiveness of our method.
+
+Second, we explore disparity estimation. The log-its of our unnormalized blurred map are potentially linearly correlated with the ground-truth disparity. Therefore, we compare with the state-of-the-art DP disparity estimation method, DPD-disp [27]. Following [9, 27], we use AI(1), AI(2), and  $1 - |\rho_s|$  as the evaluation metrics (the lower, the better). The AI(1), AI(2), and  $1 - |\rho_s|$  of our method, BAMBNet, and DPD-disp are 0.063/0.106/0.069, 0.130/0.184/0.096, 0.306/0.772/0.0159. Though our blur map is estimated with a single forward pass, we still achieve a reasonable performance in the disparity estimation. This potentially explains the high performance of our DP defo
+
+cus deblurring network, as obtaining the disparity prior benefits the defocus task.
+
+Limitation. As the image encoder of CLIP is trained under a classification-alike pre-training task, it will focus more on local details that help identify its scene class. Textureless regions would produce non-significant semantic reactions, e.g., large areas of wall, ceiling, or floor, and reduce the quality of the estimated blur map. It is possible to use a vision language framework that drives more sensitivity to regions with less texture.
+
+# 5. Conclusion and Broader Impact
+
+In this paper, we study end-to-end defocus deblurring of DP images, leveraging the blur-related prior knowledge from the CLIP. We first estimate a blur map with an ensemble of blur-aware and DP-aware strategies, and then use the estimated blur map as the deblurring kernel prior to restoring the DP image. We also propose a blur-aware and blur-weighting loss to regularize the restorations of the DP images during training, by distilling the knowledge of blur from CLIP. In extensive experiments, our method outperforms past works by a large margin in quantitative and qualitative restoration performance.
+
+Broader Impact. The proposed DP-aware strategy is promising to apply and extend CLIP to diverse zero-shot stereo vision tasks. We hope it will motivate future work.
+
+Acknowledgment. This work was supported in part by the Beijing Institute of Technology Research Fund Program for Young Scholars, BIT Special-Zone, and National Natural Science Foundation of China 62302045, and Miaomiao Liu was supported by the ARC fellowship and Discovery Project grant (DE180100628, DP200102274).
+
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+        "text": "Zixuan Hu $^{1}$  Xiaotong Li $^{1}$  Shixiang Tang $^{3}$  Jun Liu $^{4}$  Yichun Hu $^{1}$  Ling-Yu Duan $^{1,2*}$",
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+        "text": "<sup>3</sup> The Chinese University of Hong Kong, Hongkong, China, <sup>4</sup> Singapore University of Technology and Design, Singapore {hzxuan, hycc, lingyu}@pku.edu.cn, lixiaotong@stu.pku.edu.cn, shixiangtang@cuhk.edu.hk, jun.liu@sutd.edu.sg",
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+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
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+        "text": "The remarkable success of \"pretrain-then-finetune\" paradigm has led to a proliferation of available pre-trained models for vision tasks. This surge presents a significant challenge in efficiently choosing the most suitable pretrained models for downstream tasks. The critical aspect of this challenge lies in effectively predicting the model transferability by considering the underlying fine-tuning dynamics. Existing methods often model fine-tuning dynamics in feature space with linear transformations, which do not precisely align with the fine-tuning objective and fail to grasp the essential nonlinearity from optimization. To this end, we present LEAD, a finetuning-aligned approach based on the network output of logits. LEAD proposes a theoretical framework to model the optimization process and derives an ordinary differential equation (ODE) to depict the nonlinear evolution toward the final logit state. Additionally, we design a class-aware decomposition method to consider the varying evolution dynamics across classes and further ensure practical applicability. Integrating the closely aligned optimization objective and nonlinear modeling capabilities derived from the differential equation, our method offers a concise solution to effectively bridge the optimization gap in a single step, bypassing the lengthy fine-tuning process. The comprehensive experiments on 24 supervised and self-supervised pre-trained models across 10 downstream datasets demonstrate impressive performances and showcase its broad adaptability even in low-data scenarios.",
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+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
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+        "type": "text",
+        "text": "The \"pretrain-then-finetune\" learning paradigm has exhibited remarkable success in a wide range of computer vision tasks [6, 28], leading to an increasing number of diverse pretrained models open-sourced to the computer vision community. This surge poses a significant challenge in selecting the optimal pre-trained model for a downstream task",
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+    {
+        "type": "image",
+        "img_path": "images/2c3f6aa22c47c4b6480171e0d2ff66d7c4f64ce96d130c4892baa2e673c8f2a1.jpg",
+        "image_caption": [
+            "Figure 1. This diagram illustrates the task of model selection, which aims to rank pre-trained models for choosing the optimal one. The ground-truth ranking sequence is derived from the models' accuracy after fine-tuning. However, due to the time-intensive nature of this process, it requires to design efficient transferability metrics for accurate ranking prediction. The performance of this metric is evaluated using rank correlation, e.g., weighted Kendall's tau [42], to compare the predicted and ground-truth rankings."
+        ],
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+    {
+        "type": "text",
+        "text": "from a vast model zoo. Considering that the brute-force solution of fine-tuning all models on downstream tasks may be infeasible in many scenarios due to the substantial computational costs, the model selection task emerges [13, 47], which ranks the transferability of pre-trained models to the given task without incurring much cost, as shown in Fig. 1.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Predicting model transferability aims to efficiently estimate the final state after fine-tuning on the downstream task, without network optimization by backward propagation. Prior studies only depend on specific properties of the initial state (e.g., representation similarity [13, 14], conditional distribution [33, 47]), to serve as transferability indicators. Recent studies reveal that modeling the dynamic process of fine-tuning has become the bottleneck to design more high-quality transferability metrics. Following this philosophy, recent works propose to simulate fine-tuning dynamics on features through multiple stages of linear transformations [32, 41], achieving some promising results.",
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+    {
+        "type": "text",
+        "text": "Despite recent progress in this field, there are still two",
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+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
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+    },
+    {
+        "type": "header",
+        "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
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+    {
+        "type": "page_footnote",
+        "text": "*Corresponding Author.",
+        "bbox": [
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+    },
+    {
+        "type": "page_number",
+        "text": "28664",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "considerable gaps between existing modeled fine-tuning dynamics and the real ones: (1) Insufficient objective alignment. The designed objectives in prior works do not seamlessly align with fine-tuning, as they often focus more on enhancing class separability via feature manipulation, rather than the classification optimization for both the feature and output spaces. (2) Disregarding nonlinear modeling. Existing methods relying solely on linear transformations cannot well capture the intricate nonlinear changes in the feature space during optimization. Such constraints contribute to growing deviations in dynamic modeling and result in unreliable predictions of the final state.",
+        "bbox": [
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "Delving deeper into the optimization process, we focus on modeling the dynamic changes within the output space (i.e., logits for classification), which not only more closely relates to the fine-tuning objective but also embeds the overall nonlinear dynamics from the network optimization during fine-tuning. Building upon this foundation, we introduce an insightful framework to depict the trajectory of logits toward their final state in a dynamical modeling system. To capture and understand this evolution process of the logit space, the framework provides a discrete iterative optimization equation via gradient analysis and captures nonlinear logit space changes during optimization.",
+        "bbox": [
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "In contrast to the extensive iterations required in fine-tuning optimization, we further extend the framework to propose a new transferability metric \"Logits Evolution Analysis through Dynamical Equation (LEAD)\", to seize the final evolutionary state in a single step. We perform a mathematical derivation to convert the discrete process into a continuous differential equation and simplify it into an ordinary differential equation (ODE) by leveraging the classical analysis tool, Neural Tangent Kernel (NTK) [26]. This ODE concisely models the nonlinear evolution in logit space through its closed-form solution, allowing for real-time estimation of logits. Additionally, we introduce a class-aware decomposition method to enhance prediction accuracy and break the barrier of theoretical assumption of NTK. As a result, our method provides a direct estimation of the evolution by incorporating both the initial model state and the impact of fine-tuning evolution, serving as an effective indicator assessing model transferability.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The contributions of this work are three-fold. (1) To the best of our knowledge, we are the first to explore model transferability by modeling the evolution process in the logit space. (2) We propose LEAD, a novel transferability metric with two key components: a theoretical framework providing a closed-form solution to depict the logits evolution towards the final state, and a class-aware decomposition method to guarantee the practical applicability of theoretical findings and improve predictive precision. (3) We validate the effectiveness and generalizability of our method through experiments on 24 different pre-trained",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "models across 10 downstream datasets, achieving SOTA results with an average of  $17\\%$  gain in the rank correlation. In addition, our method can be naturally extended to low-data scenarios while maintaining competitive performance.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "2.1. Transferability Metric",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "The challenge of efficiently ranking pre-trained models has captured much interest of researchers, leading to the development of various metrics to evaluate the model transferability [2, 3, 12, 18, 36, 38, 47, 52]. For example, RSA [13], DDS [14] and GBC [38] are methods based on the distance measurements of the feature space. RSA and DDS assess transferability by evaluating the representation similarity between pre-trained and downstream datasets. GBC employs the Bhattacharyya coefficient to measure class separability in the feature space. Nsleep [33] and Logme [52] estimate transferability by analyzing the conditional distribution, with Nsleep utilizing Gaussian mixture model and Logme employing Bayesian optimization. However, these methods treat network outputs as static and overlook the changes introduced by the training process, leading to less effectiveness in scenes with larger fine-tuning dynamics.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Recently, SFDA [41] and PED [32] propose to simulate changes in the feature space, respectively projecting the features into a Fisher space and utilizing a physically-inspired model to enhance the class separability, achieving impacts similar to fine-tuning. While these methods achieve some improvements, they solely concentrate on the feature space, disregarding the dynamic changes introduced by the classifier, which is jointly optimized with the backbone. Additionally, they utilize linear transformations to simulate the intricate variations in fine-tuning, resulting in a significant limitation in simulation precision. Instead, our LEAD employs the ordinary differential equation to analyze logit dynamics, maintaining a closely aligned objective and simulating the nonlinear changes in fine-tuning.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2.2. Neural Tangent Kernel",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Studying the behavior of neural network optimization processes has been an enduring challenge due to their nonlinearity and nonconvexity. Neural Tangent Kernel (NTK) [20, 26], serving as a theoretical tool to characterize the optimization process, has attracted much research attention. Some studies have explored its theoretical properties and applications. Notable works include the NTK's property of remaining constant under infinite network width [26], the explanation of the instability of training [48], the analysis of its bias and variance under finite width [20], and its acceleration algorithm [35]. While NTK can analyze network trainability [26, 35], it is constrained by the requirement of infinite width and neglects the consideration of initial log-its, resulting in the inability to predict the changes starting",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "28665",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "from the initial state for a finite-width network. To tackle these issues, we innovatively propose an analysis framework leveraging the property of NTK, suitable for model selection problems to bridge the gap between the initial and final states of finite-width networks.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3. Methodology",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In this section, we first present the problem setup for the task of model selection. Then we analyze training mechanisms to model the fine-tuning optimization in a discrete process. Finally, we propose a transferability metric that converts the discrete process into a continuous dynamical equation with a concise solution to directly seize the evolution destination of logits, and feed updated logits into Cross-Entropy loss to assess transferability, as shown in Fig. 2.",
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "3.1. Problem Setup",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Consider  $M$  pre-trained models  $\\{\\Psi_m\\}_{m=1}^M$  and a downstream dataset  $\\mathcal{T} = \\{x_n, y_n\\}_{n=1}^N$  with  $K$  classes, where model  $\\Psi$  consists of its backbone  $f$  which outputs the encoded feature,  $N$  is the number of images in the downstream task. The purpose of model selection is to design an efficient algorithm to predict the ranking of the performance of  $M$  pre-trained models after fine-tuning.",
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "Specifically, given the ground-truth performance rankings  $\\{G_m\\}_{m=1}^M$  of pre-trained models after fine-tuning and the predicted ranking  $\\{P_m\\}_{m=1}^M$  by model selection algorithms, we can leverage the commonly-used rank-based correlation, i.e., the weighted Kendalls'  $\\tau_w$ , to evaluate the effectiveness of the proposed model selection methods, i.e.,",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\tau_ {w} = \\frac {1}{\\sum_ {i \\neq j} w _ {i j}} \\cdot \\sum_ {i \\neq j} w _ {i j} \\operatorname {s i g n} \\left(G _ {i} - G _ {j}\\right) \\cdot \\operatorname {s i g n} \\left(P _ {i} - P _ {j}\\right), \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $w_{ij} = \\frac{1}{i + j}$  and  $\\mathrm{sign}(\\cdot)$  is the signum function. A larger  $\\tau_w$  indicates more consistencies between the predicted ranking and the ground truth, which means a better model selection algorithm.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.2. Revisiting the Fine-tuning Optimization",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "When a pre-trained model  $\\Psi$  transfers to a downstream task  $\\mathcal{T} \\coloneqq \\{\\mathcal{X},\\mathcal{Y}\\}$ , it undergoes extensive optimization for evolving from its initial state (before fine-tuning) to the final state (after fine-tuning), resulting in complex changes in both feature space and output space. Since the transferability metric is designed to evaluate the final state without fine-tuning, it is essential and challenging to model the optimization process without lengthy computations, bridging the gap between the initial and the final state. To gain insights into the underlying optimization mechanisms, we conduct an analysis to compare the prior arts with fine-tuning to revisit the evolution process toward the final state.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Recent works SFDA [41] and PED [32] (called simulation methods) aim to approximate fine-tuning procedures",
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "by simulating feature dynamics. They design an objective function  $U$  to assess the class separability of the feature space. Then, they apply linear transformations to increase  $U$  and feed modified features into a classifier to update logits, as shown below:",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nA, b = \\arg \\max  _ {A, b} U (A \\cdot f (\\mathcal {X}) + b, \\mathcal {Y}), \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\Delta \\mathcal {F} (\\mathcal {X}) = \\mathcal {C} (A \\cdot f (\\mathcal {X}) + b) - \\mathcal {C} (f (\\mathcal {X})),\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $A, b$  denote linear transformation parameters,  $\\mathcal{C}$  denotes a machine learning classifier and  $\\mathcal{F}$  denotes the function that outputs logits. As a result of the optimization in Eq. (2), the objective of enhancing class separability is achieved. However, fine-tuning directly minimizes the gap between predicted logits and labels and performs gradient descent on parameters to update the output logits as follows:",
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\Delta \\theta = - \\eta \\cdot \\frac {\\mathrm {d} \\mathcal {L} (\\mathcal {F} (\\mathcal {X} , \\theta) , \\mathcal {Y})}{\\mathrm {d} \\theta},\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "equation",
+        "text": "\n$$\n\\Delta \\mathcal {F} (\\mathcal {X}) = \\mathcal {F} (\\mathcal {X}, \\theta + \\Delta \\theta) - \\mathcal {F} (\\mathcal {X}, \\theta) \\approx \\Delta \\theta \\cdot \\frac {\\mathrm {d} \\mathcal {F}}{\\mathrm {d} \\theta} \\tag {3}\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "equation",
+        "text": "\n$$\n= - \\eta \\cdot \\frac {\\mathrm {d} \\mathcal {L}}{\\mathrm {d} \\theta} \\cdot \\frac {\\mathrm {d} \\mathcal {F}}{\\mathrm {d} \\theta} = - \\eta \\cdot \\frac {\\mathrm {d} \\mathcal {L}}{\\mathrm {d} \\mathcal {F}} \\left(\\frac {\\mathrm {d} \\mathcal {F}}{\\mathrm {d} \\theta} \\cdot \\frac {\\mathrm {d} \\mathcal {F}}{\\mathrm {d} \\theta}\\right),\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "where  $\\eta$  denotes the learning rate,  $\\mathcal{L}$  denotes loss function, and  $\\theta$  denotes parameters of  $\\mathcal{F}$ . Eq. (3) provides the variation of logits within one step, capturing the nonlinear dynamics based on gradients. When comparing the optimization outlined in Eq. (2) and Eq. (3), it becomes evident that simulation methods differ from fine-tuning in terms of objectives and optimization approaches.",
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "Despite preliminary exploration, such simulation methods come with severe limitations due to these inconsistencies, leading to deviations in predicting the final state, as illustrated in Fig. 3. Specifically, simulation methods aim to enhance class separability within the feature space, whereas fine-tuning drives logits closer to labels. The insufficient objective alignment introduces distinct inductive bias compared to fine-tuning, resulting in notable variations in modeling dynamics [27, 34]. Moreover, due to the nonlinear nature of neural networks and complex parameter interactions, linear approximations in simulation methods often fail to accurately capture the dynamic changes [21]. Such limitations hinder the effective modeling of nonlinearity, further constraining modeling precision.",
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+    {
+        "type": "text",
+        "text": "3.3. Modeling Logits Evolution Process through Dynamical Equation",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "To address the aforementioned problems, our study delves deeper into the optimization analysis from Eq. (3). In fact, unlike features, the logits derived from the optimization output naturally align with the fine-tuning objectives and reflect the inherent nonlinearity from gradient descent. Therefore,",
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+        "type": "page_number",
+        "text": "28666",
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+    {
+        "type": "image",
+        "img_path": "images/afd73633fe40bc8a1e10ada7da220617e5f53e607aef417db3824deb6a4ce21c.jpg",
+        "image_caption": [],
+        "image_footnote": [],
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+    {
+        "type": "image",
+        "img_path": "images/772c7f10ffb50c6f1a01eeb70f507672a56d23c57a1a790ab18c4238c5c4ccae.jpg",
+        "image_caption": [
+            "Figure 2. Comparison of different approaches for modeling the evolution process. (a) Fine-tuning iteratively updates parameters via gradient descent, revealing authentic logits evolution trajectory and classification accuracy for ground-truth ranking. (b) Recent works (e.g., SFDA [41], PED [32]) perform linear transformations in feature space to enhance class separability, updating logits with modified features. The ranking score is determined by Cross-Entropy loss on updated logits. While these approaches simulate fine-tuning impact on features, they often suffer huge deviations from the authentic results. (c) Our method, LEAD, transforms the discrete logit evolution during fine-tuning into a gradient-based dynamical equation to capture nonlinear changes and can efficiently predict the final state through the closed-form solution. It establishes an analysis framework linking the initial and final states, enabling the precise prediction in one step."
+        ],
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+        "page_idx": 3
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+    {
+        "type": "text",
+        "text": "it provides a particularly relevant entry point to analyze dynamical changes during fine-tuning and assess the model transferability through its evolution process.",
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+    {
+        "type": "text",
+        "text": "While the dynamical process of logit space analyzed by Eq. (3) remains consistent with fine-tuning, there still lacks an efficient approach for capturing logits evolution, due to the discrete process of iterating over thousands of steps by traditional optimization. To this end, we propose a new transferability metric called \"Logits Evolution Analysis through Dynamical equation (LEAD)\", that bridges the evolution process from the initial logit space towards the final state. In contrast to extensive optimization iterations, our method proposes a dynamical analysis framework for analyzing the nonlinear effects within the logit space, providing an efficient prediction to capture the final state with a concise solution in a single step.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Theoretical Background. In our LEAD, we innovatively introduce the Neural Tangent Kernel (NTK) to simplify the dynamical equation. Here, we provide a brief introduction to the definition of the NTK kernel function and the constant-preserving property that we utilize.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\hat {\\Phi} _ {\\theta_ {t}} (\\mathcal {X}, \\mathcal {X}) \\triangleq \\nabla_ {\\theta_ {t}} \\mathcal {F} (\\mathcal {X}; \\theta_ {t}) \\nabla_ {\\theta_ {t}} \\mathcal {F} (\\mathcal {X}; \\theta_ {t}) ^ {\\top}, (4) \\\\ \\Phi (\\mathcal {X}, \\mathcal {X}) \\triangleq \\lim  _ {l \\rightarrow \\infty} \\hat {\\Phi} _ {\\theta_ {t}} (\\mathcal {X}, \\mathcal {X}), (4) \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            122,
+            753,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\nabla$  denotes the Laplace Operator, and  $l$  denotes the root mean square of the widths of all layers in the network. The kernel function  $\\hat{\\Phi}_{\\theta_t}$  remains invariant throughout the training process as  $l$  approaches infinity with an approximation error of  $O\\left(\\frac{1}{l^2}\\right)$  [20, 26]. For simplicity, in the remainder of this paper, we denote functions at time  $t$  as:",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/86f95734fc810786cb98edbae5ec9033cac5a37e77337b4e6c0b793079762518.jpg",
+        "image_caption": [
+            "Figure 3. Comparison of the average prediction of final state logits across various methods on VOC2007 [16], where the actual result stems from fine-tuning. Closer to actual results indicates more accurate modeling of the final state. Simulation methods (SFDA, PED) capture the correct trend but exhibit a large deviation from the actual results, affecting the accuracy of model ranking."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "$\\mathcal{F}_t(\\cdot)\\triangleq \\mathcal{F}(\\cdot ,\\theta_t),\\hat{\\Phi}_t(\\cdot)\\triangleq \\hat{\\Phi}_{\\theta_t}(\\mathcal{X},\\mathcal{X}),\\Phi \\triangleq \\Phi (\\mathcal{X},\\mathcal{X}).$",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Dynamical Equation and Closed-form Solution. To bypass the complexity of iterative computations, we extend the analysis in Eq. (3) and theoretically derive a dynamical equation that is efficient for analysis. Specifically, we seek for a mathematical derivation through the theory of limit approximation to convert the discrete process into a continuous differential equation, enabling us to track the trajectory of logits in the solution space of the equation. Furthermore, we leverage the property of the NTK in Eq. (4) to simplify the equation into an Ordinary Differential Equation (ODE) with an initial value condition. Due to space constraints, we directly provide the equation and the detailed proof can be found in the Appendix.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\frac {\\mathrm {d} \\mathcal {F} _ {t}}{\\mathrm {d} t} = - \\eta \\cdot \\Phi \\cdot \\frac {\\mathrm {d} \\mathcal {L} _ {t}}{\\mathrm {d} \\mathcal {F} _ {t}}, \\mathcal {F} _ {0} = l o g _ {i n i t}, \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "28667",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\text{loginit}$  is the initial state of logits obtained through feeding features and labels of downstream datasets to a classification algorithm. Compared to the discrete process, our proposed ODE depicts the continuous evolution of the finetuning dynamics, allowing for a more flexible modeling approach. It transforms discrete gradient effects into equivalent differential effects in continuous time, preserving the capability for modeling nonlinear changes and providing precise prediction of the evolution process. Furthermore, unlike employing numerical methods as the ODE solver, we can directly obtain its closed-form solution through integration over time dimension, allowing us to bypass the lengthy evolution process and reach the optimization destination in a single step, as shown below:",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbb {E} \\left(\\mathcal {F} _ {t} (\\mathcal {X})\\right) = \\left(\\mathbb {I} - e ^ {- \\eta \\Phi \\cdot t}\\right) \\mathcal {Y} + e ^ {- \\eta \\Phi \\cdot t} \\cdot \\log_ {\\text {i n i t}}. \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "As depicted in Eq. (6), the solution is derived by interpolating between the one-hot label and the initial observation of logits, with the interpolation coefficients determined by the NTK matrix. It comprises two crucial elements:  $\\text{log}_{\\text{init}}$ , representing the value of logits before optimization and determining the start of the evolution process; and  $\\Phi$ , indicating the convergence rate to the label and determining the trajectory of logit evolution. Our proposed framework efficiently models the evolution process, enabling a prediction of real-time changes.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Class-aware Decomposition. While Eq. (6) provides the theoretical result for the final state, computing the value of  $\\Phi$  under finite width remains challenging. Prior studies [20, 53] indicate that, even with finite width, the convergence rate can be assessed by using the eigenvalues of the initial state NTK matrix  $\\hat{\\Phi}_0$ . Inspired by this empirical finding, we further conduct a decomposition approach to bridge theory and practice, utilizing the eigenvalue decomposition on  $\\hat{\\Phi}_0$  to replace the convergence rate determined by  $\\Phi$  in Eq. (6) with eigenvalues.",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Due to the network exhibiting varying classification abilities across different classes, their convergence behavior and evolution dynamics also differ during the fine-tuning process. To enhance the modeling of behaviors in different classes, we separately compute NTK for each class, rather than mixing them together, to decouple the respective optimization effect. Specifically, we extract  $n$  samples of each class to calculate their respective NTK matrices and perform decomposition to obtain eigenvalues. The average eigenvalue of each class serves as the unified parameter to determine the interpolation coefficient for this class:",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbb {E} \\left(\\mathcal {F} _ {t} (x)\\right) = \\left(\\mathbb {I} - e ^ {- \\eta \\bar {\\lambda} \\cdot t}\\right) y + e ^ {- \\eta \\bar {\\lambda} \\cdot t} \\cdot \\log_ {i n i t}, \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $x, y$  is a given sample and its one-hot label,  $\\overline{\\lambda}$  is the average eigenvalue of the NTK matrix associated with the class of  $x$ . Building upon the conclusion of Eq. (6), Eq.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "(7) avoids the demand of infinite width, enabling practical computability of the prediction results. As shown in Fig. 2, we employ the results of Eq. (7) to efficiently obtain predictions for the final state logits. Subsequently, following the common practice [32, 33, 41], we feed predictions into the Cross-Entropy loss to obtain the transferability score for model ranking.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Summary. Our method explicitly models the fine-tuning optimization through the theoretical analysis framework and provides a concise dynamical solution to bypass the lengthy optimization process in a single step, which seamlessly integrates the initial state observations and the evolution trajectory towards the final state. Therefore, we can efficiently predict the final logit state through this dynamical solution. Through comparing logit prediction accuracy among different models, it can serve as an effective metric for predicting model transferability.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "To demonstrate the effectiveness and robustness of our approach, we evaluate LEAD on diverse pre-trained models, including both supervised and self-supervised convolutional neural networks. Our evaluation spans 10 widely used classification benchmarks in transfer learning, employing weighted Kendall's  $\\tau_w$  as rank correlation to evaluate the transferability metric. Additionally, we highlight the effectiveness of LEAD in the low-data regime, where only  $2/5/10$  samples are available per class.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.1. Implementation Details",
+        "text_level": 1,
+        "bbox": [
+            498,
+            529,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Given a pre-trained model  $\\Psi$ , we append a random initialized [22] MLP  $h$  as a classification head after its backbone  $f$ , and combine them as  $\\mathcal{F} \\coloneqq h \\circ f$  to produce logits. To compute the logits in the final state, we only need to derive the NTK matrix of each class and  $log_{init}$  through Eq. (7). We follow the approach in [35] to compute the NTK matrix and employ a robust and efficient machine learning classifier, the multi-class SVM [49], to generate  $log_{init}$ . Due to space constraints, we provide a more detailed explanation and pseudocode in the Appendix.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.2. Benchmarks",
+        "text_level": 1,
+        "bbox": [
+            500,
+            710,
+            635,
+            726
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Target Datasets. We employ 10 classification benchmarks commonly utilized in transfer learning research including Caltech-101 [17], Stanford Cars [29], CIFAR10 [30], CIFAR100 [30], DTD [10], Oxford 102 Flowers [37], Food-101 [4], Oxford-IIIT Pets [39], SUN397 [51], and VOC2007 [16]. These datasets encompass abundant characteristics, including backgrounds, textures, and coarse/fine-grained scenes, spanning diverse fields.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Ground Truth Rank. To conduct the ground truth ranking for the model zoo, we follow the approach in [41] and [52]. Specifically, we employ a grid search strategy to determine",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "28668",
+        "bbox": [
+            478,
+            944,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/53306db3195106ed608cf304254ce6720c67983e0cbd5c2889f21459be68f674.jpg",
+        "table_caption": [
+            "Table 1. Performance comparisons of different transferability metrics on the supervised model zoo. We measure the performance with weighted Kendall's  $\\tau_w$  and a larger  $\\tau_w$  represents a better prediction rank. The best results are in bold and the second-best are in underline."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td rowspan=\"2\">Reference</td><td colspan=\"10\">Downstream Target Dataset</td></tr><tr><td>Food</td><td>Caltech</td><td>Flowers</td><td>Cars</td><td>CIFAR100</td><td>DTD</td><td>CIFAR10</td><td>Pets</td><td>SUN397</td><td>VOC2007</td></tr><tr><td>PARC [3]</td><td>NeurIPS&#x27;21</td><td>0.363</td><td>0.422</td><td>0.066</td><td>0.135</td><td>-0.092</td><td>0.536</td><td>0.310</td><td>0.114</td><td>-0.097</td><td>0.707</td></tr><tr><td>Logme [52]</td><td>ICML&#x27;21</td><td>0.336</td><td>0.349</td><td>0.425</td><td>0.538</td><td>0.603</td><td>0.651</td><td>0.783</td><td>0.372</td><td>0.440</td><td>0.673</td></tr><tr><td>Nsleep [33]</td><td>CVPR&#x27;21</td><td>0.504</td><td>0.678</td><td>0.292</td><td>0.435</td><td>0.686</td><td>0.452</td><td>0.656</td><td>0.686</td><td>0.770</td><td>0.645</td></tr><tr><td>PACTran [12]</td><td>ECCV&#x27;22</td><td>0.709</td><td>0.372</td><td>0.480</td><td>0.151</td><td>0.742</td><td>0.372</td><td>0.757</td><td>0.451</td><td>0.422</td><td>0.536</td></tr><tr><td>SFDA [41]</td><td>ECCV&#x27;22</td><td>0.534</td><td>0.597</td><td>0.421</td><td>0.472</td><td>0.749</td><td>0.421</td><td>0.817</td><td>0.625</td><td>0.562</td><td>0.728</td></tr><tr><td>GBC [38]</td><td>CVPR&#x27;22</td><td>0.844</td><td>0.430</td><td>0.348</td><td>0.735</td><td>0.830</td><td>0.480</td><td>0.866</td><td>0.358</td><td>0.574</td><td>0.654</td></tr><tr><td>ETran [18]</td><td>ICCV&#x27;23</td><td>0.709</td><td>0.627</td><td>0.534</td><td>0.557</td><td>0.749</td><td>0.605</td><td>0.719</td><td>0.651</td><td>0.577</td><td>0.673</td></tr><tr><td>PED [32]</td><td>ICCV&#x27;23</td><td>0.573</td><td>0.597</td><td>0.451</td><td>0.472</td><td>0.749</td><td>0.421</td><td>0.770</td><td>0.625</td><td>0.562</td><td>0.728</td></tr><tr><td>LEAD</td><td>This paper</td><td>0.892</td><td>0.698</td><td>0.786</td><td>0.586</td><td>0.835</td><td>0.689</td><td>0.791</td><td>0.841</td><td>0.609</td><td>0.743</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "the actual performance of each model in the downstream task. This strategy involves trying various learning rates from the set  $\\{10^{-1}, 10^{-2}, 10^{-3}, 10^{-4}\\}$  and different weight decay values from the set  $\\{0, 10^{-6}, 10^{-5}, 10^{-4}, 10^{-3}\\}$ . To ensure reliability, we repeat each experiment 5 times with different random seeds and take the average as the result.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.3. Evaluation on Supervised Models",
+        "text_level": 1,
+        "bbox": [
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+            396,
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+            412
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Model Zoo. We construct a Model Zoo that includes 12 CNN models supervised pre-trained on ImageNet [11], covering widely-used architectures: ResNet-34 [23], ResNet-50 [23], ResNet-101 [23], ResNet-152 [23], DenseNet-121 [25], DenseNet-161 [25], DenseNet-169 [25], DenseNet-201 [25], MNet-A1 [45], MobileNetV2 [40], GoogleNet [43], and InceptionV3 [44]. The accuracy results of these models after fine-tuning can be found in the Appendix.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Result Analysis. To show the effectiveness of LEAD, we compare it with prior arts, such as Bayesian-based Logme, Separability-based GBC, and simulation methods SFDA and PED. As shown in Tab. 1, simulation methods consider underlying dynamic effects and exhibit promising performances on some datasets. However, as the aforementioned analysis in Sec. 3.2 shows, the bias in the simulation process causes these methods to have unstable improvements, particularly resulting in unsatisfactory performance on Flowers, Food, and Pets. Benefiting from a precise analysis of the evolution, our LEAD yields a performance gain of  $+0.335$ ,  $+0.319$ ,  $+0.216$  compared to PED on these three datasets, respectively. Overall, LEAD achieves the best  $\\tau_w$  on 7 target datasets and obtains an average  $\\tau_w$  of 0.747 which is relatively  $18\\%$  better than the latest SOTA ETran [18]. Our experiments highlight the importance of accurate modeling of dynamics and confirm the effectiveness of our method to model the evolution process through the dynamical equation.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.4. Evaluation on Self-supervised Models",
+        "text_level": 1,
+        "bbox": [
+            76,
+            833,
+            405,
+            849
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Model Zoo. Self-supervised learning models (SSL models) have shown their efficacy in transfer learning and often display superior generalization performance compared",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "to Supervised models. To illustrate the broad applicability of our approach, inspired by [32, 41], we assemble a self-supervised model zoo trained on ImageNet with BYOL [19], Infomin [46], PCLv1 [31], PCLv2 [31], Selav2 [1], InsDis [50], SimCLRv1 [7], SimCLRv2 [8], MoCov1 [24], MoCov2 [9], DeepClusterv2 [5], and SWAV [6].",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Result Analysis. Due to differing pre-training and downstream classification objectives, SSL models undergo larger dynamic changes during the fine-tuning process, leading to distinct transferability properties compared to supervised models [15]. As shown in Tab. 1 and 2, methods that disregard dynamics (e.g. PARC, Nsleep) perform competitively in the supervised model zoo, but fail on some datasets for SSL models. For example, Nsleep and PARC have a negative small rank correlation on VOC2007 (-0.101) and CIFAR100 (-0.136), respectively. To maintain fairness, we refrain from comparing with GBC [38] in the SSL model zoo, which is designed for supervised scenarios. On the contrary, SFDA and PED exhibit better performances due to consideration of training dynamics. Nevertheless, the limitation of the simulating process still hinders their performance. Compared to them, LEAD achieves a consistent improvement on 7 datasets and obtains an average  $\\tau_w$  of 0.746 which is relatively  $15\\%$  better than PED (0.648). The results validate the effectiveness of LEAD for SSL models.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.5. Evaluation on Low-data Regime",
+        "text_level": 1,
+        "bbox": [
+            498,
+            683,
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Experimental Settings. In practical application, privacy and resource constraints may limit our access to the entire downstream dataset. To explore the utilization boundary, we evaluate whether LEAD can provide effective model ranking only using limited samples. We follow three data settings in PACTran [12] with increasing average number of samples per class  $\\{2,5,10\\}$  and divide 10 datasets into two groups according to the number of classes:  $100+$  classes, including Food, Caltech, Flowers, Cars, CIFAR100, and SUN397; 10-99 classes, including DTD, CIFAR10, Pets, and VOC2007. For each setting, we repeatedly sample 5 times for evaluation and take the average as the result.",
+        "bbox": [
+            496,
+            703,
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+            883
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Result Analysis. As shown in Tab. 3, all methods, in-",
+        "bbox": [
+            500,
+            885,
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+            901
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "28669",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/280a395d418e0a632e7a7933c2d5f798a08610cd9966d7d43289875207612f96.jpg",
+        "table_caption": [
+            "Table 2. Performance comparisons on the self-supervised model zoo. The best results are in bold and the second-best are in underline."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td rowspan=\"2\">Reference</td><td colspan=\"10\">Downstream Target Dataset</td></tr><tr><td>Food</td><td>Caltech</td><td>Flowers</td><td>Cars</td><td>CIFAR100</td><td>DTD</td><td>CIFAR10</td><td>Pets</td><td>SUN397</td><td>VOC2007</td></tr><tr><td>PARC [3]</td><td>NeurIPS&#x27;21</td><td>0.359</td><td>0.196</td><td>0.622</td><td>0.424</td><td>-0.136</td><td>0.447</td><td>0.147</td><td>0.496</td><td>-0.006</td><td>0.618</td></tr><tr><td>Logme [52]</td><td>ICML&#x27;21</td><td>0.570</td><td>0.051</td><td>0.604</td><td>0.375</td><td>-0.008</td><td>0.627</td><td>0.295</td><td>0.684</td><td>0.217</td><td>0.158</td></tr><tr><td>Nsleep [33]</td><td>CVPR&#x27;21</td><td>0.574</td><td>0.525</td><td>0.534</td><td>0.486</td><td>0.276</td><td>0.641</td><td>-0.044</td><td>0.792</td><td>0.719</td><td>-0.101</td></tr><tr><td>PACTran [12]</td><td>ECCV&#x27;22</td><td>0.720</td><td>0.622</td><td>0.601</td><td>0.474</td><td>0.529</td><td>0.614</td><td>0.477</td><td>0.641</td><td>0.638</td><td>0.620</td></tr><tr><td>SFDA [41]</td><td>ECCV&#x27;22</td><td>0.685</td><td>0.523</td><td>0.749</td><td>0.515</td><td>0.548</td><td>0.773</td><td>0.619</td><td>0.586</td><td>0.698</td><td>0.568</td></tr><tr><td>ETran [18]</td><td>ICCV&#x27;23</td><td>0.465</td><td>0.405</td><td>0.644</td><td>0.587</td><td>0.650</td><td>0.214</td><td>0.606</td><td>0.338</td><td>0.520</td><td>0.376</td></tr><tr><td>PED [32]</td><td>ICCV&#x27;23</td><td>0.581</td><td>0.614</td><td>0.777</td><td>0.649</td><td>0.568</td><td>0.907</td><td>0.673</td><td>0.462</td><td>0.661</td><td>0.583</td></tr><tr><td>LEAD</td><td>This paper</td><td>0.860</td><td>0.780</td><td>0.725</td><td>0.663</td><td>0.776</td><td>0.825</td><td>0.713</td><td>0.629</td><td>0.760</td><td>0.723</td></tr></table>",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/ddf1ad6e63472cda2967e11a0a1f7b9d6c98097fc163b549cb1b64d29d575b34.jpg",
+        "table_caption": [
+            "Table 3. Performance comparisons with different  $N / K$ , where  $K$  is the number of classes,  $N$  is the number of samples for computing the metric. We divide 10 benchmarks into two groups according to the number of classes: 100+ classes and 10-99 classes, and evaluate the average of  $\\tau_w$  on the two groups. Additionally, we also provide the average results on the 10 benchmarks, recorded as Avg. The best results are denoted in bold, the second best results are denoted in underline, and - denotes cannot give a valid ranking."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td colspan=\"11\">Supervised / Self-supervised pre-trained Model</td></tr><tr><td rowspan=\"2\">Method</td><td colspan=\"3\">N/K = 2</td><td colspan=\"3\">N/K = 5</td><td colspan=\"3\">N/K = 10</td><td></td></tr><tr><td>100+ classes</td><td>10-99 classes</td><td>Avg</td><td>100+ classes</td><td>10-99 classes</td><td>Avg</td><td>100+ classes</td><td>10-99 classes</td><td>Avg</td><td></td></tr><tr><td>GBC</td><td>0.17 / 0.32</td><td>0.10 / 0.17</td><td>0.13 / 0.25</td><td>0.45 / 0.40</td><td>0.22 / 0.18</td><td>0.36 / 0.31</td><td>0.59 / 0.42</td><td>0.42 / 0.22</td><td>0.52 / 0.34</td><td></td></tr><tr><td>PACTran</td><td>0.43 / 0.49</td><td>0.20 / 0.39</td><td>0.33 / 0.45</td><td>0.42 / 0.48</td><td>0.31 / 0.44</td><td>0.38 / 0.47</td><td>0.56 / 0.52</td><td>0.48 / 0.46</td><td>0.53 / 0.50</td><td></td></tr><tr><td>ETran</td><td>0.42 / 0.43</td><td>0.12 / 0.41</td><td>0.29 / 0.42</td><td>0.48 / 0.47</td><td>0.31 / 0.38</td><td>0.41 / 0.43</td><td>0.56 / 0.47</td><td>0.56 / 0.48</td><td>0.56 / 0.48</td><td></td></tr><tr><td>PED</td><td>- / 0.36</td><td>- / 0.24</td><td>- / 0.31</td><td>- / 0.43</td><td>- / 0.35</td><td>- / 0.40</td><td>0.30 / 0.50</td><td>0.22 / 0.56</td><td>0.27 / 0.52</td><td></td></tr><tr><td>LEAD</td><td>0.45 / 0.48</td><td>0.51 / 0.45</td><td>0.47 / 0.46</td><td>0.48 / 0.49</td><td>0.64 / 0.53</td><td>0.54 / 0.51</td><td>0.65 / 0.53</td><td>0.64 / 0.60</td><td>0.64 / 0.56</td><td></td></tr></table>",
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+    {
+        "type": "text",
+        "text": "cluding PACTran designed for this scenario, exhibit significant performance declines under low-data settings. For instance, ETran's performance in the supervised model zoo drops from 0.64 with the entire dataset to 0.29, 0.41, and 0.56 in three low-data settings. Moreover, some methods, such as SFDA and PED fail to provide prediction rankings in some settings. For example, when  $N / K = 2,5$ , PED cannot correctly evaluate class separability due to insufficient data, imposing huge changes to completely separate different classes. This leads to all models perfectly classifying all samples, resulting in identical scores that cannot be ranked. In contrast, our LEAD achieves stable results, ensuring  $\\tau_w \\geq 0.45$  even in extreme settings like  $N / K = 2$ , and consistently outperforms other methods. For example, under  $N / K = 10$ , its average  $\\tau_w$  in the supervised model zoo reaches 0.64, which is relatively  $14\\%$  better than the latest SOTA ETran (0.56) and is equivalent to the latest SOTA on the complete dataset, with less than  $5\\%$  of data size. The results demonstrate the robustness of our method in the face of data limitations.",
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+    {
+        "type": "text",
+        "text": "5. Ablation Study and Efficiency Analysis",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "In this section, without loss of generality, we conduct ablation studies on Caltech, CIFAR10, and VOC2007, building upon the evaluation of SSL models in Sec. 4.4 for saving time. We conduct separate experiments to analyze the impact of interpolation coefficients, a key component of LEAD, aiming to delve into the influence of hyperparameters and implementation details, gaining insights into key",
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+    },
+    {
+        "type": "text",
+        "text": "factors contributing to LEAD's effectiveness. Additionally, we provide a runtime comparison to verify efficiency, and more ablation study results are provided in the appendix.",
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+    {
+        "type": "text",
+        "text": "5.1. Interpolation Coefficient",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The interpolation coefficients are determined by time coefficient  $t$  and the NTK matrix. We conduct ablation experiments on these two key factors:",
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+    {
+        "type": "text",
+        "text": "Time Coefficient  $t$ . As we model the discrete process as a continuous ODE, the continuous variable  $t$  is proportional to the number of updates, determining the progress of the evolution process. In Fig. 4, we evaluate our method under varied time settings, keeping the unit as 1e6 consistent across all experiments. It is evident that performance improves as the time increases within a specific range. However, if the dynamic effect persists for an extended period (e.g., 10.0), all model predictions converge too closely to the ground-truth label, reducing discrimination for model ranking. Hence, we set the time coefficient as 1 by default.",
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+    {
+        "type": "image",
+        "img_path": "images/d8befea459eb8901a1a723d8409b407c7f5f958b1a950897281e0ed8c9dfe50a.jpg",
+        "image_caption": [],
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+    {
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+        "img_path": "images/1b3c6d2bb15e3a12791b480ffe8032eff56a800c64b8ddf7c8ef96a1d83c0eba.jpg",
+        "image_caption": [
+            "Figure 4. The left picture shows the performance gain in  $\\tau_w$  with respect to different time  $t$  and the right shows the performance in different sample sizes for each class NTK."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "page_number",
+        "text": "28670",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Sample Size for NTK. To enhance the perception of different dynamic intensities of classes, we propose the class-aware decomposition that employs  $S$  samples of each class to obtain NTK matrix and perform spectrum analysis to derive eigenvalues. In Fig. 4, we conduct ablation experiments to explore the effect of varying  $S$ . We observe that performance generally improves as  $S$  increases, and gradually reaches stability. This demonstrates that when the sample size reaches a certain size, eigenvalues reliably capture differences in dynamic intensity, offering a refined analysis result of the dynamics. Therefore, we set  $S = 64$  to ensure the method's efficiency and stability in all experiments.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5.2. Running Time Comparison",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "In experiment results, we have demonstrated the effectiveness of LEAD in various scenarios. In this section, we highlight the computational efficiency of LEAD. With the concise solution in Eq. (7), LEAD predicts the final state only requiring the NTK matrix and  $\\text{log}_{init}$ . As shown in Tab. 4, the running time of LEAD is about half that of simulation methods (45s compared to 92s), ranking second after GBC which displays unstable performance. Notably, LEAD takes 3s to compute the NTK, while feature extraction takes 420s, resulting in only a marginal  $0.7\\%$  increase in GPU time. The time to compute  $\\text{log}_{init}$  is 42s CPU time, indicating significant potential for exploring faster classification algorithms to further reduce the overall time.",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/353febb933a476c50c193c6ea429c60bf7e23388e63e622dbfdea7ad1647a374.jpg",
+        "table_caption": [
+            "Table 4. The comparisons of average running time on CIFAR10."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Metrics</td><td>PARC</td><td>NLEEP</td><td>PACTran</td><td>SFDA</td><td>GBC</td><td>PED</td><td>Ours</td></tr><tr><td>Running Time</td><td>111s</td><td>1430s</td><td>77s</td><td>92s</td><td>26s</td><td>97s</td><td>45s</td></tr></table>",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "6. Visualization and Analysis",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In this section, we validate our approach through some visualizations and these results clearly illustrate how our model effectively addresses the model selection problem.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "6.1. Logit Prediction",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "We have conducted a comparison of the predicted logits distribution on VOC2007 using different methods, as illustrated in Fig. 3. Notably, predictions obtained by LEAD closely match the authentic distribution after fine-tuning. To provide further quantitative analysis, we visualize the average bias in predicted logits in Fig. 5. Across three datasets, our method exhibits a substantial reduction compared to simulation methods, achieving nearly a  $50\\%$  overall reduction. This visualization highlights the precision of our dynamical equation-based approach in capturing logit evolution for more accurate ranking sequences.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/5730efca410870bc74277eafa6b7679899fbff59307e049120384f6d9a9826e7.jpg",
+        "image_caption": [
+            "Figure 5. Comparison of the average difference between logits predicted by different methods and logits after fine-tuning. The difference is calculated utilizing the Euclidean distance."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "6.2. Rank Variation",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "By employing our method, we can refine models that have poor initial observation but show better progress during training. To assess the effectiveness of our approach, we conduct a visualization comparing the model rankings between the initial observations and our predicted final state, as shown in Fig. 6. The results clearly illustrate a substantial enhancement in the calibration of model rankings when using our refined observations, with the optimal model now positioned closely to the reference line in the figure. Notably, models starting from an initially unfavorable point can be rapidly elevated to achieve a superior ranking, highlighting the effectiveness of our methodology.",
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+    {
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+        "img_path": "images/2f3583d5c16fb243a02f5b430a4256595b02cb4df51f2e295eacd8a799197982.jpg",
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+    {
+        "type": "image",
+        "img_path": "images/c6876fb90cafd3d8cdb83f6640d4e998b199078d9922496892cbbb318c52a4ff.jpg",
+        "image_caption": [],
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+    },
+    {
+        "type": "image",
+        "img_path": "images/47164e21d643dbb8ece11d0d1697e86c74aac8c23ea55f72173eb84e597ae7c1.jpg",
+        "image_caption": [],
+        "image_footnote": [],
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+    },
+    {
+        "type": "image",
+        "img_path": "images/075db0296cb59584eb3a8b14d5d198af5096a3c0919fb40315dd6521e9dd9594.jpg",
+        "image_caption": [
+            "Figure 6. The variation in model ranking, utilizing initial states (first row) and predicted final states of LEAD (second row). Results span three datasets, from left to right: CIFAR10, Caltech, and VOC2007. Shaded areas reflect the range of the ranking error."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/1b4b2ab39d6d5f3823aa39cfe2de811aba1c89e26dfe2f179ef288de09157e83.jpg",
+        "image_caption": [],
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+    },
+    {
+        "type": "image",
+        "img_path": "images/126bb530f74b06ea081490901547b8ad5456047169c6db2349993f4dba8e19d6.jpg",
+        "image_caption": [],
+        "image_footnote": [],
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "7. Conclusions and Future Work",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "In this work, we propose a dynamical equation designed to capture the evolution process within the logit space, offering an efficient solution for assessing model transferability. We construct a theoretical analysis framework and further devise a more practical and precise solution. And we demonstrate its consistent effectiveness across various scenarios including supervised and self-supervised, full-data and low-data settings. In future work, we intend to expand the current analysis framework beyond classification to cover a broader range of downstream tasks. We hope that our work can enhance the understanding of optimization mechanisms in deep neural networks and shed light on other fields, such as the design of optimization algorithms.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Acknowledgement",
+        "text_level": 1,
+        "bbox": [
+            500,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "This work was supported by the National Natural Science Foundation of China under Grant 62088102, in part by the PKU-NTU Joint Research Institute (JRI) sponsored by a donation from the Ng Teng Fong Charitable Foundation and in part by AI Joint Lab of Future Urban Infrastructure sponsored by Fuzhou Chengtou New Infrastructure Group and Boyun Vision Co. Ltd.",
+        "bbox": [
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+    },
+    {
+        "type": "page_number",
+        "text": "28671",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "References",
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+        "bbox": [
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+            104
+        ],
+        "page_idx": 8
+    },
+    {
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2024/LEAD_ Exploring Logit Space Evolution for Model Selection/cac4214c-e8ea-4c89-8778-e0818b32709b_origin.pdf

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2024/LEAD_ Exploring Logit Space Evolution for Model Selection/full.md

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+# LEAD: Exploring Logit Space Evolution for Model Selection
+
+Zixuan Hu $^{1}$  Xiaotong Li $^{1}$  Shixiang Tang $^{3}$  Jun Liu $^{4}$  Yichun Hu $^{1}$  Ling-Yu Duan $^{1,2*}$
+
+$^{1}$  School of Computer Science, Peking University, Beijing, China,  $^{2}$  Peng Cheng Laboratory, Shenzhen, China,
+
+<sup>3</sup> The Chinese University of Hong Kong, Hongkong, China, <sup>4</sup> Singapore University of Technology and Design, Singapore {hzxuan, hycc, lingyu}@pku.edu.cn, lixiaotong@stu.pku.edu.cn, shixiangtang@cuhk.edu.hk, jun.liu@sutd.edu.sg
+
+# Abstract
+
+The remarkable success of "pretrain-then-finetune" paradigm has led to a proliferation of available pre-trained models for vision tasks. This surge presents a significant challenge in efficiently choosing the most suitable pretrained models for downstream tasks. The critical aspect of this challenge lies in effectively predicting the model transferability by considering the underlying fine-tuning dynamics. Existing methods often model fine-tuning dynamics in feature space with linear transformations, which do not precisely align with the fine-tuning objective and fail to grasp the essential nonlinearity from optimization. To this end, we present LEAD, a finetuning-aligned approach based on the network output of logits. LEAD proposes a theoretical framework to model the optimization process and derives an ordinary differential equation (ODE) to depict the nonlinear evolution toward the final logit state. Additionally, we design a class-aware decomposition method to consider the varying evolution dynamics across classes and further ensure practical applicability. Integrating the closely aligned optimization objective and nonlinear modeling capabilities derived from the differential equation, our method offers a concise solution to effectively bridge the optimization gap in a single step, bypassing the lengthy fine-tuning process. The comprehensive experiments on 24 supervised and self-supervised pre-trained models across 10 downstream datasets demonstrate impressive performances and showcase its broad adaptability even in low-data scenarios.
+
+# 1. Introduction
+
+The "pretrain-then-finetune" learning paradigm has exhibited remarkable success in a wide range of computer vision tasks [6, 28], leading to an increasing number of diverse pretrained models open-sourced to the computer vision community. This surge poses a significant challenge in selecting the optimal pre-trained model for a downstream task
+
+![](images/2c3f6aa22c47c4b6480171e0d2ff66d7c4f64ce96d130c4892baa2e673c8f2a1.jpg)  
+Figure 1. This diagram illustrates the task of model selection, which aims to rank pre-trained models for choosing the optimal one. The ground-truth ranking sequence is derived from the models' accuracy after fine-tuning. However, due to the time-intensive nature of this process, it requires to design efficient transferability metrics for accurate ranking prediction. The performance of this metric is evaluated using rank correlation, e.g., weighted Kendall's tau [42], to compare the predicted and ground-truth rankings.
+
+from a vast model zoo. Considering that the brute-force solution of fine-tuning all models on downstream tasks may be infeasible in many scenarios due to the substantial computational costs, the model selection task emerges [13, 47], which ranks the transferability of pre-trained models to the given task without incurring much cost, as shown in Fig. 1.
+
+Predicting model transferability aims to efficiently estimate the final state after fine-tuning on the downstream task, without network optimization by backward propagation. Prior studies only depend on specific properties of the initial state (e.g., representation similarity [13, 14], conditional distribution [33, 47]), to serve as transferability indicators. Recent studies reveal that modeling the dynamic process of fine-tuning has become the bottleneck to design more high-quality transferability metrics. Following this philosophy, recent works propose to simulate fine-tuning dynamics on features through multiple stages of linear transformations [32, 41], achieving some promising results.
+
+Despite recent progress in this field, there are still two
+
+considerable gaps between existing modeled fine-tuning dynamics and the real ones: (1) Insufficient objective alignment. The designed objectives in prior works do not seamlessly align with fine-tuning, as they often focus more on enhancing class separability via feature manipulation, rather than the classification optimization for both the feature and output spaces. (2) Disregarding nonlinear modeling. Existing methods relying solely on linear transformations cannot well capture the intricate nonlinear changes in the feature space during optimization. Such constraints contribute to growing deviations in dynamic modeling and result in unreliable predictions of the final state.
+
+Delving deeper into the optimization process, we focus on modeling the dynamic changes within the output space (i.e., logits for classification), which not only more closely relates to the fine-tuning objective but also embeds the overall nonlinear dynamics from the network optimization during fine-tuning. Building upon this foundation, we introduce an insightful framework to depict the trajectory of logits toward their final state in a dynamical modeling system. To capture and understand this evolution process of the logit space, the framework provides a discrete iterative optimization equation via gradient analysis and captures nonlinear logit space changes during optimization.
+
+In contrast to the extensive iterations required in fine-tuning optimization, we further extend the framework to propose a new transferability metric "Logits Evolution Analysis through Dynamical Equation (LEAD)", to seize the final evolutionary state in a single step. We perform a mathematical derivation to convert the discrete process into a continuous differential equation and simplify it into an ordinary differential equation (ODE) by leveraging the classical analysis tool, Neural Tangent Kernel (NTK) [26]. This ODE concisely models the nonlinear evolution in logit space through its closed-form solution, allowing for real-time estimation of logits. Additionally, we introduce a class-aware decomposition method to enhance prediction accuracy and break the barrier of theoretical assumption of NTK. As a result, our method provides a direct estimation of the evolution by incorporating both the initial model state and the impact of fine-tuning evolution, serving as an effective indicator assessing model transferability.
+
+The contributions of this work are three-fold. (1) To the best of our knowledge, we are the first to explore model transferability by modeling the evolution process in the logit space. (2) We propose LEAD, a novel transferability metric with two key components: a theoretical framework providing a closed-form solution to depict the logits evolution towards the final state, and a class-aware decomposition method to guarantee the practical applicability of theoretical findings and improve predictive precision. (3) We validate the effectiveness and generalizability of our method through experiments on 24 different pre-trained
+
+models across 10 downstream datasets, achieving SOTA results with an average of  $17\%$  gain in the rank correlation. In addition, our method can be naturally extended to low-data scenarios while maintaining competitive performance.
+
+# 2. Related Work
+
+# 2.1. Transferability Metric
+
+The challenge of efficiently ranking pre-trained models has captured much interest of researchers, leading to the development of various metrics to evaluate the model transferability [2, 3, 12, 18, 36, 38, 47, 52]. For example, RSA [13], DDS [14] and GBC [38] are methods based on the distance measurements of the feature space. RSA and DDS assess transferability by evaluating the representation similarity between pre-trained and downstream datasets. GBC employs the Bhattacharyya coefficient to measure class separability in the feature space. Nsleep [33] and Logme [52] estimate transferability by analyzing the conditional distribution, with Nsleep utilizing Gaussian mixture model and Logme employing Bayesian optimization. However, these methods treat network outputs as static and overlook the changes introduced by the training process, leading to less effectiveness in scenes with larger fine-tuning dynamics.
+
+Recently, SFDA [41] and PED [32] propose to simulate changes in the feature space, respectively projecting the features into a Fisher space and utilizing a physically-inspired model to enhance the class separability, achieving impacts similar to fine-tuning. While these methods achieve some improvements, they solely concentrate on the feature space, disregarding the dynamic changes introduced by the classifier, which is jointly optimized with the backbone. Additionally, they utilize linear transformations to simulate the intricate variations in fine-tuning, resulting in a significant limitation in simulation precision. Instead, our LEAD employs the ordinary differential equation to analyze logit dynamics, maintaining a closely aligned objective and simulating the nonlinear changes in fine-tuning.
+
+# 2.2. Neural Tangent Kernel
+
+Studying the behavior of neural network optimization processes has been an enduring challenge due to their nonlinearity and nonconvexity. Neural Tangent Kernel (NTK) [20, 26], serving as a theoretical tool to characterize the optimization process, has attracted much research attention. Some studies have explored its theoretical properties and applications. Notable works include the NTK's property of remaining constant under infinite network width [26], the explanation of the instability of training [48], the analysis of its bias and variance under finite width [20], and its acceleration algorithm [35]. While NTK can analyze network trainability [26, 35], it is constrained by the requirement of infinite width and neglects the consideration of initial log-its, resulting in the inability to predict the changes starting
+
+from the initial state for a finite-width network. To tackle these issues, we innovatively propose an analysis framework leveraging the property of NTK, suitable for model selection problems to bridge the gap between the initial and final states of finite-width networks.
+
+# 3. Methodology
+
+In this section, we first present the problem setup for the task of model selection. Then we analyze training mechanisms to model the fine-tuning optimization in a discrete process. Finally, we propose a transferability metric that converts the discrete process into a continuous dynamical equation with a concise solution to directly seize the evolution destination of logits, and feed updated logits into Cross-Entropy loss to assess transferability, as shown in Fig. 2.
+
+# 3.1. Problem Setup
+
+Consider  $M$  pre-trained models  $\{\Psi_m\}_{m=1}^M$  and a downstream dataset  $\mathcal{T} = \{x_n, y_n\}_{n=1}^N$  with  $K$  classes, where model  $\Psi$  consists of its backbone  $f$  which outputs the encoded feature,  $N$  is the number of images in the downstream task. The purpose of model selection is to design an efficient algorithm to predict the ranking of the performance of  $M$  pre-trained models after fine-tuning.
+
+Specifically, given the ground-truth performance rankings  $\{G_m\}_{m=1}^M$  of pre-trained models after fine-tuning and the predicted ranking  $\{P_m\}_{m=1}^M$  by model selection algorithms, we can leverage the commonly-used rank-based correlation, i.e., the weighted Kendalls'  $\tau_w$ , to evaluate the effectiveness of the proposed model selection methods, i.e.,
+
+$$
+\tau_ {w} = \frac {1}{\sum_ {i \neq j} w _ {i j}} \cdot \sum_ {i \neq j} w _ {i j} \operatorname {s i g n} \left(G _ {i} - G _ {j}\right) \cdot \operatorname {s i g n} \left(P _ {i} - P _ {j}\right), \tag {1}
+$$
+
+where  $w_{ij} = \frac{1}{i + j}$  and  $\mathrm{sign}(\cdot)$  is the signum function. A larger  $\tau_w$  indicates more consistencies between the predicted ranking and the ground truth, which means a better model selection algorithm.
+
+# 3.2. Revisiting the Fine-tuning Optimization
+
+When a pre-trained model  $\Psi$  transfers to a downstream task  $\mathcal{T} \coloneqq \{\mathcal{X},\mathcal{Y}\}$ , it undergoes extensive optimization for evolving from its initial state (before fine-tuning) to the final state (after fine-tuning), resulting in complex changes in both feature space and output space. Since the transferability metric is designed to evaluate the final state without fine-tuning, it is essential and challenging to model the optimization process without lengthy computations, bridging the gap between the initial and the final state. To gain insights into the underlying optimization mechanisms, we conduct an analysis to compare the prior arts with fine-tuning to revisit the evolution process toward the final state.
+
+Recent works SFDA [41] and PED [32] (called simulation methods) aim to approximate fine-tuning procedures
+
+by simulating feature dynamics. They design an objective function  $U$  to assess the class separability of the feature space. Then, they apply linear transformations to increase  $U$  and feed modified features into a classifier to update logits, as shown below:
+
+$$
+A, b = \arg \max  _ {A, b} U (A \cdot f (\mathcal {X}) + b, \mathcal {Y}), \tag {2}
+$$
+
+$$
+\Delta \mathcal {F} (\mathcal {X}) = \mathcal {C} (A \cdot f (\mathcal {X}) + b) - \mathcal {C} (f (\mathcal {X})),
+$$
+
+where  $A, b$  denote linear transformation parameters,  $\mathcal{C}$  denotes a machine learning classifier and  $\mathcal{F}$  denotes the function that outputs logits. As a result of the optimization in Eq. (2), the objective of enhancing class separability is achieved. However, fine-tuning directly minimizes the gap between predicted logits and labels and performs gradient descent on parameters to update the output logits as follows:
+
+$$
+\Delta \theta = - \eta \cdot \frac {\mathrm {d} \mathcal {L} (\mathcal {F} (\mathcal {X} , \theta) , \mathcal {Y})}{\mathrm {d} \theta},
+$$
+
+$$
+\Delta \mathcal {F} (\mathcal {X}) = \mathcal {F} (\mathcal {X}, \theta + \Delta \theta) - \mathcal {F} (\mathcal {X}, \theta) \approx \Delta \theta \cdot \frac {\mathrm {d} \mathcal {F}}{\mathrm {d} \theta} \tag {3}
+$$
+
+$$
+= - \eta \cdot \frac {\mathrm {d} \mathcal {L}}{\mathrm {d} \theta} \cdot \frac {\mathrm {d} \mathcal {F}}{\mathrm {d} \theta} = - \eta \cdot \frac {\mathrm {d} \mathcal {L}}{\mathrm {d} \mathcal {F}} \left(\frac {\mathrm {d} \mathcal {F}}{\mathrm {d} \theta} \cdot \frac {\mathrm {d} \mathcal {F}}{\mathrm {d} \theta}\right),
+$$
+
+where  $\eta$  denotes the learning rate,  $\mathcal{L}$  denotes loss function, and  $\theta$  denotes parameters of  $\mathcal{F}$ . Eq. (3) provides the variation of logits within one step, capturing the nonlinear dynamics based on gradients. When comparing the optimization outlined in Eq. (2) and Eq. (3), it becomes evident that simulation methods differ from fine-tuning in terms of objectives and optimization approaches.
+
+Despite preliminary exploration, such simulation methods come with severe limitations due to these inconsistencies, leading to deviations in predicting the final state, as illustrated in Fig. 3. Specifically, simulation methods aim to enhance class separability within the feature space, whereas fine-tuning drives logits closer to labels. The insufficient objective alignment introduces distinct inductive bias compared to fine-tuning, resulting in notable variations in modeling dynamics [27, 34]. Moreover, due to the nonlinear nature of neural networks and complex parameter interactions, linear approximations in simulation methods often fail to accurately capture the dynamic changes [21]. Such limitations hinder the effective modeling of nonlinearity, further constraining modeling precision.
+
+# 3.3. Modeling Logits Evolution Process through Dynamical Equation
+
+To address the aforementioned problems, our study delves deeper into the optimization analysis from Eq. (3). In fact, unlike features, the logits derived from the optimization output naturally align with the fine-tuning objectives and reflect the inherent nonlinearity from gradient descent. Therefore,
+
+![](images/afd73633fe40bc8a1e10ada7da220617e5f53e607aef417db3824deb6a4ce21c.jpg)
+
+![](images/799fab120c21ac44732bf9677d4919e8a10a9f12d1704ade2fb1d619870bd7b3.jpg)
+
+![](images/772c7f10ffb50c6f1a01eeb70f507672a56d23c57a1a790ab18c4238c5c4ccae.jpg)  
+Figure 2. Comparison of different approaches for modeling the evolution process. (a) Fine-tuning iteratively updates parameters via gradient descent, revealing authentic logits evolution trajectory and classification accuracy for ground-truth ranking. (b) Recent works (e.g., SFDA [41], PED [32]) perform linear transformations in feature space to enhance class separability, updating logits with modified features. The ranking score is determined by Cross-Entropy loss on updated logits. While these approaches simulate fine-tuning impact on features, they often suffer huge deviations from the authentic results. (c) Our method, LEAD, transforms the discrete logit evolution during fine-tuning into a gradient-based dynamical equation to capture nonlinear changes and can efficiently predict the final state through the closed-form solution. It establishes an analysis framework linking the initial and final states, enabling the precise prediction in one step.
+
+it provides a particularly relevant entry point to analyze dynamical changes during fine-tuning and assess the model transferability through its evolution process.
+
+While the dynamical process of logit space analyzed by Eq. (3) remains consistent with fine-tuning, there still lacks an efficient approach for capturing logits evolution, due to the discrete process of iterating over thousands of steps by traditional optimization. To this end, we propose a new transferability metric called "Logits Evolution Analysis through Dynamical equation (LEAD)", that bridges the evolution process from the initial logit space towards the final state. In contrast to extensive optimization iterations, our method proposes a dynamical analysis framework for analyzing the nonlinear effects within the logit space, providing an efficient prediction to capture the final state with a concise solution in a single step.
+
+Theoretical Background. In our LEAD, we innovatively introduce the Neural Tangent Kernel (NTK) to simplify the dynamical equation. Here, we provide a brief introduction to the definition of the NTK kernel function and the constant-preserving property that we utilize.
+
+$$
+\begin{array}{l} \hat {\Phi} _ {\theta_ {t}} (\mathcal {X}, \mathcal {X}) \triangleq \nabla_ {\theta_ {t}} \mathcal {F} (\mathcal {X}; \theta_ {t}) \nabla_ {\theta_ {t}} \mathcal {F} (\mathcal {X}; \theta_ {t}) ^ {\top}, (4) \\ \Phi (\mathcal {X}, \mathcal {X}) \triangleq \lim  _ {l \rightarrow \infty} \hat {\Phi} _ {\theta_ {t}} (\mathcal {X}, \mathcal {X}), (4) \\ \end{array}
+$$
+
+where  $\nabla$  denotes the Laplace Operator, and  $l$  denotes the root mean square of the widths of all layers in the network. The kernel function  $\hat{\Phi}_{\theta_t}$  remains invariant throughout the training process as  $l$  approaches infinity with an approximation error of  $O\left(\frac{1}{l^2}\right)$  [20, 26]. For simplicity, in the remainder of this paper, we denote functions at time  $t$  as:
+
+![](images/86f95734fc810786cb98edbae5ec9033cac5a37e77337b4e6c0b793079762518.jpg)  
+Figure 3. Comparison of the average prediction of final state logits across various methods on VOC2007 [16], where the actual result stems from fine-tuning. Closer to actual results indicates more accurate modeling of the final state. Simulation methods (SFDA, PED) capture the correct trend but exhibit a large deviation from the actual results, affecting the accuracy of model ranking.
+
+$\mathcal{F}_t(\cdot)\triangleq \mathcal{F}(\cdot ,\theta_t),\hat{\Phi}_t(\cdot)\triangleq \hat{\Phi}_{\theta_t}(\mathcal{X},\mathcal{X}),\Phi \triangleq \Phi (\mathcal{X},\mathcal{X}).$
+
+Dynamical Equation and Closed-form Solution. To bypass the complexity of iterative computations, we extend the analysis in Eq. (3) and theoretically derive a dynamical equation that is efficient for analysis. Specifically, we seek for a mathematical derivation through the theory of limit approximation to convert the discrete process into a continuous differential equation, enabling us to track the trajectory of logits in the solution space of the equation. Furthermore, we leverage the property of the NTK in Eq. (4) to simplify the equation into an Ordinary Differential Equation (ODE) with an initial value condition. Due to space constraints, we directly provide the equation and the detailed proof can be found in the Appendix.
+
+$$
+\frac {\mathrm {d} \mathcal {F} _ {t}}{\mathrm {d} t} = - \eta \cdot \Phi \cdot \frac {\mathrm {d} \mathcal {L} _ {t}}{\mathrm {d} \mathcal {F} _ {t}}, \mathcal {F} _ {0} = l o g _ {i n i t}, \tag {5}
+$$
+
+where  $\text{loginit}$  is the initial state of logits obtained through feeding features and labels of downstream datasets to a classification algorithm. Compared to the discrete process, our proposed ODE depicts the continuous evolution of the finetuning dynamics, allowing for a more flexible modeling approach. It transforms discrete gradient effects into equivalent differential effects in continuous time, preserving the capability for modeling nonlinear changes and providing precise prediction of the evolution process. Furthermore, unlike employing numerical methods as the ODE solver, we can directly obtain its closed-form solution through integration over time dimension, allowing us to bypass the lengthy evolution process and reach the optimization destination in a single step, as shown below:
+
+$$
+\mathbb {E} \left(\mathcal {F} _ {t} (\mathcal {X})\right) = \left(\mathbb {I} - e ^ {- \eta \Phi \cdot t}\right) \mathcal {Y} + e ^ {- \eta \Phi \cdot t} \cdot \log_ {\text {i n i t}}. \tag {6}
+$$
+
+As depicted in Eq. (6), the solution is derived by interpolating between the one-hot label and the initial observation of logits, with the interpolation coefficients determined by the NTK matrix. It comprises two crucial elements:  $\text{log}_{\text{init}}$ , representing the value of logits before optimization and determining the start of the evolution process; and  $\Phi$ , indicating the convergence rate to the label and determining the trajectory of logit evolution. Our proposed framework efficiently models the evolution process, enabling a prediction of real-time changes.
+
+Class-aware Decomposition. While Eq. (6) provides the theoretical result for the final state, computing the value of  $\Phi$  under finite width remains challenging. Prior studies [20, 53] indicate that, even with finite width, the convergence rate can be assessed by using the eigenvalues of the initial state NTK matrix  $\hat{\Phi}_0$ . Inspired by this empirical finding, we further conduct a decomposition approach to bridge theory and practice, utilizing the eigenvalue decomposition on  $\hat{\Phi}_0$  to replace the convergence rate determined by  $\Phi$  in Eq. (6) with eigenvalues.
+
+Due to the network exhibiting varying classification abilities across different classes, their convergence behavior and evolution dynamics also differ during the fine-tuning process. To enhance the modeling of behaviors in different classes, we separately compute NTK for each class, rather than mixing them together, to decouple the respective optimization effect. Specifically, we extract  $n$  samples of each class to calculate their respective NTK matrices and perform decomposition to obtain eigenvalues. The average eigenvalue of each class serves as the unified parameter to determine the interpolation coefficient for this class:
+
+$$
+\mathbb {E} \left(\mathcal {F} _ {t} (x)\right) = \left(\mathbb {I} - e ^ {- \eta \bar {\lambda} \cdot t}\right) y + e ^ {- \eta \bar {\lambda} \cdot t} \cdot \log_ {i n i t}, \tag {7}
+$$
+
+where  $x, y$  is a given sample and its one-hot label,  $\overline{\lambda}$  is the average eigenvalue of the NTK matrix associated with the class of  $x$ . Building upon the conclusion of Eq. (6), Eq.
+
+(7) avoids the demand of infinite width, enabling practical computability of the prediction results. As shown in Fig. 2, we employ the results of Eq. (7) to efficiently obtain predictions for the final state logits. Subsequently, following the common practice [32, 33, 41], we feed predictions into the Cross-Entropy loss to obtain the transferability score for model ranking.
+
+Summary. Our method explicitly models the fine-tuning optimization through the theoretical analysis framework and provides a concise dynamical solution to bypass the lengthy optimization process in a single step, which seamlessly integrates the initial state observations and the evolution trajectory towards the final state. Therefore, we can efficiently predict the final logit state through this dynamical solution. Through comparing logit prediction accuracy among different models, it can serve as an effective metric for predicting model transferability.
+
+# 4. Experiments
+
+To demonstrate the effectiveness and robustness of our approach, we evaluate LEAD on diverse pre-trained models, including both supervised and self-supervised convolutional neural networks. Our evaluation spans 10 widely used classification benchmarks in transfer learning, employing weighted Kendall's  $\tau_w$  as rank correlation to evaluate the transferability metric. Additionally, we highlight the effectiveness of LEAD in the low-data regime, where only  $2/5/10$  samples are available per class.
+
+# 4.1. Implementation Details
+
+Given a pre-trained model  $\Psi$ , we append a random initialized [22] MLP  $h$  as a classification head after its backbone  $f$ , and combine them as  $\mathcal{F} \coloneqq h \circ f$  to produce logits. To compute the logits in the final state, we only need to derive the NTK matrix of each class and  $log_{init}$  through Eq. (7). We follow the approach in [35] to compute the NTK matrix and employ a robust and efficient machine learning classifier, the multi-class SVM [49], to generate  $log_{init}$ . Due to space constraints, we provide a more detailed explanation and pseudocode in the Appendix.
+
+# 4.2. Benchmarks
+
+Target Datasets. We employ 10 classification benchmarks commonly utilized in transfer learning research including Caltech-101 [17], Stanford Cars [29], CIFAR10 [30], CIFAR100 [30], DTD [10], Oxford 102 Flowers [37], Food-101 [4], Oxford-IIIT Pets [39], SUN397 [51], and VOC2007 [16]. These datasets encompass abundant characteristics, including backgrounds, textures, and coarse/fine-grained scenes, spanning diverse fields.
+
+Ground Truth Rank. To conduct the ground truth ranking for the model zoo, we follow the approach in [41] and [52]. Specifically, we employ a grid search strategy to determine
+
+Table 1. Performance comparisons of different transferability metrics on the supervised model zoo. We measure the performance with weighted Kendall's  $\tau_w$  and a larger  $\tau_w$  represents a better prediction rank. The best results are in bold and the second-best are in underline.  
+
+<table><tr><td rowspan="2">Method</td><td rowspan="2">Reference</td><td colspan="10">Downstream Target Dataset</td></tr><tr><td>Food</td><td>Caltech</td><td>Flowers</td><td>Cars</td><td>CIFAR100</td><td>DTD</td><td>CIFAR10</td><td>Pets</td><td>SUN397</td><td>VOC2007</td></tr><tr><td>PARC [3]</td><td>NeurIPS&#x27;21</td><td>0.363</td><td>0.422</td><td>0.066</td><td>0.135</td><td>-0.092</td><td>0.536</td><td>0.310</td><td>0.114</td><td>-0.097</td><td>0.707</td></tr><tr><td>Logme [52]</td><td>ICML&#x27;21</td><td>0.336</td><td>0.349</td><td>0.425</td><td>0.538</td><td>0.603</td><td>0.651</td><td>0.783</td><td>0.372</td><td>0.440</td><td>0.673</td></tr><tr><td>Nsleep [33]</td><td>CVPR&#x27;21</td><td>0.504</td><td>0.678</td><td>0.292</td><td>0.435</td><td>0.686</td><td>0.452</td><td>0.656</td><td>0.686</td><td>0.770</td><td>0.645</td></tr><tr><td>PACTran [12]</td><td>ECCV&#x27;22</td><td>0.709</td><td>0.372</td><td>0.480</td><td>0.151</td><td>0.742</td><td>0.372</td><td>0.757</td><td>0.451</td><td>0.422</td><td>0.536</td></tr><tr><td>SFDA [41]</td><td>ECCV&#x27;22</td><td>0.534</td><td>0.597</td><td>0.421</td><td>0.472</td><td>0.749</td><td>0.421</td><td>0.817</td><td>0.625</td><td>0.562</td><td>0.728</td></tr><tr><td>GBC [38]</td><td>CVPR&#x27;22</td><td>0.844</td><td>0.430</td><td>0.348</td><td>0.735</td><td>0.830</td><td>0.480</td><td>0.866</td><td>0.358</td><td>0.574</td><td>0.654</td></tr><tr><td>ETran [18]</td><td>ICCV&#x27;23</td><td>0.709</td><td>0.627</td><td>0.534</td><td>0.557</td><td>0.749</td><td>0.605</td><td>0.719</td><td>0.651</td><td>0.577</td><td>0.673</td></tr><tr><td>PED [32]</td><td>ICCV&#x27;23</td><td>0.573</td><td>0.597</td><td>0.451</td><td>0.472</td><td>0.749</td><td>0.421</td><td>0.770</td><td>0.625</td><td>0.562</td><td>0.728</td></tr><tr><td>LEAD</td><td>This paper</td><td>0.892</td><td>0.698</td><td>0.786</td><td>0.586</td><td>0.835</td><td>0.689</td><td>0.791</td><td>0.841</td><td>0.609</td><td>0.743</td></tr></table>
+
+the actual performance of each model in the downstream task. This strategy involves trying various learning rates from the set  $\{10^{-1}, 10^{-2}, 10^{-3}, 10^{-4}\}$  and different weight decay values from the set  $\{0, 10^{-6}, 10^{-5}, 10^{-4}, 10^{-3}\}$ . To ensure reliability, we repeat each experiment 5 times with different random seeds and take the average as the result.
+
+# 4.3. Evaluation on Supervised Models
+
+Model Zoo. We construct a Model Zoo that includes 12 CNN models supervised pre-trained on ImageNet [11], covering widely-used architectures: ResNet-34 [23], ResNet-50 [23], ResNet-101 [23], ResNet-152 [23], DenseNet-121 [25], DenseNet-161 [25], DenseNet-169 [25], DenseNet-201 [25], MNet-A1 [45], MobileNetV2 [40], GoogleNet [43], and InceptionV3 [44]. The accuracy results of these models after fine-tuning can be found in the Appendix.
+
+Result Analysis. To show the effectiveness of LEAD, we compare it with prior arts, such as Bayesian-based Logme, Separability-based GBC, and simulation methods SFDA and PED. As shown in Tab. 1, simulation methods consider underlying dynamic effects and exhibit promising performances on some datasets. However, as the aforementioned analysis in Sec. 3.2 shows, the bias in the simulation process causes these methods to have unstable improvements, particularly resulting in unsatisfactory performance on Flowers, Food, and Pets. Benefiting from a precise analysis of the evolution, our LEAD yields a performance gain of  $+0.335$ ,  $+0.319$ ,  $+0.216$  compared to PED on these three datasets, respectively. Overall, LEAD achieves the best  $\tau_w$  on 7 target datasets and obtains an average  $\tau_w$  of 0.747 which is relatively  $18\%$  better than the latest SOTA ETran [18]. Our experiments highlight the importance of accurate modeling of dynamics and confirm the effectiveness of our method to model the evolution process through the dynamical equation.
+
+# 4.4. Evaluation on Self-supervised Models
+
+Model Zoo. Self-supervised learning models (SSL models) have shown their efficacy in transfer learning and often display superior generalization performance compared
+
+to Supervised models. To illustrate the broad applicability of our approach, inspired by [32, 41], we assemble a self-supervised model zoo trained on ImageNet with BYOL [19], Infomin [46], PCLv1 [31], PCLv2 [31], Selav2 [1], InsDis [50], SimCLRv1 [7], SimCLRv2 [8], MoCov1 [24], MoCov2 [9], DeepClusterv2 [5], and SWAV [6].
+
+Result Analysis. Due to differing pre-training and downstream classification objectives, SSL models undergo larger dynamic changes during the fine-tuning process, leading to distinct transferability properties compared to supervised models [15]. As shown in Tab. 1 and 2, methods that disregard dynamics (e.g. PARC, Nsleep) perform competitively in the supervised model zoo, but fail on some datasets for SSL models. For example, Nsleep and PARC have a negative small rank correlation on VOC2007 (-0.101) and CIFAR100 (-0.136), respectively. To maintain fairness, we refrain from comparing with GBC [38] in the SSL model zoo, which is designed for supervised scenarios. On the contrary, SFDA and PED exhibit better performances due to consideration of training dynamics. Nevertheless, the limitation of the simulating process still hinders their performance. Compared to them, LEAD achieves a consistent improvement on 7 datasets and obtains an average  $\tau_w$  of 0.746 which is relatively  $15\%$  better than PED (0.648). The results validate the effectiveness of LEAD for SSL models.
+
+# 4.5. Evaluation on Low-data Regime
+
+Experimental Settings. In practical application, privacy and resource constraints may limit our access to the entire downstream dataset. To explore the utilization boundary, we evaluate whether LEAD can provide effective model ranking only using limited samples. We follow three data settings in PACTran [12] with increasing average number of samples per class  $\{2,5,10\}$  and divide 10 datasets into two groups according to the number of classes:  $100+$  classes, including Food, Caltech, Flowers, Cars, CIFAR100, and SUN397; 10-99 classes, including DTD, CIFAR10, Pets, and VOC2007. For each setting, we repeatedly sample 5 times for evaluation and take the average as the result.
+
+Result Analysis. As shown in Tab. 3, all methods, in-
+
+Table 2. Performance comparisons on the self-supervised model zoo. The best results are in bold and the second-best are in underline.  
+
+<table><tr><td rowspan="2">Method</td><td rowspan="2">Reference</td><td colspan="10">Downstream Target Dataset</td></tr><tr><td>Food</td><td>Caltech</td><td>Flowers</td><td>Cars</td><td>CIFAR100</td><td>DTD</td><td>CIFAR10</td><td>Pets</td><td>SUN397</td><td>VOC2007</td></tr><tr><td>PARC [3]</td><td>NeurIPS&#x27;21</td><td>0.359</td><td>0.196</td><td>0.622</td><td>0.424</td><td>-0.136</td><td>0.447</td><td>0.147</td><td>0.496</td><td>-0.006</td><td>0.618</td></tr><tr><td>Logme [52]</td><td>ICML&#x27;21</td><td>0.570</td><td>0.051</td><td>0.604</td><td>0.375</td><td>-0.008</td><td>0.627</td><td>0.295</td><td>0.684</td><td>0.217</td><td>0.158</td></tr><tr><td>Nsleep [33]</td><td>CVPR&#x27;21</td><td>0.574</td><td>0.525</td><td>0.534</td><td>0.486</td><td>0.276</td><td>0.641</td><td>-0.044</td><td>0.792</td><td>0.719</td><td>-0.101</td></tr><tr><td>PACTran [12]</td><td>ECCV&#x27;22</td><td>0.720</td><td>0.622</td><td>0.601</td><td>0.474</td><td>0.529</td><td>0.614</td><td>0.477</td><td>0.641</td><td>0.638</td><td>0.620</td></tr><tr><td>SFDA [41]</td><td>ECCV&#x27;22</td><td>0.685</td><td>0.523</td><td>0.749</td><td>0.515</td><td>0.548</td><td>0.773</td><td>0.619</td><td>0.586</td><td>0.698</td><td>0.568</td></tr><tr><td>ETran [18]</td><td>ICCV&#x27;23</td><td>0.465</td><td>0.405</td><td>0.644</td><td>0.587</td><td>0.650</td><td>0.214</td><td>0.606</td><td>0.338</td><td>0.520</td><td>0.376</td></tr><tr><td>PED [32]</td><td>ICCV&#x27;23</td><td>0.581</td><td>0.614</td><td>0.777</td><td>0.649</td><td>0.568</td><td>0.907</td><td>0.673</td><td>0.462</td><td>0.661</td><td>0.583</td></tr><tr><td>LEAD</td><td>This paper</td><td>0.860</td><td>0.780</td><td>0.725</td><td>0.663</td><td>0.776</td><td>0.825</td><td>0.713</td><td>0.629</td><td>0.760</td><td>0.723</td></tr></table>
+
+Table 3. Performance comparisons with different  $N / K$ , where  $K$  is the number of classes,  $N$  is the number of samples for computing the metric. We divide 10 benchmarks into two groups according to the number of classes: 100+ classes and 10-99 classes, and evaluate the average of  $\tau_w$  on the two groups. Additionally, we also provide the average results on the 10 benchmarks, recorded as Avg. The best results are denoted in bold, the second best results are denoted in underline, and - denotes cannot give a valid ranking.  
+
+<table><tr><td colspan="11">Supervised / Self-supervised pre-trained Model</td></tr><tr><td rowspan="2">Method</td><td colspan="3">N/K = 2</td><td colspan="3">N/K = 5</td><td colspan="3">N/K = 10</td><td></td></tr><tr><td>100+ classes</td><td>10-99 classes</td><td>Avg</td><td>100+ classes</td><td>10-99 classes</td><td>Avg</td><td>100+ classes</td><td>10-99 classes</td><td>Avg</td><td></td></tr><tr><td>GBC</td><td>0.17 / 0.32</td><td>0.10 / 0.17</td><td>0.13 / 0.25</td><td>0.45 / 0.40</td><td>0.22 / 0.18</td><td>0.36 / 0.31</td><td>0.59 / 0.42</td><td>0.42 / 0.22</td><td>0.52 / 0.34</td><td></td></tr><tr><td>PACTran</td><td>0.43 / 0.49</td><td>0.20 / 0.39</td><td>0.33 / 0.45</td><td>0.42 / 0.48</td><td>0.31 / 0.44</td><td>0.38 / 0.47</td><td>0.56 / 0.52</td><td>0.48 / 0.46</td><td>0.53 / 0.50</td><td></td></tr><tr><td>ETran</td><td>0.42 / 0.43</td><td>0.12 / 0.41</td><td>0.29 / 0.42</td><td>0.48 / 0.47</td><td>0.31 / 0.38</td><td>0.41 / 0.43</td><td>0.56 / 0.47</td><td>0.56 / 0.48</td><td>0.56 / 0.48</td><td></td></tr><tr><td>PED</td><td>- / 0.36</td><td>- / 0.24</td><td>- / 0.31</td><td>- / 0.43</td><td>- / 0.35</td><td>- / 0.40</td><td>0.30 / 0.50</td><td>0.22 / 0.56</td><td>0.27 / 0.52</td><td></td></tr><tr><td>LEAD</td><td>0.45 / 0.48</td><td>0.51 / 0.45</td><td>0.47 / 0.46</td><td>0.48 / 0.49</td><td>0.64 / 0.53</td><td>0.54 / 0.51</td><td>0.65 / 0.53</td><td>0.64 / 0.60</td><td>0.64 / 0.56</td><td></td></tr></table>
+
+cluding PACTran designed for this scenario, exhibit significant performance declines under low-data settings. For instance, ETran's performance in the supervised model zoo drops from 0.64 with the entire dataset to 0.29, 0.41, and 0.56 in three low-data settings. Moreover, some methods, such as SFDA and PED fail to provide prediction rankings in some settings. For example, when  $N / K = 2,5$ , PED cannot correctly evaluate class separability due to insufficient data, imposing huge changes to completely separate different classes. This leads to all models perfectly classifying all samples, resulting in identical scores that cannot be ranked. In contrast, our LEAD achieves stable results, ensuring  $\tau_w \geq 0.45$  even in extreme settings like  $N / K = 2$ , and consistently outperforms other methods. For example, under  $N / K = 10$ , its average  $\tau_w$  in the supervised model zoo reaches 0.64, which is relatively  $14\%$  better than the latest SOTA ETran (0.56) and is equivalent to the latest SOTA on the complete dataset, with less than  $5\%$  of data size. The results demonstrate the robustness of our method in the face of data limitations.
+
+# 5. Ablation Study and Efficiency Analysis
+
+In this section, without loss of generality, we conduct ablation studies on Caltech, CIFAR10, and VOC2007, building upon the evaluation of SSL models in Sec. 4.4 for saving time. We conduct separate experiments to analyze the impact of interpolation coefficients, a key component of LEAD, aiming to delve into the influence of hyperparameters and implementation details, gaining insights into key
+
+factors contributing to LEAD's effectiveness. Additionally, we provide a runtime comparison to verify efficiency, and more ablation study results are provided in the appendix.
+
+# 5.1. Interpolation Coefficient
+
+The interpolation coefficients are determined by time coefficient  $t$  and the NTK matrix. We conduct ablation experiments on these two key factors:
+
+Time Coefficient  $t$ . As we model the discrete process as a continuous ODE, the continuous variable  $t$  is proportional to the number of updates, determining the progress of the evolution process. In Fig. 4, we evaluate our method under varied time settings, keeping the unit as 1e6 consistent across all experiments. It is evident that performance improves as the time increases within a specific range. However, if the dynamic effect persists for an extended period (e.g., 10.0), all model predictions converge too closely to the ground-truth label, reducing discrimination for model ranking. Hence, we set the time coefficient as 1 by default.
+
+![](images/d8befea459eb8901a1a723d8409b407c7f5f958b1a950897281e0ed8c9dfe50a.jpg)
+
+![](images/1b3c6d2bb15e3a12791b480ffe8032eff56a800c64b8ddf7c8ef96a1d83c0eba.jpg)  
+Figure 4. The left picture shows the performance gain in  $\tau_w$  with respect to different time  $t$  and the right shows the performance in different sample sizes for each class NTK.
+
+Sample Size for NTK. To enhance the perception of different dynamic intensities of classes, we propose the class-aware decomposition that employs  $S$  samples of each class to obtain NTK matrix and perform spectrum analysis to derive eigenvalues. In Fig. 4, we conduct ablation experiments to explore the effect of varying  $S$ . We observe that performance generally improves as  $S$  increases, and gradually reaches stability. This demonstrates that when the sample size reaches a certain size, eigenvalues reliably capture differences in dynamic intensity, offering a refined analysis result of the dynamics. Therefore, we set  $S = 64$  to ensure the method's efficiency and stability in all experiments.
+
+# 5.2. Running Time Comparison
+
+In experiment results, we have demonstrated the effectiveness of LEAD in various scenarios. In this section, we highlight the computational efficiency of LEAD. With the concise solution in Eq. (7), LEAD predicts the final state only requiring the NTK matrix and  $\text{log}_{init}$ . As shown in Tab. 4, the running time of LEAD is about half that of simulation methods (45s compared to 92s), ranking second after GBC which displays unstable performance. Notably, LEAD takes 3s to compute the NTK, while feature extraction takes 420s, resulting in only a marginal  $0.7\%$  increase in GPU time. The time to compute  $\text{log}_{init}$  is 42s CPU time, indicating significant potential for exploring faster classification algorithms to further reduce the overall time.
+
+Table 4. The comparisons of average running time on CIFAR10.  
+
+<table><tr><td>Metrics</td><td>PARC</td><td>NLEEP</td><td>PACTran</td><td>SFDA</td><td>GBC</td><td>PED</td><td>Ours</td></tr><tr><td>Running Time</td><td>111s</td><td>1430s</td><td>77s</td><td>92s</td><td>26s</td><td>97s</td><td>45s</td></tr></table>
+
+# 6. Visualization and Analysis
+
+In this section, we validate our approach through some visualizations and these results clearly illustrate how our model effectively addresses the model selection problem.
+
+# 6.1. Logit Prediction
+
+We have conducted a comparison of the predicted logits distribution on VOC2007 using different methods, as illustrated in Fig. 3. Notably, predictions obtained by LEAD closely match the authentic distribution after fine-tuning. To provide further quantitative analysis, we visualize the average bias in predicted logits in Fig. 5. Across three datasets, our method exhibits a substantial reduction compared to simulation methods, achieving nearly a  $50\%$  overall reduction. This visualization highlights the precision of our dynamical equation-based approach in capturing logit evolution for more accurate ranking sequences.
+
+![](images/5730efca410870bc74277eafa6b7679899fbff59307e049120384f6d9a9826e7.jpg)  
+Figure 5. Comparison of the average difference between logits predicted by different methods and logits after fine-tuning. The difference is calculated utilizing the Euclidean distance.
+
+# 6.2. Rank Variation
+
+By employing our method, we can refine models that have poor initial observation but show better progress during training. To assess the effectiveness of our approach, we conduct a visualization comparing the model rankings between the initial observations and our predicted final state, as shown in Fig. 6. The results clearly illustrate a substantial enhancement in the calibration of model rankings when using our refined observations, with the optimal model now positioned closely to the reference line in the figure. Notably, models starting from an initially unfavorable point can be rapidly elevated to achieve a superior ranking, highlighting the effectiveness of our methodology.
+
+![](images/2f3583d5c16fb243a02f5b430a4256595b02cb4df51f2e295eacd8a799197982.jpg)
+
+![](images/c6876fb90cafd3d8cdb83f6640d4e998b199078d9922496892cbbb318c52a4ff.jpg)
+
+![](images/47164e21d643dbb8ece11d0d1697e86c74aac8c23ea55f72173eb84e597ae7c1.jpg)
+
+![](images/075db0296cb59584eb3a8b14d5d198af5096a3c0919fb40315dd6521e9dd9594.jpg)  
+Figure 6. The variation in model ranking, utilizing initial states (first row) and predicted final states of LEAD (second row). Results span three datasets, from left to right: CIFAR10, Caltech, and VOC2007. Shaded areas reflect the range of the ranking error.
+
+![](images/1b4b2ab39d6d5f3823aa39cfe2de811aba1c89e26dfe2f179ef288de09157e83.jpg)
+
+![](images/126bb530f74b06ea081490901547b8ad5456047169c6db2349993f4dba8e19d6.jpg)
+
+# 7. Conclusions and Future Work
+
+In this work, we propose a dynamical equation designed to capture the evolution process within the logit space, offering an efficient solution for assessing model transferability. We construct a theoretical analysis framework and further devise a more practical and precise solution. And we demonstrate its consistent effectiveness across various scenarios including supervised and self-supervised, full-data and low-data settings. In future work, we intend to expand the current analysis framework beyond classification to cover a broader range of downstream tasks. We hope that our work can enhance the understanding of optimization mechanisms in deep neural networks and shed light on other fields, such as the design of optimization algorithms.
+
+# Acknowledgement
+
+This work was supported by the National Natural Science Foundation of China under Grant 62088102, in part by the PKU-NTU Joint Research Institute (JRI) sponsored by a donation from the Ng Teng Fong Charitable Foundation and in part by AI Joint Lab of Future Urban Infrastructure sponsored by Fuzhou Chengtou New Infrastructure Group and Boyun Vision Co. Ltd.
+
+# References
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+        "text": "LEAD: Learning Decomposition for Source-free Universal Domain Adaptation",
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+        "text": "Sanqing  $\\mathrm{Qu}^1$ , Tianpei  $\\mathrm{Zou}^1$ , Lianghua  $\\mathrm{He}^1$ , Florian Röhrbein $^2$ , Alois Knoll $^3$ , Guang Chen $^{1*}$ , Changjun Jiang $^1$",
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+        "text": "$^{1}$ Tongji University,  $^{2}$ Chemnitz University of Technology,  $^{3}$ Technical University of Munich",
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+        "text": "Abstract",
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+        "text": "Universal Domain Adaptation (UniDA) targets knowledge transfer in the presence of both covariate and label shifts. Recently, Source-free Universal Domain Adaptation (SF-UniDA) has emerged to achieve UniDA without access to source data, which tends to be more practical due to data protection policies. The main challenges lie in determining whether covariate-shifted samples belong to target-private unknown categories. Existing methods tackle this either through hand-crafted thresholding or by developing time-consuming iterative clustering strategies. In this paper, we propose a new idea of LEArning Decomposition (LEAD), which decouples features into source-known and -unknown components to identify target-private data. Technically, LEAD initially leverages the orthogonal decomposition analysis for feature decomposition. Then, LEAD builds instance-level decision boundaries to adaptively identify target-private data. Extensive experiments across various UniDA scenarios have demonstrated the effectiveness and superiority of LEAD. Notably, in the OPDA scenario on VisDA dataset, LEAD outperforms GLC by  $3.5\\%$  overall H-score and reduces  $75\\%$  time to derive pseudo-labeling decision boundaries. Besides, LEAD is also appealing in that it is complementary to most existing methods. The code is available at https://github.com/ispc-lab/LEAD.",
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+        "text": "1. Introduction",
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+        "text": "Deep neural networks (DNNs) have yielded impressive results in a variety of computer vision tasks [12, 18, 22, 42]. However, DNNs often fail to generalize well to new domains due to the discrepancy between training (source) and test (target) data distributions (i.e., covariate shift). Such a shift poses significant challenges for some safety-critical applications like autonomous driving [9, 10], or medical imaging [13, 31]. Unsupervised Domain Adaptation (DA) [16, 23] aims to address this challenge by transferring task-specific knowledge from a labeled source domain to an unlabeled target domain. Despite promising results, most",
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+        "image_caption": [
+            "Figure 1. (a) Pseudo-label accuracy curves for target-private data in the OPDA scenario on VisDA dataset. An observation is that clustering-based GLC does not work well in deriving decision boundaries for target-private data. This may be due to the curse of dimensionality, leading K-means to faintly discerning clusters. (b) Frequency distribution for the normalized feature magnitude of target data in the source-unknown space (orthogonal complement of the space spanned by source model weights). Features are on task  $(A\\to D)$  in the OPDA scenario of Office-31. The results show that target-private data are expected to involve more components from source-unknown space, even with covariate shifts."
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+        "text": "existing favorable DA methods [16, 20, 27, 45] assume that the label spaces are identical across the source and target domain, thus being only applicable to closed-set scenarios and limiting applicability to practical applications.",
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+        "text": "To handle generalized cases, Universal Domain Adaptation (UniDA) [47] was proposed to allow all potential label shifts between source and target domains. Different from existing methods specialized for Partial Domain Adaptation (PDA) [3, 4], Open-set Domain Adaptation (OSDA) [35, 46], or Open-Partial Domain Adaptation (OPDA) [44, 54], in UniDA, we have no prior knowledge about the label shift, e.g., information on matched common classes or the number of categories in the target domain. Nonetheless, most existing UniDA works [7, 25, 47] necessitate concurrent access to source and target data. This requirement becomes increasingly impractical in light of strict data protection policies [50]. In this paper, we focus on Source-free Universal Domain Adaptation (SF-UniDA) [28, 41], where only a pre-trained source model is provided for knowledge transfer rather than labeled source data.",
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+        "text": "The primary objective for UniDA is to recognize target data belonging to common categories and separate them from target-private \"unknown\" data. Existing meth",
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+        "text": "CVF",
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+    {
+        "type": "header",
+        "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
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+        "type": "page_footnote",
+        "text": "*Corresponding author: guangchen@tongji.edu.cn",
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+        "text": "23334",
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+    {
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+        "text": "ods have designed various criteria based on instance-level predictions, e.g., entropy-based [14, 47, 54], confidence-based [15, 24, 44]. However, defining a universal threshold for all scenarios is challenging and often sub-optimal. To mitigate tedious parameter-tuning, some methods start to perform source and target consensus clustering to achieve common and private data separation [7, 25]. Considering that SF-UniDA is inaccessible to source data, GLC [41] devises an iterative one-vs-all clustering strategy to realize target-private data identification. Regardless of progress, iterative clustering can be computationally intensive. Besides, due to the curse of dimensionality [2], methods like K-means are prone to overfitting and faintly discerning clusters. This can be implied to some degree from Figure 1 (a).",
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+    {
+        "type": "text",
+        "text": "In this paper, we propose to address the SF-UniDA problem from a new perspective, i.e., feature decomposition. Our launching point is that, even though target data might have shifted in the feature space, target-private data from unknown categories are likely to exhibit a higher proportion of components from the orthogonal complement (source-unknown) space spanned by source model weights. The frequency distribution of normalized feature magnitudes in the source-unknown space depicted in Figure 1 (b) basically demonstrates our argument, which has been rarely explored in the literature. To materialize our idea, we propose the LEArning Decomposition (LEAD) framework. In particular, LEAD initially leverages the orthogonal decomposition to construct source-known and -unknown space. The projection on source-unknown space is then regarded as the discriminative representation with respect to target-private categories. Different from existing thresholding methods introducing a fixed global hand-crafted threshold for all scenarios, LEAD deliberately considers the distance to the target prototypes and source anchors to establish instance-level decision boundaries. We analyze and evaluate our LEAD under a variety of SF-UniDA scenarios, ranging from PDA, OSDA, to OPDA. Extensive experiments demonstrate the effectiveness and superiority.",
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+    {
+        "type": "text",
+        "text": "The main contribution is the proposal of a LEArning Decomposition (LEAD) framework for source-free universal domain adaptation (SF-UniDA). This solution leads to elegant views for identifying target-private unknown data without tedious tuning thresholds or relying on iterative unstable clustering. Remarkably, in the OPDA scenario on VisDA, LEAD attains an H-score of  $76.6\\%$ , surpassing GLC [41] by  $3.5\\%$ . Besides, LEAD is complementary to most existing SF-UniDA methods. For instance, in the OPDA scenario on Office-Home, LEAD advances UMAD [28] with H-score improvement from  $70.1\\%$  to  $78.0\\%$ .",
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+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Unsupervised Domain Adaptation. When DNNs encounter data from a distribution that differs from their train",
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+    {
+        "type": "text",
+        "text": "ing data, inevitable performance degeneration is commonly observed. To address this issue, domain adaptation (DA) [16, 23] has been introduced, leveraging labeled data from source domains to train DNNs for unlabeled target domains in a transductive learning manner. Existing DA methods can be broadly categorized into two paradigms, namely moment matching [11, 34, 48] and adversarial learning [16, 19, 21]. Regardless of their effectiveness in various applications such as object recognition [16, 27, 39], semantic segmentation [19, 48], and object detection [8, 21], most existing approaches assume that label spaces are identical across the source and target domains, limiting their applicability.",
+        "bbox": [
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+        "type": "text",
+        "text": "Universal Domain Adaptation. There have been some approaches introduced to deal with label-shift scenarios, such as open-set domain adaptation (OSDA) [32, 35, 46], partial-set domain adaptation (PDA) [3, 4], and open-partial-set domain adaptation (OPDA) [15, 44, 54]. However, these methods are often tailored to specific scenarios and may not be readily applicable to other label shift situations. Universal domain adaptation (UniDA), on the other hand, is designed to facilitate adaptation across all potential label shift scenarios. Despite the progress in UniDA, many existing methods [5, 7, 44] necessitate simultaneous access to both source and target data, making them impractical for applications with stringent data protection policies. To address this challenge, source-free universal domain adaptation (SF-UniDA) [28, 41] has been proposed, wherein source data are only utilized for pre-training and are inaccessible during target adaptation. To promote the distinction between common and private data, existing methods often resort to manually defined thresholding or the introduction of global clustering techniques. Nevertheless, selecting an appropriate threshold for all scenarios can be both laborious and sub-optimal. Additionally, K-means clustering tends to be unstable when applied to high-dimensional data due to the curse of dimensionality [2]. Our work delves into these limitations and proposes a novel and elegant solution from the perspective of feature decomposition.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Feature Decomposition. As a fundamental technique in machine learning, feature decomposition is applied to deconstruct complex data into simpler and more interpretable components. In the field of domain adaptation and domain generalization, feature decomposition has been leveraged in various studies [6, 26, 30, 33, 38, 40] to enhance feature alignment or facilitate domain-invariant feature learning by breaking down features into content and style components. Nonetheless, the content and style decomposition design is less applicable for UniDA, as the primary challenge lies in distinguishing common and private data. In this paper, we approach the problem from the perspective of orthogonal feature decomposition and employ Independent Component Analysis to decompose features into two orthogonal parts, thereby facilitating the intended objective.",
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+        "text": "23335",
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+        "img_path": "images/eb8beafd7fe75af0f36aaa1ef4acfd447b286f8f39fe8c69684b04b60cc5fffe.jpg",
+        "image_caption": [
+            "Figure 2. (a) Illustrations of traditional universal domain adaptation (UniDA) and source-free universal domain adaptation (SF-UniDA). Traditional UniDA methods necessitate data from both source and target domains concurrently. In SF-UniDA, source data are solely utilized for pre-training. Adaptation is performed by harnessing target data and the source model  $f_{\\theta}^{s} = h_{\\theta}^{s} \\circ g_{\\theta}^{s}$ . (b) An overview of our Learning Decomposition (LEAD) framework. Pseudo-labeling is an important technique for UniDA and SF-UniDA. The primary objective is to recognize target data associated with common label sets and exclude data within the target-private label space. Different from existing methods that perform private data identification by hand-crafted thresholding on predictions or iterative global clustering, we tackle this from the viewpoint of feature decomposition. The rationale is that despite potential shifts in the feature space, target-private data are expected to encompass more components from the orthogonal complement (source-unknown) space of the source model. Technically, LEAD first performs orthogonal decomposition to decompose target features into source-known and -unknown parts, i.e.,  $\\mathbf{z}_{i,knw}^{t}$  and  $\\mathbf{z}_{i,unk}^{t}$ .  $\\| \\mathbf{z}_{i,unk}^{t}\\|_{2}$  is considered as an indicator for private data. Next, LEAD employs a two-component Gaussian Mixture Model to estimate the distribution of  $\\| \\mathbf{z}_{i,unk}^{t}\\|_{2}$ . Thereafter, LEAD devises a metric named \"common score\"  $\\epsilon_{i,c}$  that accounts for distances to both target prototypes and source anchors (derived from  $h_{\\theta}^{t}$ ) to facilitate deriving instance-level decision boundary  $\\rho_{i,c}$ . LEAD provides an elegant solution to distinguish target-private data, mitigating the need for tedious hand-crafted threshold tuning or dependence on time-consuming iterative clustering. LEAD could also serve as a complementary approach to most existing SF-UniDA methods."
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+        "img_path": "images/7ecf330707fdfa614df79bb0c5548e32eddd9d563b3d72c33366cd7e75e9087c.jpg",
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+        "text": "3. Methodology",
+        "text_level": 1,
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+        "type": "text",
+        "text": "3.1. Preliminary",
+        "text_level": 1,
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+        "type": "text",
+        "text": "In this paper, we consider a generalized and challenging case in domain adaptation: universal domain adaptation (UniDA), which aims to achieve knowledge transfer in the presence of both covariate and label shifts. In UniDA, there is a labeled source domain  $\\mathcal{D}^s = \\left\\{\\left(\\mathbf{x}_i^s,\\mathbf{y}_i^s\\right)\\right\\}_{i = 1}^{N_s}$  where  $\\mathbf{x}_i^s\\in \\mathcal{X}^s\\subset \\mathbb{R}^X,\\mathbf{y}_i^s\\in \\mathcal{Y}^s\\subset \\mathbb{R}^C$  , and an unlabeled target domain  $\\mathcal{D}^t = \\left\\{\\left(\\mathbf{x}_i^t,\\ref{eq:2.3.1}\\right)\\right\\}_{i = 1}^{N_t}$  where  $\\mathbf{x}_i^t\\in \\mathcal{X}^t\\subset \\mathbb{R}^X.$ $\\mathcal{V} = \\mathcal{V}^s\\cap \\mathcal{V}^t$  denotes the common label sets shared by source and target domains.  $\\bar{\\mathcal{V}}^s = \\mathcal{V}\\setminus \\mathcal{V}^t$  and  $\\bar{\\mathcal{V}}^t = \\mathcal{V}\\setminus \\mathcal{V}^s$  symbolizes the label sets private to source and target domain, individually. UniDA supposes that we have no prior knowledge about  $\\mathcal{V}^t$  .  $\\mathcal{V}$  and  $\\bar{\\mathcal{V}}^t$  are also unavailable. The objective is to recognize common data belonging to  $\\mathcal{V}$  and reject private data in  $\\bar{\\mathcal{V}}^t$",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Different from traditional UniDA methods that need concurrent access to source and target data, under the source-free universal domain adaptation (SF-UniDA) setting,  $\\mathcal{D}_s$  is only applicable for source model pre-training and not acces-",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "sible during adaptation. Assuming that the source model is represented as  $f_{\\theta}^{s} = h_{\\theta}^{s}\\circ g_{\\theta}^{s}$ , where  $g_{\\theta}^{s}:\\mathbb{R}^{X}\\to \\mathbb{R}^{D}$  denotes the feature extractor and  $h_\\theta^s:\\mathbb{R}^D\\to \\mathbb{R}^C$  is the classifier module. Following existing methods [27, 41], we freeze the classifier module  $h_\\theta^t = h_\\theta^s$  and only learn a target-specific feature extractor  $g_{\\theta}^{t}$  to realize model adaptation. Figure 2 (a) presents an illustration for UniDA and SF-UniDA.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The main challenge is how to distinguish common data from private data. Prior methods [25, 28, 41, 47] have designed various algorithms to encourage the separation. However, these methods perform data identification either based on hand-crafted thresholding criteria or by introducing time-consuming unstable clustering strategies. We propose to mitigate these limitations from the perspective of feature decomposition. An observation is that even though target data may have shifted in the feature space, the features of private data still include more components from the orthogonal complement (source-unknown) space of the pre-trained model. Technically, we present a novel learning decomposition (LEAD) framework. LEAD capitalizes on the orthogonal decomposition to build two orthogonal fea",
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+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "23336",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "ture spaces, i.e., source-known and -unknown space. Feature projection on source-unknown space is extracted as the descriptor for private data. Then, LEAD considers the distances to both the target prototypes and source anchors to establish instance-level decision boundaries. Figure 2 (b) manifests the architecture of our LEAD.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2. Orthogonal Feature Decomposition",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Pseudo-labeling serves as an important technique in unsupervised learning, yet many existing strategies only account for closed-set scenarios, disregarding the label-shift situations, which impairs their ability to differentiate target-private data. To fulfill the objective of common and private data separation, we propose to orthogonally decompose the feature representation into two uncorrelated parts, i.e., features associated with source-known space  $F_{knw}$  and those related to source-unknown space  $F_{unk}$ . This design stems from a simple inductive bias in favor of private data identification. Due to the lack of exposure to target data during source pre-training, particularly target-private data, the source-known space does not include any significant attributes of target-private data. Subsequently, after normalization, target-private data are expected to contain more components from source-unknown space, even with covariate shifts. This hypothesis is basically demonstrated by empirical evidence, as illustrated in Figure 1 (b).",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Formally, denoting the weight of classifier  $h_{\\theta}^{t}$  is  $W_{cls} \\in \\mathbb{R}^{C \\times D}$ . Source-known space  $F_{knw}$  can be represented as the vector space of span  $\\{\\mathbf{w}_n\\}$ , where  $\\{\\mathbf{w}_n \\in \\mathbb{R}^D | n = 1, \\dots, C\\}$  is a group weight vectors of  $W_{cls}$ . Source-unknown space  $F_{unk}$  is the orthogonal complement space of  $F_{knw}$ , i.e.,  $\\mathbb{R}^D = F_{knw} \\oplus F_{unk}$ . Nevertheless, unit orthogonality in  $\\{\\mathbf{w}_n \\in \\mathbb{R}^D | n = 1, \\dots, C\\}$  is not guaranteed (i.e., when  $n \\neq m$  ( $\\mathbf{w}_n, \\mathbf{w}_m \\neq 0$ ), making it hard to derive  $F_{unk}$ . Considering that  $F_{knw}$  and  $F_{unk}$  are the row space and null space of  $W_{cls}$ . Therefore, we employ the singular value decomposition (SVD) on  $W_{cls}$  to obtain  $F_{knw}$  and  $F_{unk}$ . Specifically,",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nW _ {c l s} = U \\Sigma V ^ {T},\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nF _ {k n w} = \\operatorname {s p a n} \\left\\{\\mathbf {v} _ {n} | _ {n = 1, \\dots , C} \\right\\}, \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nF _ {u n k} = \\operatorname {s p a n} \\left\\{\\mathbf {v} _ {n} | _ {n = C + 1, \\dots , D} \\right\\}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\Sigma \\in \\mathbb{R}^{C\\times D}$  is a diagonal matrix,  $U\\in \\mathbb{R}^{C\\times C}$  and  $V\\in \\mathbb{R}^{D\\times D}$  are both orthogonal unitary matrices.  $\\{\\mathbf{v}_n|\\mathbf{v}_n\\in \\mathbb{R}^D\\}_{n = 1}^D$  are columns of  $V$",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Assuming that  $\\mathbf{z}_i^t$  is the feature of target data  $\\mathbf{x}_i^t$  extracted from feature extractor  $g_{\\theta}^{t}$  after normalization, i.e.,  $\\mathbf{z}_i^t = g_\\theta^t (\\mathbf{x}_i^t) / ||g_\\theta^t (\\mathbf{x}_i^t)||_2$ , then  $\\mathbf{z}_i^t$  can be represented as the weighted summation of two orthogonal bases:",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {z} _ {i} ^ {t} = \\underbrace {\\sum_ {n = 1} ^ {C} l _ {n} \\cdot \\mathbf {v} _ {n}} _ {\\mathbf {z} _ {i, k n w} ^ {t}} + \\underbrace {\\sum_ {n = C + 1} ^ {D} l _ {n} \\cdot \\mathbf {v} _ {n}} _ {\\mathbf {z} _ {i, u n k} ^ {t}} \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $||\\mathbf{z}_{i,knw}^{t}||_{2}^{2} + ||\\mathbf{z}_{i,unk}^{t}||_{2}^{2} = 1$ ,  $\\mathbf{z}_{i,knw}^{t}$  and  $\\mathbf{z}_{i,unk}^{t}$  are the projections of  $\\mathbf{z}_{i}^{t}$  on  $F_{knw}$  and  $F_{unk}$ , respectively.  $l_{n} \\in \\mathbb{R}$  denotes the projection weight of  $\\mathbf{z}_{i}^{t}$  onto the unit base  $\\mathbf{v}_{n}$ . This procedure is commonly recognized as orthogonal decomposition and has been extensively studied in the context of Independent Component Analysis (ICA).",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.3. Adaptive Separation for Private Data",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Intuitively, enabled by feature decomposition, we could differentiate between common and private data by examining the dominance of  $\\mathbf{z}_{i,unk}^{t}$  over  $\\mathbf{z}_i$ . However, such a straightforward approach is not applicable to SF-UniDA due to the impact of distribution covariate shift, which often deteriorates the significance of  $\\mathbf{z}_{i,knw}^{t}$  for common data, leading to the prevalence of  $\\mathbf{z}_{i,unk}^{t}$  in the representation. Additionally, the feature extractor inevitably captures representations that are independent of  $F_{knw}$ , including background contexts [1], object textures [17], and high-frequency patterns [51], further exacerbating this issue.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "To solve this, one feasible solution is to estimate the distribution of  $\\| \\mathbf{z}_{i,unk}^{t}\\|_{2}$  to effectively calibrate these disturbances. Our observations have revealed that the empirical distributions of  $\\| \\mathbf{z}_{i,unk}^{t}\\|_{2}$  exhibit a bimodal pattern, with the presence of two distinct peaks typically indicating the modes of common and private data. Consequently, we employ a two-component Gaussian Mixture Model (GMM) to estimate the distribution  $\\| \\mathbf{z}_{i,unk}^{t}\\|_{2}$ , with the components featuring a lower mean representing the common data and those with a higher mean corresponding to the private data. In particular, we denote  $\\mu_{com}$  and  $\\mu_{pri}$  as the expectation for common and private data, where  $\\mu_{com} < \\mu_{pri}$ .",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In the light of  $\\mu_{com}$  and  $\\mu_{pri}$ , an intuitive practice is to treat all common and private categories equally. Accordingly, common and private data can be separated by establishing  $(\\mu_{com} + \\mu_{pri}) / 2$  as the threshold, where data with  $\\| \\mathbf{z}_{i,unk}^t\\| _2$  below the threshold are recognized as common data, while those above are identified as private data. Despite its reasonable effectiveness, it discounts the inconsistency of covariate shifts across each category. Moreover, it fails to account for the variability in covariate shifts even among samples from the same category. These considerations motivate us to devise an instance-level decision strategy to achieve accurate and effective data identification.",
+        "bbox": [
+            496,
+            568,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Concretely, we first leverage top-  $K$  sampling to construct target prototypes, denoted as  $\\{\\mathbf{c}_c^t\\in \\mathbb{R}^D |_{c = 1,\\dots ,C}\\}$  for each common category, adhering to the procedure in [29, 41]. Similar to [41], we empirically set  $K = N_{t} / \\tilde{C}_{t}$ , where  $N_{t}$  represents the amount of target data, and  $\\tilde{C}_t$  signifies the estimated count of target categories. Diverging from [41], we additionally collect source anchors from  $W_{cls}$ , denoted as  $\\{\\mathbf{c}_c^s\\in \\mathbb{R}^D |_{c = 1,\\ldots ,C}\\}$  to assist us handle scenarios involving source-private categories. The construct of target prototypes through top-  $K$  sampling fails to consider these sce",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "23337",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "narios, making it susceptible to misidentifying private data as common. Further details regarding the target prototype construction are included in the supplementary.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Thereafter, we propose a novel metric, common score  $\\epsilon_{i,c}$ , which deliberately considers the distance of  $\\mathbf{z}_i^t$  to the target prototype  $\\mathbf{c}_c^t$  and source anchor  $\\mathbf{c}_c^s$  to facilitate us in deriving instance-level decision boundaries. Formally, this metric is defined as:",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} d (\\mathbf {a}, \\mathbf {b}) = 1. 0 - \\cos (\\mathbf {a}, \\mathbf {b}), \\\\ \\epsilon_ {i, c} ^ {t} = 1. 0 - \\exp \\left(d \\left(\\mathbf {z} _ {i} ^ {t}, \\mathbf {c} _ {c} ^ {t}\\right) - 1. 0\\right), \\\\ \\epsilon_ {i, c} ^ {s} = \\exp \\left(- d \\left(\\mathbf {z} _ {i} ^ {t}, \\mathbf {c} _ {c} ^ {s}\\right)\\right), \\tag {3} \\\\ \\epsilon_ {i, c} = \\sqrt {\\epsilon_ {i , c} ^ {t} \\cdot \\epsilon_ {i , c} ^ {s}} \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            143,
+            218,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\epsilon_{i,c}^{t}$  and  $\\epsilon_{i,c}^{s}$  denote the common score from target prototype and source anchor viewpoint, respectively. Both  $\\epsilon_{i,c}^{t}$  and  $\\epsilon_{i,c}^{s}$  are clipped to the [0, 1] before fusion. We then utilize geometric mean to calculate fused common score, due to its advantage in multi-criteria decision-making. Note that we leverage different formulas to calculate  $\\epsilon_{i,c}^{t}$  and  $\\epsilon_{i,c}^{s}$ . Under the same condition, i.e.,  $d(\\mathbf{z}_i^t,\\mathbf{c}_c^s) = d(\\mathbf{z}_i^t,\\mathbf{c}_c^t)$ ,  $\\epsilon_{i,c}^{s}$  is greater than  $\\epsilon_{i,c}^{t}$ . The spirit behind is that instances exhibiting proximity to source anchors are likely to be common data. Conversely, instances in close proximity to target prototypes do not guarantee their recognition.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Given the computed common score  $\\epsilon_{i,c}$  and the estimated distribution for  $\\| \\mathbf{z}_{i,unk}^t\\| _2$  we introduce the following pseudo-labeling strategy to effectively distinguish between common and private data instances:",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\rho_ {i, c} = \\mu_ {c} + \\epsilon_ {i, c} \\cdot (\\mu_ {p r i} - \\mu_ {c}), \\\\ \\tilde {\\mathbf {y}} _ {i} ^ {t} = \\left\\{ \\begin{array}{l l} \\text {u n k n o w n}, & \\text {i f} \\| \\mathbf {z} _ {i, u n k} ^ {t} \\| _ {2} \\geq \\rho_ {i, c} \\\\ \\mathbb {1} (\\operatorname {a r g m a x} (\\epsilon_ {i})), & \\text {i f} \\| \\mathbf {z} _ {i, u n k} ^ {t} \\| _ {2} <   \\rho_ {i, c} \\end{array} \\right. \\tag {4} \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            116,
+            550,
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+            609
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mu_{c}$  denotes the expectation of  $\\| \\mathbf{z}_{i,unk}^{t}\\|_{2}$  for the  $c$ -th category, derived using the identical top- $K$  sampling technique employed during the construction of the target prototypes.  $\\rho_{i,c}$  represents the instance-level decision boundary, which accounts for the potential covariate shifts across each category, as well as the data instances corresponding to both target prototypes and source anchors.  $\\mathbb{1}$  denotes the one-hot encoding operator,  $\\tilde{\\mathbf{y}}_i^t$  is the pseudo-label for  $\\mathbf{x}_i^t$ .",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.4. Optimization Objectives",
+        "text_level": 1,
+        "bbox": [
+            76,
+            755,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "To encourage the separation between common and private data, the optimization process involves three distinct objectives, including pseudo-label learning, feature decomposition regularization, and feature consensus regularization.",
+        "bbox": [
+            75,
+            780,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Pseudo-label Learning. With the pseudo labels derived from Eq. 4, we apply the cross-entropy loss for model adaptation. Nevertheless, instead of assigning equal importance to all pseudo-labels, we introduce a Student's  $t$  distribution",
+        "bbox": [
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+            840,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/a63a3c988cd5626ca6b60b3f9f8a9dfa676cb1af1dec014996b5469046b8633e.jpg",
+        "table_caption": [
+            "Table 1. Details of class split.  $\\mathcal{V},\\bar{\\mathcal{V}}_s$  , and  $\\bar{\\mathcal{V}}_t$  signifies the common class, source-private class, and target-private class, respectively."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Dataset</td><td colspan=\"3\">Class Split(γ/γs/γt)</td></tr><tr><td>OPDA</td><td>OSDA</td><td>PDA</td></tr><tr><td>Office-31 [43]</td><td>10/10/11</td><td>10/0/11</td><td>10/21/0</td></tr><tr><td>Office-Home [49]</td><td>10/5/50</td><td>25/0/40</td><td>25/40/0</td></tr><tr><td>VisDA [36]</td><td>6/3/3</td><td>6/0/6</td><td>6/6/0</td></tr><tr><td>DomainNet [37]</td><td>150/50/145</td><td>-</td><td>-</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "to characterize the certainty associated with each pseudolabel, taking into account the distance between  $\\| \\mathbf{z}_{i,unk}^t\\| _2$  and  $\\rho_{i,c}$ . Specifically,",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\tau_ {i} ^ {t} \\propto 1 - \\left(1 + \\frac {\\left(\\rho_ {i , \\kappa} - \\| \\mathbf {z} _ {i , u n k} ^ {t} \\| _ {2}\\right) ^ {2}}{\\alpha}\\right) ^ {- \\frac {\\alpha + 1}{2}}, \\\\ \\mathcal {L} _ {c e} = - \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\tau_ {i} ^ {t} \\cdot \\sum_ {c = 1} ^ {C} \\tilde {y} _ {i, c} ^ {t} \\log \\delta_ {c} \\left(f _ {\\theta} ^ {t} \\left(\\mathbf {x} _ {i} ^ {t}\\right)\\right) \\tag {5} \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            544,
+            265,
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+            354
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\tau_{i}^{t}$  denotes the certainty,  $\\kappa = \\mathrm{argmax}(\\epsilon_{i,c}),\\alpha = 1\\mathrm{e - }4$  by default.  $\\delta_c(f_\\theta^t (\\mathbf{x}_i^t))$  is the  $c$  -th soft-max probability for  $\\mathbf{x}_i^t$ $\\tilde{y}_{i,c}^{t}$  corresponds to  $c$  -th one-hot encoded pseudo-label for  $\\tilde{\\mathbf{y}}_i^t$  . For those instances pseudo-labeled as private data, we refrain from introducing an additional  $C + 1$  -th class, instead employing a uniform distribution to represent them.",
+        "bbox": [
+            498,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Feature Decomposition Regularization. To promote the discriminability of  $\\mathbf{z}_{i,unk}^{t}$  for identifying private data, we impose a feature decomposition regularizer. Concretely,",
+        "bbox": [
+            498,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} p _ {i} = \\frac {\\exp \\left(\\left\\| \\mathbf {z} _ {i , u n k} ^ {t} \\right\\| _ {2}\\right)}{\\exp \\left(\\left\\| \\mathbf {z} _ {i , u n k} ^ {t} \\right\\| _ {2}\\right) + \\exp \\left(\\left\\| \\mathbf {z} _ {i , k n w} ^ {t} \\right\\| _ {2}\\right)}, \\tag {6} \\\\ \\mathcal {L} _ {r e g} = - \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\tau_ {i} ^ {t} \\cdot \\left(\\hat {y} _ {i} ^ {t} \\log \\left(p _ {i}\\right) + \\left(1 - \\hat {y} _ {i} ^ {t}\\right) \\log \\left(1 - p _ {i}\\right)\\right) \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "$\\hat{y}_i^t = 1$  or 0 means pseudo-labeled as private/common data.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Feature Consensus Regularization. Recent studies [41, 52, 53] in SFDA and SF-UniDA observe that incorporating consensus regularization with nearest neighbors in feature space could assist models in achieving more stable performance. Following them, we integrate the objective  $\\mathcal{L}_{con}$  into LEAD. More details are included in the supplementary.",
+        "bbox": [
+            498,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Overall Optimization Objective. Taking into account the discussions above, the eventual loss function is defined as:",
+        "bbox": [
+            498,
+            709,
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+            739
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} = \\lambda \\cdot \\mathcal {L} _ {c e} + \\mathcal {L} _ {r e g} + \\mathcal {L} _ {c o n} \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            601,
+            747,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\lambda > 0$  is a trade-off hyper-parameter.",
+        "bbox": [
+            500,
+            776,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
+        "bbox": [
+            500,
+            806,
+            632,
+            824
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.1. Experimental Setup",
+        "text_level": 1,
+        "bbox": [
+            500,
+            830,
+            689,
+            848
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Dataset. We empirically verify the effectiveness of our LEAD on four datasets, including Office-31 [43], OfficeHome [49], VisDA [36], and DomainNet [37]. For a",
+        "bbox": [
+            498,
+            854,
+            890,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "23338",
+        "bbox": [
+            478,
+            944,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/9a09f18cf3a35f75cf607e1133d29483859eeb71f049092cdfbc96ffca3ac348.jpg",
+        "table_caption": [
+            "Table 2. H-score (\\%) comparison in OPDA scenario on Office-Home. U denotes methods applicable for all potential label-shift scenarios (i.e., OPDA, OSDA, and PDA). SF represents source data-free. CF indicates model adaptation without time-consuming K-means clustering."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Methods</td><td>U</td><td>SF</td><td>CF</td><td>Ar2Cl</td><td>Ar2Pr</td><td>Ar2Re</td><td>Cl2Ar</td><td>Cl2Pr</td><td>Cl2Re</td><td>Pr2Ar</td><td>Pr2Cl</td><td>Pr2Re</td><td>Re2Ar</td><td>Re2Cl</td><td>Re2Pr</td><td>Avg</td></tr><tr><td>CMU [15]</td><td>✘</td><td>✘</td><td>✓</td><td>56.0</td><td>56.9</td><td>59.2</td><td>67.0</td><td>64.3</td><td>67.8</td><td>54.7</td><td>51.1</td><td>66.4</td><td>68.2</td><td>57.9</td><td>69.7</td><td>61.6</td></tr><tr><td>DANCE [47]</td><td>✓</td><td>✘</td><td>✓</td><td>61.0</td><td>60.4</td><td>64.9</td><td>65.7</td><td>58.8</td><td>61.8</td><td>73.1</td><td>61.2</td><td>66.6</td><td>67.7</td><td>62.4</td><td>63.7</td><td>63.9</td></tr><tr><td>DCC [25]</td><td>✓</td><td>✘</td><td>✘</td><td>58.0</td><td>54.1</td><td>58.0</td><td>74.6</td><td>70.6</td><td>77.5</td><td>64.3</td><td>73.6</td><td>74.9</td><td>81.0</td><td>75.1</td><td>80.4</td><td>70.2</td></tr><tr><td>OVANet [44]</td><td>✘</td><td>✘</td><td>✓</td><td>62.8</td><td>75.6</td><td>78.6</td><td>70.7</td><td>68.8</td><td>75.0</td><td>71.3</td><td>58.6</td><td>80.5</td><td>76.1</td><td>64.1</td><td>78.9</td><td>71.8</td></tr><tr><td>GATE [7]</td><td>✓</td><td>✘</td><td>✓</td><td>63.8</td><td>75.9</td><td>81.4</td><td>74.0</td><td>72.1</td><td>79.8</td><td>74.7</td><td>70.3</td><td>82.7</td><td>79.1</td><td>71.5</td><td>81.7</td><td>75.6</td></tr><tr><td>UniOT [5]</td><td>✘</td><td>✘</td><td>✓</td><td>67.3</td><td>80.5</td><td>86.0</td><td>73.5</td><td>77.3</td><td>84.3</td><td>75.5</td><td>63.3</td><td>86.0</td><td>77.8</td><td>65.4</td><td>81.9</td><td>76.6</td></tr><tr><td>Source-only</td><td>-</td><td>-</td><td>-</td><td>47.3</td><td>71.6</td><td>81.9</td><td>51.5</td><td>57.2</td><td>69.4</td><td>56.0</td><td>40.3</td><td>76.6</td><td>61.4</td><td>44.2</td><td>73.5</td><td>60.9</td></tr><tr><td>SHOT-O [27]</td><td>✘</td><td>✓</td><td>✓</td><td>32.9</td><td>29.5</td><td>39.6</td><td>56.8</td><td>30.1</td><td>41.1</td><td>54.9</td><td>35.4</td><td>42.3</td><td>58.5</td><td>33.5</td><td>33.3</td><td>40.7</td></tr><tr><td>LEAD</td><td>✓</td><td>✓</td><td>✓</td><td>62.7</td><td>78.1</td><td>86.4</td><td>70.6</td><td>76.3</td><td>83.4</td><td>75.3</td><td>60.6</td><td>86.2</td><td>75.4</td><td>60.7</td><td>83.7</td><td>75.0</td></tr><tr><td>UMAD [28]</td><td>✘</td><td>✓</td><td>✓</td><td>61.1</td><td>76.3</td><td>82.7</td><td>70.7</td><td>67.7</td><td>75.7</td><td>64.4</td><td>55.7</td><td>76.3</td><td>73.2</td><td>60.4</td><td>77.2</td><td>70.1</td></tr><tr><td>+ LEAD</td><td>✓</td><td>✓</td><td>✓</td><td>65.2</td><td>82.6</td><td>87.4</td><td>78.0</td><td>76.5</td><td>87.5</td><td>79.8</td><td>65.0</td><td>88.4</td><td>79.4</td><td>63.0</td><td>83.5</td><td>78.0 (+7.9)</td></tr><tr><td>GLC [41]</td><td>✓</td><td>✓</td><td>✘</td><td>64.3</td><td>78.2</td><td>89.8</td><td>63.1</td><td>81.7</td><td>89.1</td><td>77.6</td><td>54.2</td><td>88.9</td><td>80.7</td><td>54.2</td><td>85.9</td><td>75.6</td></tr><tr><td>+ LEAD</td><td>✓</td><td>✓</td><td>✘</td><td>65.7</td><td>79.7</td><td>88.7</td><td>65.0</td><td>80.3</td><td>88.5</td><td>77.6</td><td>57.4</td><td>88.9</td><td>78.9</td><td>57.8</td><td>85.5</td><td>76.2 (+0.6)</td></tr></table>",
+        "bbox": [
+            83,
+            119,
+            883,
+            297
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/0dab7245e0c03f88b06bfead93890c266a666a8af263b4e87d10ab7b7fbfbfdf.jpg",
+        "table_caption": [
+            "Table 3. H-score (\\%) comparison in OPDA scenario on Office-31, VisDA, and DomainNet. Some results are cited from UMAD [28]."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Methods</td><td rowspan=\"2\">U</td><td rowspan=\"2\">SF</td><td rowspan=\"2\">CF</td><td colspan=\"7\">Office-31</td><td colspan=\"7\">DomainNet</td><td>VisDA</td></tr><tr><td>A2D</td><td>A2W</td><td>D2A</td><td>D2W</td><td>W2A</td><td>W2D</td><td>Avg</td><td>P2R</td><td>P2S</td><td>R2P</td><td>R2S</td><td>S2P</td><td>S2R</td><td>Avg</td><td>S2R</td></tr><tr><td>CMU [15]</td><td>X</td><td>X</td><td>✓</td><td>68.1</td><td>67.3</td><td>71.4</td><td>79.3</td><td>72.2</td><td>80.4</td><td>73.1</td><td>50.8</td><td>45.1</td><td>52.2</td><td>45.6</td><td>44.8</td><td>51.0</td><td>48.3</td><td>32.9</td></tr><tr><td>DANCE [47]</td><td>✓</td><td>X</td><td>✓</td><td>78.6</td><td>71.5</td><td>79.9</td><td>91.4</td><td>72.2</td><td>87.9</td><td>80.3</td><td>21.0</td><td>37.0</td><td>47.3</td><td>46.7</td><td>27.7</td><td>21.0</td><td>33.5</td><td>42.8</td></tr><tr><td>DCC [25]</td><td>✓</td><td>X</td><td>X</td><td>88.5</td><td>78.5</td><td>70.2</td><td>79.3</td><td>75.9</td><td>88.6</td><td>80.2</td><td>56.9</td><td>43.7</td><td>50.3</td><td>43.3</td><td>44.9</td><td>56.2</td><td>49.2</td><td>43.0</td></tr><tr><td>OVANet [44]</td><td>X</td><td>X</td><td>✓</td><td>85.8</td><td>79.4</td><td>80.1</td><td>95.4</td><td>84.0</td><td>94.3</td><td>86.5</td><td>56.0</td><td>47.1</td><td>51.7</td><td>44.9</td><td>47.4</td><td>57.2</td><td>50.7</td><td>53.1</td></tr><tr><td>GATE [7]</td><td>✓</td><td>X</td><td>✓</td><td>87.7</td><td>81.6</td><td>84.2</td><td>94.8</td><td>83.4</td><td>94.1</td><td>87.6</td><td>57.4</td><td>48.7</td><td>52.8</td><td>47.6</td><td>49.5</td><td>56.3</td><td>52.1</td><td>56.4</td></tr><tr><td>UniOT [5]</td><td>X</td><td>X</td><td>✓</td><td>87.0</td><td>88.5</td><td>88.4</td><td>98.8</td><td>87.6</td><td>96.6</td><td>91.1</td><td>59.3</td><td>51.8</td><td>47.8</td><td>48.3</td><td>46.8</td><td>58.3</td><td>52.0</td><td>57.3</td></tr><tr><td>Source-only</td><td>-</td><td>-</td><td>-</td><td>70.9</td><td>63.2</td><td>39.6</td><td>77.3</td><td>52.2</td><td>86.4</td><td>64.9</td><td>57.3</td><td>38.2</td><td>47.8</td><td>38.4</td><td>32.2</td><td>48.2</td><td>43.7</td><td>25.7</td></tr><tr><td>SHOT-O [27]</td><td>X</td><td>✓</td><td>✓</td><td>73.5</td><td>67.2</td><td>59.3</td><td>88.3</td><td>77.1</td><td>84.4</td><td>75.0</td><td>35.0</td><td>30.8</td><td>37.2</td><td>28.3</td><td>31.9</td><td>32.2</td><td>32.6</td><td>44.0</td></tr><tr><td>LEAD</td><td>✓</td><td>✓</td><td>✓</td><td>85.4</td><td>85.0</td><td>86.3</td><td>90.9</td><td>86.2</td><td>93.1</td><td>87.8</td><td>59.9</td><td>46.1</td><td>51.3</td><td>45.0</td><td>45.9</td><td>56.3</td><td>50.8</td><td>76.6</td></tr><tr><td>UMAD [28]</td><td>X</td><td>✓</td><td>✓</td><td>79.1</td><td>77.4</td><td>87.4</td><td>90.7</td><td>90.4</td><td>97.2</td><td>87.0</td><td>59.0</td><td>44.3</td><td>50.1</td><td>42.1</td><td>32.0</td><td>55.3</td><td>47.1</td><td>58.3</td></tr><tr><td>+ LEAD</td><td>✓</td><td>✓</td><td>✓</td><td>88.7</td><td>89.2</td><td>90.8</td><td>95.8</td><td>90.4</td><td>97.1</td><td>92.0 (+5.0)</td><td>59.3</td><td>46.0</td><td>49.8</td><td>43.8</td><td>43.9</td><td>56.0</td><td>49.8 (+2.7)</td><td>67.2 (+8.9)</td></tr><tr><td>GLC [41]</td><td>✓</td><td>✓</td><td>X</td><td>81.5</td><td>84.5</td><td>89.8</td><td>90.4</td><td>88.4</td><td>92.3</td><td>87.8</td><td>63.3</td><td>50.5</td><td>54.9</td><td>50.9</td><td>49.6</td><td>61.3</td><td>55.1</td><td>73.1</td></tr><tr><td>+ LEAD</td><td>✓</td><td>✓</td><td>X</td><td>83.0</td><td>86.8</td><td>87.6</td><td>92.0</td><td>87.1</td><td>93.2</td><td>88.3 (+0.5)</td><td>63.5</td><td>50.7</td><td>55.1</td><td>51.6</td><td>49.9</td><td>61.3</td><td>55.4 (+0.3)</td><td>76.8 (+3.7)</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "fair comparison, we evaluate LEAD on partial-set domain adaptation (PDA), open-set domain adaptation (OSDA), and open-partial-set domain adaptation (OPDA). Details of classes split are summarized in Table 1.",
+        "bbox": [
+            75,
+            518,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Evaluation. We utilize the same evaluation metric as previous works. In PDA scenarios, we report the classification accuracy for evaluation. In OSDA and OPDA scenarios, we report the H-score for performance comparison, which is a harmonic mean of accuracy over common data and accuracy over private data. It is worth noting that LEAD can be incorporated effortlessly into most existing SF-UniDA methods, for potential performance improvement. To demonstrate this merit, we integrate LEAD with two representative methods: UMAD [28] and GLC [41].",
+        "bbox": [
+            75,
+            579,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Implementation Details. All the experiments are conducted on a single RTX-3090 GPU with PyTorch-1.10. We adopt the same network architecture as existing baseline methods. During target model adaptation, we apply the SGD optimizer with momentum 0.9. The batch size is set to 64 for all experiments. The learning rate is set to 1e-3 for Office-31 and Office-Home, and 1e-4 for VisDA and DomainNet. As for  $\\lambda$ , it is set to 0.3 for Office-31, 1.0 for VisDA, and 2.0 for Office-Home and DomainNet. During inference, we adopt the same protocol like [41]. More details are presented in the supplementary.",
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.2. Experimental Results",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Results for OPDA Scenarios. To verify the effectiveness of LEAD, we first conduct experiments in the most challenging OPDA scenarios, where both source and target domains contain private data. Table 2 summarizes the results on Office-Home, and Table 3 details the results on Office-31, DomainNet, and VisDA. These results demonstrate that LEAD achieves performance surpassing or comparable to existing methods based on K-means clustering for segregating common and private data. In comparison with methods without clustering, LEAD achieves significantly superior performance. For instance, on Office-Home, DomainNet, and VisDA datasets, LEAD outperforms UMAD by  $4.9\\%$ ,  $3.7\\%$ , and  $18.3\\%$ , respectively. We attribute this to our instance-level adaptive decision strategy, which effectively circumvents the limitations imposed by a fixed threshold. While GLC achieves commendable performance on its own, the integration with LEAD further amplifies its effectiveness. For example, LEAD improves GLC in the H-score on VisDA from  $73.1\\%$  to  $76.8\\%$ . The integration with LEAD proves even more significant against UMAD, with the H-score on Office-Home and VisDA boosting from  $70.1\\% /58.3\\%$  to  $78.0\\% /67.2\\%$ , respectively.",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Results for OSDA Scenarios. We then conduct experiments in OSDA scenarios, where only the target domain",
+        "bbox": [
+            498,
+            869,
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+            900
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "23339",
+        "bbox": [
+            478,
+            944,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/47886e4aedf11d69aff94161c0fff93be7c4ce632a071a6da120faf703753b01.jpg",
+        "table_caption": [
+            "Table 4. H-score (%) comparison in OSDA scenario on Office-Home, Office-31, and VisDA."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Methods</td><td rowspan=\"2\">U SF CF</td><td colspan=\"15\">Office-Home</td><td colspan=\"7\">Office-31</td><td>VisDA</td></tr><tr><td>Ar2Cl</td><td>Ar2Pr</td><td>Ar2Re</td><td>Cl2Ar</td><td>Cl2Pr</td><td>Cl2Re</td><td>Pr2Ar</td><td>Pr2Cl</td><td>Pr2Re</td><td>Re2Ar</td><td>Re2Cl</td><td>Re2Pr</td><td>Avg</td><td>A2D</td><td>A2W</td><td>D2A</td><td>D2W</td><td>W2A</td><td>W2D</td><td>Avg</td><td>S2R</td><td></td><td></td></tr><tr><td>CMU [15]</td><td>X X Y</td><td>55.0</td><td>57.0</td><td>59.0</td><td>59.3</td><td>58.2</td><td>60.6</td><td>59.2</td><td>51.3</td><td>61.2</td><td>61.9</td><td>53.5</td><td>55.3</td><td>57.6</td><td>52.6</td><td>55.7</td><td>76.5</td><td>75.9</td><td>65.8</td><td>64.7</td><td>65.2</td><td>54.2</td><td></td><td></td></tr><tr><td>DANCE [47]</td><td>✓ X Y</td><td>6.5</td><td>9.0</td><td>9.9</td><td>20.4</td><td>10.4</td><td>9.2</td><td>28.4</td><td>12.8</td><td>12.6</td><td>14.2</td><td>7.9</td><td>13.2</td><td>12.9</td><td>84.9</td><td>78.8</td><td>79.1</td><td>78.8</td><td>68.3</td><td>78.8</td><td>79.8</td><td>67.5</td><td></td><td></td></tr><tr><td>DCC [25]</td><td>✓ X X</td><td>56.1</td><td>67.5</td><td>66.7</td><td>49.6</td><td>66.5</td><td>64.0</td><td>55.8</td><td>53.0</td><td>70.5</td><td>61.6</td><td>57.2</td><td>71.9</td><td>61.7</td><td>58.3</td><td>54.8</td><td>67.2</td><td>89.4</td><td>85.3</td><td>80.9</td><td>72.7</td><td>59.6</td><td></td><td></td></tr><tr><td>OVANet [44]</td><td>X X Y</td><td>58.6</td><td>66.3</td><td>69.9</td><td>62.0</td><td>65.2</td><td>68.6</td><td>59.8</td><td>53.4</td><td>69.3</td><td>68.7</td><td>59.6</td><td>66.7</td><td>64.0</td><td>90.5</td><td>88.3</td><td>86.7</td><td>98.2</td><td>88.3</td><td>98.4</td><td>91.7</td><td>66.1</td><td></td><td></td></tr><tr><td>GATE [7]</td><td>✓ X Y</td><td>63.8</td><td>70.5</td><td>75.8</td><td>66.4</td><td>67.9</td><td>71.7</td><td>67.3</td><td>61.5</td><td>76.0</td><td>70.4</td><td>61.8</td><td>75.1</td><td>69.0</td><td>88.4</td><td>86.5</td><td>84.2</td><td>95.0</td><td>86.1</td><td>96.7</td><td>89.5</td><td>70.8</td><td></td><td></td></tr><tr><td>Source-only</td><td>- - -</td><td>46.1</td><td>63.3</td><td>72.9</td><td>42.8</td><td>54.0</td><td>58.7</td><td>47.8</td><td>36.1</td><td>66.2</td><td>60.8</td><td>45.3</td><td>68.2</td><td>55.2</td><td>78.2</td><td>72.1</td><td>44.2</td><td>82.2</td><td>52.1</td><td>88.8</td><td>69.6</td><td>29.1</td><td></td><td></td></tr><tr><td>SHOT-O [27]</td><td>X Y Y</td><td>37.7</td><td>41.8</td><td>48.4</td><td>56.4</td><td>39.8</td><td>40.9</td><td>60.0</td><td>41.5</td><td>49.7</td><td>61.8</td><td>41.4</td><td>43.6</td><td>46.9</td><td>80.2</td><td>71.6</td><td>64.3</td><td>93.1</td><td>64.0</td><td>91.8</td><td>77.5</td><td>28.1</td><td></td><td></td></tr><tr><td>LEAD</td><td>✓ Y Y</td><td>60.7</td><td>70.8</td><td>76.5</td><td>61.0</td><td>68.6</td><td>70.8</td><td>65.5</td><td>59.8</td><td>74.2</td><td>64.8</td><td>57.7</td><td>75.8</td><td>67.2</td><td>84.9</td><td>85.1</td><td>90.2</td><td>94.8</td><td>90.3</td><td>96.5</td><td>90.3</td><td>74.2</td><td></td><td></td></tr><tr><td>UMAD [28]</td><td>X Y Y</td><td>59.2</td><td>71.8</td><td>76.6</td><td>63.5</td><td>69.0</td><td>71.9</td><td>62.5</td><td>54.6</td><td>72.8</td><td>66.5</td><td>57.9</td><td>70.7</td><td>66.4</td><td>88.5</td><td>84.4</td><td>86.8</td><td>95.0</td><td>88.2</td><td>95.9</td><td>89.8</td><td>66.8</td><td></td><td></td></tr><tr><td>+ LEAD</td><td>✓ Y Y</td><td>62.6</td><td>73.6</td><td>77.3</td><td>61.3</td><td>66.2</td><td>70.7</td><td>63.3</td><td>54.6</td><td>75.1</td><td>66.7</td><td>63.5</td><td>75.6</td><td>67.6</td><td>90.4</td><td>89.6</td><td>90.3</td><td>95.4</td><td>90.7</td><td>97.3</td><td>92.3</td><td>70.2</td><td></td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>+2.5</td><td></td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr></table>",
+        "bbox": [
+            83,
+            106,
+            885,
+            308
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/9799ab231a02b84e086c5cdd46936f9c56a9f8bfdc9ebbfabed18fcc72a0edbf.jpg",
+        "table_caption": [
+            "Table 5. Accuracy comparison (%) in PDA scenario on Office-Home, Office-31, and VisDA."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Methods</td><td rowspan=\"2\">U SF CF</td><td colspan=\"15\">Office-Home</td><td colspan=\"7\">Office-31</td><td>VisDA</td></tr><tr><td>Ar2Cl</td><td>Ar2Pr</td><td>Ar2Re</td><td>Cl2Ar</td><td>Cl2Pr</td><td>Cl2Re</td><td>Pr2Ar</td><td>Pr2Cl</td><td>Pr2Re</td><td>Re2Ar</td><td>Re2Cl</td><td>Re2Pr</td><td colspan=\"2\">Avg</td><td>A2D</td><td>A2W</td><td>D2A</td><td>D2W</td><td>W2A</td><td>W2D</td><td>Avg</td><td>S2R</td><td></td></tr><tr><td>CMU [15]</td><td>X X X</td><td>50.9</td><td>74.2</td><td>78.4</td><td>62.2</td><td>64.1</td><td>72.5</td><td>63.5</td><td>47.9</td><td>78.3</td><td>72.4</td><td>54.7</td><td>78.9</td><td colspan=\"2\">66.5</td><td>84.1</td><td>84.2</td><td>69.2</td><td>97.2</td><td>66.8</td><td>98.8</td><td>83.4</td><td>65.5</td><td></td></tr><tr><td>DANCE [47]</td><td>✓ X X</td><td>53.6</td><td>73.2</td><td>84.9</td><td>70.8</td><td>67.3</td><td>82.6</td><td>70.0</td><td>50.9</td><td>84.8</td><td>77.0</td><td>55.9</td><td>81.8</td><td colspan=\"2\">71.1</td><td>77.1</td><td>71.2</td><td>83.7</td><td>94.6</td><td>92.6</td><td>96.8</td><td>86.0</td><td>73.7</td><td></td></tr><tr><td>DCC [25]</td><td>✓ X X</td><td>54.2</td><td>47.5</td><td>57.5</td><td>83.8</td><td>71.6</td><td>86.2</td><td>63.7</td><td>65.0</td><td>75.2</td><td>85.5</td><td>78.2</td><td>82.6</td><td colspan=\"2\">70.9</td><td>87.3</td><td>81.3</td><td>95.4</td><td>100.0</td><td>95.5</td><td>100.0</td><td>93.3</td><td>72.4</td><td></td></tr><tr><td>OVANet [44]</td><td>X X X</td><td>34.1</td><td>54.6</td><td>72.1</td><td>42.4</td><td>47.3</td><td>55.9</td><td>38.2</td><td>26.2</td><td>61.7</td><td>56.7</td><td>35.8</td><td>68.9</td><td colspan=\"2\">49.5</td><td>69.4</td><td>61.7</td><td>61.4</td><td>90.2</td><td>66.4</td><td>98.7</td><td>74.6</td><td>34.3</td><td></td></tr><tr><td>GATE [7]</td><td>✓ X X</td><td>55.8</td><td>75.9</td><td>85.3</td><td>73.6</td><td>70.2</td><td>83.0</td><td>72.1</td><td>59.5</td><td>84.7</td><td>79.6</td><td>63.9</td><td>83.8</td><td colspan=\"2\">74.0</td><td>89.5</td><td>86.2</td><td>93.5</td><td>100.0</td><td>94.4</td><td>98.6</td><td>93.7</td><td>75.6</td><td></td></tr><tr><td>Source-only</td><td>- - -</td><td>45.9</td><td>69.2</td><td>81.1</td><td>55.7</td><td>61.2</td><td>64.8</td><td>60.7</td><td>41.1</td><td>75.8</td><td>70.5</td><td>49.9</td><td>78.4</td><td colspan=\"2\">62.9</td><td>90.4</td><td>79.3</td><td>79.3</td><td>95.9</td><td>84.3</td><td>98.1</td><td>87.8</td><td>42.8</td><td></td></tr><tr><td>SHOT-P [27]</td><td>X X Y</td><td>64.7</td><td>85.1</td><td>90.1</td><td>75.1</td><td>73.9</td><td>84.2</td><td>76.4</td><td>64.1</td><td>90.3</td><td>80.7</td><td>63.3</td><td>85.5</td><td colspan=\"2\">77.8</td><td>89.8</td><td>84.4</td><td>92.2</td><td>96.6</td><td>92.2</td><td>99.4</td><td>92.4</td><td>74.2</td><td></td></tr><tr><td>LEAD</td><td>✓ Y Y</td><td>58.2</td><td>83.1</td><td>87.0</td><td>70.5</td><td>75.4</td><td>83.3</td><td>73.7</td><td>50.4</td><td>83.7</td><td>78.3</td><td>58.7</td><td>83.2</td><td colspan=\"2\">73.8</td><td>89.8</td><td>93.9</td><td>95.6</td><td>98.6</td><td>96.0</td><td>99.4</td><td>95.5</td><td>75.3</td><td></td></tr><tr><td>UMAD [28]</td><td>X Y Y</td><td>51.2</td><td>66.5</td><td>79.2</td><td>63.1</td><td>62.9</td><td>68.2</td><td>63.3</td><td>56.4</td><td>75.9</td><td>74.5</td><td>55.9</td><td>78.3</td><td colspan=\"2\">66.3</td><td>85.4</td><td>85.1</td><td>83.5</td><td>97.6</td><td>86.2</td><td>99.4</td><td>89.5</td><td>68.5</td><td></td></tr><tr><td>+ LEAD</td><td>✓ Y Y</td><td>61.1</td><td>78.2</td><td>87.5</td><td>70.5</td><td>78.5</td><td>81.8</td><td>74.1</td><td>60.4</td><td>83.3</td><td>78.8</td><td>63.2</td><td>82.1</td><td colspan=\"2\">75.0</td><td>89.2</td><td>90.8</td><td>90.6</td><td>98.0</td><td>93.0</td><td>100.0</td><td>93.6</td><td>78.1</td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td colspan=\"2\">+8.7</td><td></td><td></td><td></td><td></td><td></td><td>+4.1</td><td>+9.6</td><td></td><td></td></tr><tr><td>GLC [41]</td><td>✓ Y X</td><td>55.9</td><td>79.0</td><td>87.5</td><td>72.5</td><td>71.8</td><td>82.7</td><td>74.9</td><td>41.7</td><td>82.4</td><td>77.3</td><td>60.4</td><td>84.3</td><td colspan=\"2\">72.5</td><td>89.8</td><td>89.8</td><td>92.8</td><td>96.6</td><td>96.1</td><td>99.4</td><td>94.1</td><td>76.2</td><td></td></tr><tr><td>+ LEAD</td><td>✓ Y X</td><td>56.6</td><td>81.2</td><td>88.1</td><td>72.5</td><td>72.2</td><td>83.2</td><td>75.3</td><td>43.6</td><td>83.4</td><td>78.2</td><td>59.7</td><td>84.2</td><td colspan=\"2\">73.2</td><td>89.8</td><td>93.2</td><td>95.6</td><td>96.9</td><td>96.0</td><td>99.4</td><td>95.1</td><td>75.5</td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td colspan=\"2\">+0.7</td><td></td><td></td><td></td><td></td><td></td><td>+1.0</td><td>-0.7</td><td></td><td></td></tr></table>",
+        "bbox": [
+            83,
+            329,
+            885,
+            529
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "involves private data. Table 4 lists the results, demonstrating the superiority of LEAD against baselines. Specifically, LEAD obtains the H-score of  $67.2\\%$ ,  $90.3\\%$ , and  $74.2\\%$  on Office-Home, Office-31, and VisDA datasets, respectively. Similar to the observations in OPDA scenarios, LEAD also exhibits performance improvement to existing methods. LEAD improves the H-score of UMAD by  $1.2\\%$ ,  $2.5\\%$ , and  $3.4\\%$  across the Office-Home, Office-31, and VisDA datasets, respectively. The results again verify the merit of LEAD when incorporated with existing methods.",
+        "bbox": [
+            75,
+            537,
+            468,
+            686
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Results for PDA Scenarios. Finally, we verify the effectiveness of LEAD in PDA scenarios, where the target domain's label sets are subsets of those in the source domain. Results presented in Table 5 show that LEAD achieves superior performance even compared to methods tailored for PDA. In particular, LEAD attains the overall accuracy of  $73.8\\%$ ,  $95.5\\%$ , and  $75.3\\%$  on Office-Home, Office-31, and VisDA datasets, individually. LEAD contributes the accuracy increase of  $8.7\\%$ ,  $4.1\\%$ , and  $9.6\\%$  to UMAD on these datasets. Note that, there is a slight degradation  $(-0.7\\%)$  for GLC w/ LEAD. It may arise from gradient conflict, causing the optimization process to inadvertently compromise one objective in favor of improving the overall objective. We will pursue better integration strategies in future work.",
+        "bbox": [
+            75,
+            688,
+            470,
+            900
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/c90a4677647c45b282f23ca537a6582cb00335312a1c7e6fb53dc819b5cbce01.jpg",
+        "table_caption": [
+            "Table 6. Ablation studies of LEAD in OPDA scenarios."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Lce</td><td>Lreg</td><td>Lcon</td><td>Office-31</td><td>Office-Home</td><td>VisDA</td></tr><tr><td>-</td><td>-</td><td>-</td><td>64.9</td><td>60.9</td><td>25.7</td></tr><tr><td>✓</td><td>-</td><td>-</td><td>82.0</td><td>73.6</td><td>61.5</td></tr><tr><td>✓</td><td>✓</td><td>-</td><td>84.5</td><td>74.5</td><td>67.3</td></tr><tr><td>✓</td><td>-</td><td>✓</td><td>87.2</td><td>74.5</td><td>75.7</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>87.8</td><td>75.0</td><td>76.6</td></tr></table>",
+        "bbox": [
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+            637
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.3. Experimental Analysis",
+        "text_level": 1,
+        "bbox": [
+            500,
+            643,
+            710,
+            657
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Ablation Study. To assess the contribution of different components within LEAD, we carry out extensive ablation studies in OPDA scenarios. The results, detailed in Table 6, confirm that each component is not only effective but also complementary to the others.",
+        "bbox": [
+            496,
+            659,
+            890,
+            734
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Efficiency Comparison. As previously stated, LEAD employs the distance to target prototypes and source anchors for adaptive pseudo-labeling. This design, in contrast to clustering-based methods, notably reduces the need for computational resources. Table 7 juxtaposes the runtime of GLC [41] and LEAD in OPDA scenarios. It is clear that LEAD requires minimal resources for deriving decision boundaries, whereas GLC's resource demands escalate dramatically with data scale. In particular, on DomainNet, with about 0.6 million images across 345 categories, GLC averages 897.65 seconds, while LEAD takes only 0.29 sec",
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+            900
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "23340",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/272dc3cb2d8c736b11cf92868aefcd5a1556bce19c89b588cbf4274e63087ebf.jpg",
+        "image_caption": [
+            "(a) Sensitivity to  $\\lambda$"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/039a3a74b32629a546ea44434469cf1ba504d2e9fc48a5d3968bb893703994ba.jpg",
+        "image_caption": [
+            "(b) H-score convergence"
+        ],
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+        "bbox": [
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+        "img_path": "images/5adf2f4b6957ee926f84826bf54253e771ca8d412b05a8741ebed93b861bb315.jpg",
+        "image_caption": [
+            "(c)  $\\mathrm{Ar}\\rightarrow \\mathrm{Pr}$  in OPDA"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/a3f8ae72befbceebaf4610de0e38520614dac47bcf9abf0b8500ba7a595ff590.jpg",
+        "image_caption": [
+            "(d)  $\\mathrm{Re}\\rightarrow \\mathrm{Cl}$  in OPDA"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "table",
+        "img_path": "images/5ebce39355cfec23b6551945fdd5ff2ce164625d4882035dd7c0bc7fc97ab209.jpg",
+        "table_caption": [
+            "Table 7. Runtime (s) to derive pseudo-label decision boundaries."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>Office-31</td><td>Office-Home</td><td>VisDA</td><td>DomainNet</td></tr><tr><td>GLC [41]</td><td>0.19</td><td>0.51</td><td>0.46</td><td>897.65</td></tr><tr><td>LEAD</td><td>0.02</td><td>0.02</td><td>0.11</td><td>0.29</td></tr></table>",
+        "bbox": [
+            81,
+            270,
+            460,
+            316
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "onds on the same platform. Moreover, LEAD also shows substantial resource savings even on normal-scale datasets, e.g., on VisDA with over  $75\\%$  reduction.",
+        "bbox": [
+            75,
+            319,
+            467,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Parameter Sensitivity. We investigate the parameter sensitivity of  $\\lambda$  on Office-31 in OPDA scenarios, where the range of  $\\lambda$  is set to [0.1, 0.2, 0.3, 0.4, 0.5]. Figure 3 (a) illustrates that the results are stable around the selected parameter  $\\lambda = 0.3$ . Through oracle validation, we may find the optimal parameter configuration for this setting is  $\\lambda = 0.1$ .",
+        "bbox": [
+            75,
+            364,
+            468,
+            455
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Training Stability. Figure 3 (b) visualizes the training curves of our LEAD on VisDA in OPDA scenarios. Generally, the training procedure of LEAD is stable and effective.",
+        "bbox": [
+            75,
+            457,
+            468,
+            502
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Varying Unknown Classes. With the rise in unknown private classes, accurately distinguishing common from private data becomes more challenging. To examine the robustness of our LEAD, we compared it with GLC and UMAD in OPDA scenarios using the Office-Home dataset. The results in Figure 3 (c-d) show that LEAD achieves stable results and consistently boosts existing methods.",
+        "bbox": [
+            75,
+            503,
+            468,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Effect of Instance-level Decision Boundary. To evaluate the contribution of our instance-level pseudo-labeling strategy, we conduct a comparison against the intuitive design, which uses the average of  $\\mu_{\\text{com}}$  and  $\\mu_{\\text{pri}}$  as the threshold. As depicted in Figure 4 (a), instance-level decision boundary strategy significantly outperforms the vanilla global decision design (75.0% vs 63.1% on Office-Home in OPDA scenarios). We attribute this to that vanilla design discounts the inconsistency of covariate shifts across categories, and also the variability among samples from the same category.",
+        "bbox": [
+            75,
+            612,
+            468,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Exploration with Entropy as the Indicator. Contrasting with existing threshold-based methods that utilize Entropy as the indicator for differentiating common and private data, we propose decomposing the feature and using the projection  $\\mathbf{z}_{i,unk}^{t}$  on the source-unknown space as an alternative indicator. To empirically substantiate the superiority, we remold our framework to incorporate Entropy as the indicator. Figure 4 (b) depicts the results. An observation is that while employing entropy as the indicator within our framework is",
+        "bbox": [
+            75,
+            763,
+            468,
+            900
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/3f2ae93e6a3123e54df700f932bcee05fe553c6c6eeed04979dfea9a7f441902.jpg",
+        "image_caption": [
+            "Figure 3. Robustness analysis. (a) shows the sensitivity to  $\\lambda$  on Office-31. (b) presents the H-score curves on VisDA. (c-d) present robustness analysis when varying the unknown private categories.",
+            "(a) Effect of Instance-level Decision Boundary",
+            "Figure 4. Methodology analysis. (a) compares the effectiveness of our instance-level decision strategy against the vanilla global decision strategy. (b) examines the efficacy of using Entropy as the indicator for private data."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            519,
+            244,
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+            354
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/862ba535973c6ca976f54376d3e3fe936843dd25a2033bfb58ea613f8a1c298d.jpg",
+        "image_caption": [
+            "(b) Exploration with Entropy as the Indicator"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            694,
+            244,
+            864,
+            354
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "feasible, its performance is inferior compared to  $\\mathbf{z}_{i,unk}^{t}$ . We speculate that this inferiority might result from entropy's limited capacity to distinguish between common samples with high uncertainty and private unknown samples.",
+        "bbox": [
+            496,
+            422,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5. Conclusion",
+        "text_level": 1,
+        "bbox": [
+            500,
+            496,
+            617,
+            512
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we delve into source-free universal domain adaptation (SF-UniDA). Different from existing methods that leverage hand-crafted thresholding strategies or feature-clustering algorithms, we propose a novel idea of LEArning Decomposition (LEAD) tailored for SF-UniDA. Technically, LEAD first decomposes features into source-known and -unknown two parts, then establishes instance-level decision boundaries for pseudo-labeling. It offers an elegant view to identify target-private unknown data without tedious tuning a threshold or relying on unstable clustering. Extensive experiments across various scenarios have verified the effectiveness of our LEAD. Besides, it is appealing in view that LEAD can be seamlessly incorporated into existing methods to further boost performance. Remarkably, LEAD improves UMAC by  $7.9\\%$  overall H-score in the OPDA scenario on Office-Home dataset.",
+        "bbox": [
+            496,
+            523,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Acknowledgment: This work is supported by the National Natural Science Foundation of China (No. 62372329), in part by the National Key Research and Development Program of China (No. 2021YFB2501104), in part by Shanghai Rising Star Program (No.21QC1400900), in part by Tongji-Qomolo Autonomous Driving Commercial Vehicle Joint Lab Project, and in part by Xiaomi Young Talents Program, and in part by the International Exchange Program for Graduate Students, Tongji University (No.2023020053).",
+        "bbox": [
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+    },
+    {
+        "type": "page_number",
+        "text": "23341",
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+    },
+    {
+        "type": "text",
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2024/LEAD_ Learning Decomposition for Source-free Universal Domain Adaptation/68e710b5-658b-4bb7-a5db-feae6ea998dd_origin.pdf

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2024/LEAD_ Learning Decomposition for Source-free Universal Domain Adaptation/full.md

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+# LEAD: Learning Decomposition for Source-free Universal Domain Adaptation
+
+Sanqing  $\mathrm{Qu}^1$ , Tianpei  $\mathrm{Zou}^1$ , Lianghua  $\mathrm{He}^1$ , Florian Röhrbein $^2$ , Alois Knoll $^3$ , Guang Chen $^{1*}$ , Changjun Jiang $^1$
+
+$^{1}$ Tongji University,  $^{2}$ Chemnitz University of Technology,  $^{3}$ Technical University of Munich
+
+# Abstract
+
+Universal Domain Adaptation (UniDA) targets knowledge transfer in the presence of both covariate and label shifts. Recently, Source-free Universal Domain Adaptation (SF-UniDA) has emerged to achieve UniDA without access to source data, which tends to be more practical due to data protection policies. The main challenges lie in determining whether covariate-shifted samples belong to target-private unknown categories. Existing methods tackle this either through hand-crafted thresholding or by developing time-consuming iterative clustering strategies. In this paper, we propose a new idea of LEArning Decomposition (LEAD), which decouples features into source-known and -unknown components to identify target-private data. Technically, LEAD initially leverages the orthogonal decomposition analysis for feature decomposition. Then, LEAD builds instance-level decision boundaries to adaptively identify target-private data. Extensive experiments across various UniDA scenarios have demonstrated the effectiveness and superiority of LEAD. Notably, in the OPDA scenario on VisDA dataset, LEAD outperforms GLC by  $3.5\%$  overall H-score and reduces  $75\%$  time to derive pseudo-labeling decision boundaries. Besides, LEAD is also appealing in that it is complementary to most existing methods. The code is available at https://github.com/ispc-lab/LEAD.
+
+# 1. Introduction
+
+Deep neural networks (DNNs) have yielded impressive results in a variety of computer vision tasks [12, 18, 22, 42]. However, DNNs often fail to generalize well to new domains due to the discrepancy between training (source) and test (target) data distributions (i.e., covariate shift). Such a shift poses significant challenges for some safety-critical applications like autonomous driving [9, 10], or medical imaging [13, 31]. Unsupervised Domain Adaptation (DA) [16, 23] aims to address this challenge by transferring task-specific knowledge from a labeled source domain to an unlabeled target domain. Despite promising results, most
+
+![](images/eedb42aa8eec51aebbbdf6588d9e6093c0cee0ecfc340e4655e0416bee70ea83.jpg)  
+Figure 1. (a) Pseudo-label accuracy curves for target-private data in the OPDA scenario on VisDA dataset. An observation is that clustering-based GLC does not work well in deriving decision boundaries for target-private data. This may be due to the curse of dimensionality, leading K-means to faintly discerning clusters. (b) Frequency distribution for the normalized feature magnitude of target data in the source-unknown space (orthogonal complement of the space spanned by source model weights). Features are on task  $(A\to D)$  in the OPDA scenario of Office-31. The results show that target-private data are expected to involve more components from source-unknown space, even with covariate shifts.
+
+![](images/311904e7893df586bad37f09500ec8d8c0e403d392f568a50a4fba25e4cff427.jpg)
+
+existing favorable DA methods [16, 20, 27, 45] assume that the label spaces are identical across the source and target domain, thus being only applicable to closed-set scenarios and limiting applicability to practical applications.
+
+To handle generalized cases, Universal Domain Adaptation (UniDA) [47] was proposed to allow all potential label shifts between source and target domains. Different from existing methods specialized for Partial Domain Adaptation (PDA) [3, 4], Open-set Domain Adaptation (OSDA) [35, 46], or Open-Partial Domain Adaptation (OPDA) [44, 54], in UniDA, we have no prior knowledge about the label shift, e.g., information on matched common classes or the number of categories in the target domain. Nonetheless, most existing UniDA works [7, 25, 47] necessitate concurrent access to source and target data. This requirement becomes increasingly impractical in light of strict data protection policies [50]. In this paper, we focus on Source-free Universal Domain Adaptation (SF-UniDA) [28, 41], where only a pre-trained source model is provided for knowledge transfer rather than labeled source data.
+
+The primary objective for UniDA is to recognize target data belonging to common categories and separate them from target-private "unknown" data. Existing meth
+
+ods have designed various criteria based on instance-level predictions, e.g., entropy-based [14, 47, 54], confidence-based [15, 24, 44]. However, defining a universal threshold for all scenarios is challenging and often sub-optimal. To mitigate tedious parameter-tuning, some methods start to perform source and target consensus clustering to achieve common and private data separation [7, 25]. Considering that SF-UniDA is inaccessible to source data, GLC [41] devises an iterative one-vs-all clustering strategy to realize target-private data identification. Regardless of progress, iterative clustering can be computationally intensive. Besides, due to the curse of dimensionality [2], methods like K-means are prone to overfitting and faintly discerning clusters. This can be implied to some degree from Figure 1 (a).
+
+In this paper, we propose to address the SF-UniDA problem from a new perspective, i.e., feature decomposition. Our launching point is that, even though target data might have shifted in the feature space, target-private data from unknown categories are likely to exhibit a higher proportion of components from the orthogonal complement (source-unknown) space spanned by source model weights. The frequency distribution of normalized feature magnitudes in the source-unknown space depicted in Figure 1 (b) basically demonstrates our argument, which has been rarely explored in the literature. To materialize our idea, we propose the LEArning Decomposition (LEAD) framework. In particular, LEAD initially leverages the orthogonal decomposition to construct source-known and -unknown space. The projection on source-unknown space is then regarded as the discriminative representation with respect to target-private categories. Different from existing thresholding methods introducing a fixed global hand-crafted threshold for all scenarios, LEAD deliberately considers the distance to the target prototypes and source anchors to establish instance-level decision boundaries. We analyze and evaluate our LEAD under a variety of SF-UniDA scenarios, ranging from PDA, OSDA, to OPDA. Extensive experiments demonstrate the effectiveness and superiority.
+
+The main contribution is the proposal of a LEArning Decomposition (LEAD) framework for source-free universal domain adaptation (SF-UniDA). This solution leads to elegant views for identifying target-private unknown data without tedious tuning thresholds or relying on iterative unstable clustering. Remarkably, in the OPDA scenario on VisDA, LEAD attains an H-score of  $76.6\%$ , surpassing GLC [41] by  $3.5\%$ . Besides, LEAD is complementary to most existing SF-UniDA methods. For instance, in the OPDA scenario on Office-Home, LEAD advances UMAD [28] with H-score improvement from  $70.1\%$  to  $78.0\%$ .
+
+# 2. Related Work
+
+Unsupervised Domain Adaptation. When DNNs encounter data from a distribution that differs from their train
+
+ing data, inevitable performance degeneration is commonly observed. To address this issue, domain adaptation (DA) [16, 23] has been introduced, leveraging labeled data from source domains to train DNNs for unlabeled target domains in a transductive learning manner. Existing DA methods can be broadly categorized into two paradigms, namely moment matching [11, 34, 48] and adversarial learning [16, 19, 21]. Regardless of their effectiveness in various applications such as object recognition [16, 27, 39], semantic segmentation [19, 48], and object detection [8, 21], most existing approaches assume that label spaces are identical across the source and target domains, limiting their applicability.
+
+Universal Domain Adaptation. There have been some approaches introduced to deal with label-shift scenarios, such as open-set domain adaptation (OSDA) [32, 35, 46], partial-set domain adaptation (PDA) [3, 4], and open-partial-set domain adaptation (OPDA) [15, 44, 54]. However, these methods are often tailored to specific scenarios and may not be readily applicable to other label shift situations. Universal domain adaptation (UniDA), on the other hand, is designed to facilitate adaptation across all potential label shift scenarios. Despite the progress in UniDA, many existing methods [5, 7, 44] necessitate simultaneous access to both source and target data, making them impractical for applications with stringent data protection policies. To address this challenge, source-free universal domain adaptation (SF-UniDA) [28, 41] has been proposed, wherein source data are only utilized for pre-training and are inaccessible during target adaptation. To promote the distinction between common and private data, existing methods often resort to manually defined thresholding or the introduction of global clustering techniques. Nevertheless, selecting an appropriate threshold for all scenarios can be both laborious and sub-optimal. Additionally, K-means clustering tends to be unstable when applied to high-dimensional data due to the curse of dimensionality [2]. Our work delves into these limitations and proposes a novel and elegant solution from the perspective of feature decomposition.
+
+Feature Decomposition. As a fundamental technique in machine learning, feature decomposition is applied to deconstruct complex data into simpler and more interpretable components. In the field of domain adaptation and domain generalization, feature decomposition has been leveraged in various studies [6, 26, 30, 33, 38, 40] to enhance feature alignment or facilitate domain-invariant feature learning by breaking down features into content and style components. Nonetheless, the content and style decomposition design is less applicable for UniDA, as the primary challenge lies in distinguishing common and private data. In this paper, we approach the problem from the perspective of orthogonal feature decomposition and employ Independent Component Analysis to decompose features into two orthogonal parts, thereby facilitating the intended objective.
+
+![](images/eb8beafd7fe75af0f36aaa1ef4acfd447b286f8f39fe8c69684b04b60cc5fffe.jpg)  
+Figure 2. (a) Illustrations of traditional universal domain adaptation (UniDA) and source-free universal domain adaptation (SF-UniDA). Traditional UniDA methods necessitate data from both source and target domains concurrently. In SF-UniDA, source data are solely utilized for pre-training. Adaptation is performed by harnessing target data and the source model  $f_{\theta}^{s} = h_{\theta}^{s} \circ g_{\theta}^{s}$ . (b) An overview of our Learning Decomposition (LEAD) framework. Pseudo-labeling is an important technique for UniDA and SF-UniDA. The primary objective is to recognize target data associated with common label sets and exclude data within the target-private label space. Different from existing methods that perform private data identification by hand-crafted thresholding on predictions or iterative global clustering, we tackle this from the viewpoint of feature decomposition. The rationale is that despite potential shifts in the feature space, target-private data are expected to encompass more components from the orthogonal complement (source-unknown) space of the source model. Technically, LEAD first performs orthogonal decomposition to decompose target features into source-known and -unknown parts, i.e.,  $\mathbf{z}_{i,knw}^{t}$  and  $\mathbf{z}_{i,unk}^{t}$ .  $\| \mathbf{z}_{i,unk}^{t}\|_{2}$  is considered as an indicator for private data. Next, LEAD employs a two-component Gaussian Mixture Model to estimate the distribution of  $\| \mathbf{z}_{i,unk}^{t}\|_{2}$ . Thereafter, LEAD devises a metric named "common score"  $\epsilon_{i,c}$  that accounts for distances to both target prototypes and source anchors (derived from  $h_{\theta}^{t}$ ) to facilitate deriving instance-level decision boundary  $\rho_{i,c}$ . LEAD provides an elegant solution to distinguish target-private data, mitigating the need for tedious hand-crafted threshold tuning or dependence on time-consuming iterative clustering. LEAD could also serve as a complementary approach to most existing SF-UniDA methods.
+
+![](images/7ecf330707fdfa614df79bb0c5548e32eddd9d563b3d72c33366cd7e75e9087c.jpg)
+
+# 3. Methodology
+
+# 3.1. Preliminary
+
+In this paper, we consider a generalized and challenging case in domain adaptation: universal domain adaptation (UniDA), which aims to achieve knowledge transfer in the presence of both covariate and label shifts. In UniDA, there is a labeled source domain  $\mathcal{D}^s = \left\{\left(\mathbf{x}_i^s,\mathbf{y}_i^s\right)\right\}_{i = 1}^{N_s}$  where  $\mathbf{x}_i^s\in \mathcal{X}^s\subset \mathbb{R}^X,\mathbf{y}_i^s\in \mathcal{Y}^s\subset \mathbb{R}^C$  , and an unlabeled target domain  $\mathcal{D}^t = \left\{\left(\mathbf{x}_i^t,\ref{eq:2.3.1}\right)\right\}_{i = 1}^{N_t}$  where  $\mathbf{x}_i^t\in \mathcal{X}^t\subset \mathbb{R}^X.$ $\mathcal{V} = \mathcal{V}^s\cap \mathcal{V}^t$  denotes the common label sets shared by source and target domains.  $\bar{\mathcal{V}}^s = \mathcal{V}\setminus \mathcal{V}^t$  and  $\bar{\mathcal{V}}^t = \mathcal{V}\setminus \mathcal{V}^s$  symbolizes the label sets private to source and target domain, individually. UniDA supposes that we have no prior knowledge about  $\mathcal{V}^t$  .  $\mathcal{V}$  and  $\bar{\mathcal{V}}^t$  are also unavailable. The objective is to recognize common data belonging to  $\mathcal{V}$  and reject private data in  $\bar{\mathcal{V}}^t$
+
+Different from traditional UniDA methods that need concurrent access to source and target data, under the source-free universal domain adaptation (SF-UniDA) setting,  $\mathcal{D}_s$  is only applicable for source model pre-training and not acces-
+
+sible during adaptation. Assuming that the source model is represented as  $f_{\theta}^{s} = h_{\theta}^{s}\circ g_{\theta}^{s}$ , where  $g_{\theta}^{s}:\mathbb{R}^{X}\to \mathbb{R}^{D}$  denotes the feature extractor and  $h_\theta^s:\mathbb{R}^D\to \mathbb{R}^C$  is the classifier module. Following existing methods [27, 41], we freeze the classifier module  $h_\theta^t = h_\theta^s$  and only learn a target-specific feature extractor  $g_{\theta}^{t}$  to realize model adaptation. Figure 2 (a) presents an illustration for UniDA and SF-UniDA.
+
+The main challenge is how to distinguish common data from private data. Prior methods [25, 28, 41, 47] have designed various algorithms to encourage the separation. However, these methods perform data identification either based on hand-crafted thresholding criteria or by introducing time-consuming unstable clustering strategies. We propose to mitigate these limitations from the perspective of feature decomposition. An observation is that even though target data may have shifted in the feature space, the features of private data still include more components from the orthogonal complement (source-unknown) space of the pre-trained model. Technically, we present a novel learning decomposition (LEAD) framework. LEAD capitalizes on the orthogonal decomposition to build two orthogonal fea
+
+ture spaces, i.e., source-known and -unknown space. Feature projection on source-unknown space is extracted as the descriptor for private data. Then, LEAD considers the distances to both the target prototypes and source anchors to establish instance-level decision boundaries. Figure 2 (b) manifests the architecture of our LEAD.
+
+# 3.2. Orthogonal Feature Decomposition
+
+Pseudo-labeling serves as an important technique in unsupervised learning, yet many existing strategies only account for closed-set scenarios, disregarding the label-shift situations, which impairs their ability to differentiate target-private data. To fulfill the objective of common and private data separation, we propose to orthogonally decompose the feature representation into two uncorrelated parts, i.e., features associated with source-known space  $F_{knw}$  and those related to source-unknown space  $F_{unk}$ . This design stems from a simple inductive bias in favor of private data identification. Due to the lack of exposure to target data during source pre-training, particularly target-private data, the source-known space does not include any significant attributes of target-private data. Subsequently, after normalization, target-private data are expected to contain more components from source-unknown space, even with covariate shifts. This hypothesis is basically demonstrated by empirical evidence, as illustrated in Figure 1 (b).
+
+Formally, denoting the weight of classifier  $h_{\theta}^{t}$  is  $W_{cls} \in \mathbb{R}^{C \times D}$ . Source-known space  $F_{knw}$  can be represented as the vector space of span  $\{\mathbf{w}_n\}$ , where  $\{\mathbf{w}_n \in \mathbb{R}^D | n = 1, \dots, C\}$  is a group weight vectors of  $W_{cls}$ . Source-unknown space  $F_{unk}$  is the orthogonal complement space of  $F_{knw}$ , i.e.,  $\mathbb{R}^D = F_{knw} \oplus F_{unk}$ . Nevertheless, unit orthogonality in  $\{\mathbf{w}_n \in \mathbb{R}^D | n = 1, \dots, C\}$  is not guaranteed (i.e., when  $n \neq m$  ( $\mathbf{w}_n, \mathbf{w}_m \neq 0$ ), making it hard to derive  $F_{unk}$ . Considering that  $F_{knw}$  and  $F_{unk}$  are the row space and null space of  $W_{cls}$ . Therefore, we employ the singular value decomposition (SVD) on  $W_{cls}$  to obtain  $F_{knw}$  and  $F_{unk}$ . Specifically,
+
+$$
+W _ {c l s} = U \Sigma V ^ {T},
+$$
+
+$$
+F _ {k n w} = \operatorname {s p a n} \left\{\mathbf {v} _ {n} | _ {n = 1, \dots , C} \right\}, \tag {1}
+$$
+
+$$
+F _ {u n k} = \operatorname {s p a n} \left\{\mathbf {v} _ {n} | _ {n = C + 1, \dots , D} \right\}
+$$
+
+where  $\Sigma \in \mathbb{R}^{C\times D}$  is a diagonal matrix,  $U\in \mathbb{R}^{C\times C}$  and  $V\in \mathbb{R}^{D\times D}$  are both orthogonal unitary matrices.  $\{\mathbf{v}_n|\mathbf{v}_n\in \mathbb{R}^D\}_{n = 1}^D$  are columns of  $V$
+
+Assuming that  $\mathbf{z}_i^t$  is the feature of target data  $\mathbf{x}_i^t$  extracted from feature extractor  $g_{\theta}^{t}$  after normalization, i.e.,  $\mathbf{z}_i^t = g_\theta^t (\mathbf{x}_i^t) / ||g_\theta^t (\mathbf{x}_i^t)||_2$ , then  $\mathbf{z}_i^t$  can be represented as the weighted summation of two orthogonal bases:
+
+$$
+\mathbf {z} _ {i} ^ {t} = \underbrace {\sum_ {n = 1} ^ {C} l _ {n} \cdot \mathbf {v} _ {n}} _ {\mathbf {z} _ {i, k n w} ^ {t}} + \underbrace {\sum_ {n = C + 1} ^ {D} l _ {n} \cdot \mathbf {v} _ {n}} _ {\mathbf {z} _ {i, u n k} ^ {t}} \tag {2}
+$$
+
+where  $||\mathbf{z}_{i,knw}^{t}||_{2}^{2} + ||\mathbf{z}_{i,unk}^{t}||_{2}^{2} = 1$ ,  $\mathbf{z}_{i,knw}^{t}$  and  $\mathbf{z}_{i,unk}^{t}$  are the projections of  $\mathbf{z}_{i}^{t}$  on  $F_{knw}$  and  $F_{unk}$ , respectively.  $l_{n} \in \mathbb{R}$  denotes the projection weight of  $\mathbf{z}_{i}^{t}$  onto the unit base  $\mathbf{v}_{n}$ . This procedure is commonly recognized as orthogonal decomposition and has been extensively studied in the context of Independent Component Analysis (ICA).
+
+# 3.3. Adaptive Separation for Private Data
+
+Intuitively, enabled by feature decomposition, we could differentiate between common and private data by examining the dominance of  $\mathbf{z}_{i,unk}^{t}$  over  $\mathbf{z}_i$ . However, such a straightforward approach is not applicable to SF-UniDA due to the impact of distribution covariate shift, which often deteriorates the significance of  $\mathbf{z}_{i,knw}^{t}$  for common data, leading to the prevalence of  $\mathbf{z}_{i,unk}^{t}$  in the representation. Additionally, the feature extractor inevitably captures representations that are independent of  $F_{knw}$ , including background contexts [1], object textures [17], and high-frequency patterns [51], further exacerbating this issue.
+
+To solve this, one feasible solution is to estimate the distribution of  $\| \mathbf{z}_{i,unk}^{t}\|_{2}$  to effectively calibrate these disturbances. Our observations have revealed that the empirical distributions of  $\| \mathbf{z}_{i,unk}^{t}\|_{2}$  exhibit a bimodal pattern, with the presence of two distinct peaks typically indicating the modes of common and private data. Consequently, we employ a two-component Gaussian Mixture Model (GMM) to estimate the distribution  $\| \mathbf{z}_{i,unk}^{t}\|_{2}$ , with the components featuring a lower mean representing the common data and those with a higher mean corresponding to the private data. In particular, we denote  $\mu_{com}$  and  $\mu_{pri}$  as the expectation for common and private data, where  $\mu_{com} < \mu_{pri}$ .
+
+In the light of  $\mu_{com}$  and  $\mu_{pri}$ , an intuitive practice is to treat all common and private categories equally. Accordingly, common and private data can be separated by establishing  $(\mu_{com} + \mu_{pri}) / 2$  as the threshold, where data with  $\| \mathbf{z}_{i,unk}^t\| _2$  below the threshold are recognized as common data, while those above are identified as private data. Despite its reasonable effectiveness, it discounts the inconsistency of covariate shifts across each category. Moreover, it fails to account for the variability in covariate shifts even among samples from the same category. These considerations motivate us to devise an instance-level decision strategy to achieve accurate and effective data identification.
+
+Concretely, we first leverage top-  $K$  sampling to construct target prototypes, denoted as  $\{\mathbf{c}_c^t\in \mathbb{R}^D |_{c = 1,\dots ,C}\}$  for each common category, adhering to the procedure in [29, 41]. Similar to [41], we empirically set  $K = N_{t} / \tilde{C}_{t}$ , where  $N_{t}$  represents the amount of target data, and  $\tilde{C}_t$  signifies the estimated count of target categories. Diverging from [41], we additionally collect source anchors from  $W_{cls}$ , denoted as  $\{\mathbf{c}_c^s\in \mathbb{R}^D |_{c = 1,\ldots ,C}\}$  to assist us handle scenarios involving source-private categories. The construct of target prototypes through top-  $K$  sampling fails to consider these sce
+
+narios, making it susceptible to misidentifying private data as common. Further details regarding the target prototype construction are included in the supplementary.
+
+Thereafter, we propose a novel metric, common score  $\epsilon_{i,c}$ , which deliberately considers the distance of  $\mathbf{z}_i^t$  to the target prototype  $\mathbf{c}_c^t$  and source anchor  $\mathbf{c}_c^s$  to facilitate us in deriving instance-level decision boundaries. Formally, this metric is defined as:
+
+$$
+\begin{array}{l} d (\mathbf {a}, \mathbf {b}) = 1. 0 - \cos (\mathbf {a}, \mathbf {b}), \\ \epsilon_ {i, c} ^ {t} = 1. 0 - \exp \left(d \left(\mathbf {z} _ {i} ^ {t}, \mathbf {c} _ {c} ^ {t}\right) - 1. 0\right), \\ \epsilon_ {i, c} ^ {s} = \exp \left(- d \left(\mathbf {z} _ {i} ^ {t}, \mathbf {c} _ {c} ^ {s}\right)\right), \tag {3} \\ \epsilon_ {i, c} = \sqrt {\epsilon_ {i , c} ^ {t} \cdot \epsilon_ {i , c} ^ {s}} \\ \end{array}
+$$
+
+where  $\epsilon_{i,c}^{t}$  and  $\epsilon_{i,c}^{s}$  denote the common score from target prototype and source anchor viewpoint, respectively. Both  $\epsilon_{i,c}^{t}$  and  $\epsilon_{i,c}^{s}$  are clipped to the [0, 1] before fusion. We then utilize geometric mean to calculate fused common score, due to its advantage in multi-criteria decision-making. Note that we leverage different formulas to calculate  $\epsilon_{i,c}^{t}$  and  $\epsilon_{i,c}^{s}$ . Under the same condition, i.e.,  $d(\mathbf{z}_i^t,\mathbf{c}_c^s) = d(\mathbf{z}_i^t,\mathbf{c}_c^t)$ ,  $\epsilon_{i,c}^{s}$  is greater than  $\epsilon_{i,c}^{t}$ . The spirit behind is that instances exhibiting proximity to source anchors are likely to be common data. Conversely, instances in close proximity to target prototypes do not guarantee their recognition.
+
+Given the computed common score  $\epsilon_{i,c}$  and the estimated distribution for  $\| \mathbf{z}_{i,unk}^t\| _2$  we introduce the following pseudo-labeling strategy to effectively distinguish between common and private data instances:
+
+$$
+\begin{array}{l} \rho_ {i, c} = \mu_ {c} + \epsilon_ {i, c} \cdot (\mu_ {p r i} - \mu_ {c}), \\ \tilde {\mathbf {y}} _ {i} ^ {t} = \left\{ \begin{array}{l l} \text {u n k n o w n}, & \text {i f} \| \mathbf {z} _ {i, u n k} ^ {t} \| _ {2} \geq \rho_ {i, c} \\ \mathbb {1} (\operatorname {a r g m a x} (\epsilon_ {i})), & \text {i f} \| \mathbf {z} _ {i, u n k} ^ {t} \| _ {2} <   \rho_ {i, c} \end{array} \right. \tag {4} \\ \end{array}
+$$
+
+where  $\mu_{c}$  denotes the expectation of  $\| \mathbf{z}_{i,unk}^{t}\|_{2}$  for the  $c$ -th category, derived using the identical top- $K$  sampling technique employed during the construction of the target prototypes.  $\rho_{i,c}$  represents the instance-level decision boundary, which accounts for the potential covariate shifts across each category, as well as the data instances corresponding to both target prototypes and source anchors.  $\mathbb{1}$  denotes the one-hot encoding operator,  $\tilde{\mathbf{y}}_i^t$  is the pseudo-label for  $\mathbf{x}_i^t$ .
+
+# 3.4. Optimization Objectives
+
+To encourage the separation between common and private data, the optimization process involves three distinct objectives, including pseudo-label learning, feature decomposition regularization, and feature consensus regularization.
+
+Pseudo-label Learning. With the pseudo labels derived from Eq. 4, we apply the cross-entropy loss for model adaptation. Nevertheless, instead of assigning equal importance to all pseudo-labels, we introduce a Student's  $t$  distribution
+
+Table 1. Details of class split.  $\mathcal{V},\bar{\mathcal{V}}_s$  , and  $\bar{\mathcal{V}}_t$  signifies the common class, source-private class, and target-private class, respectively.  
+
+<table><tr><td rowspan="2">Dataset</td><td colspan="3">Class Split(γ/γs/γt)</td></tr><tr><td>OPDA</td><td>OSDA</td><td>PDA</td></tr><tr><td>Office-31 [43]</td><td>10/10/11</td><td>10/0/11</td><td>10/21/0</td></tr><tr><td>Office-Home [49]</td><td>10/5/50</td><td>25/0/40</td><td>25/40/0</td></tr><tr><td>VisDA [36]</td><td>6/3/3</td><td>6/0/6</td><td>6/6/0</td></tr><tr><td>DomainNet [37]</td><td>150/50/145</td><td>-</td><td>-</td></tr></table>
+
+to characterize the certainty associated with each pseudolabel, taking into account the distance between  $\| \mathbf{z}_{i,unk}^t\| _2$  and  $\rho_{i,c}$ . Specifically,
+
+$$
+\begin{array}{l} \tau_ {i} ^ {t} \propto 1 - \left(1 + \frac {\left(\rho_ {i , \kappa} - \| \mathbf {z} _ {i , u n k} ^ {t} \| _ {2}\right) ^ {2}}{\alpha}\right) ^ {- \frac {\alpha + 1}{2}}, \\ \mathcal {L} _ {c e} = - \frac {1}{N} \sum_ {i = 1} ^ {N} \tau_ {i} ^ {t} \cdot \sum_ {c = 1} ^ {C} \tilde {y} _ {i, c} ^ {t} \log \delta_ {c} \left(f _ {\theta} ^ {t} \left(\mathbf {x} _ {i} ^ {t}\right)\right) \tag {5} \\ \end{array}
+$$
+
+where  $\tau_{i}^{t}$  denotes the certainty,  $\kappa = \mathrm{argmax}(\epsilon_{i,c}),\alpha = 1\mathrm{e - }4$  by default.  $\delta_c(f_\theta^t (\mathbf{x}_i^t))$  is the  $c$  -th soft-max probability for  $\mathbf{x}_i^t$ $\tilde{y}_{i,c}^{t}$  corresponds to  $c$  -th one-hot encoded pseudo-label for  $\tilde{\mathbf{y}}_i^t$  . For those instances pseudo-labeled as private data, we refrain from introducing an additional  $C + 1$  -th class, instead employing a uniform distribution to represent them.
+
+Feature Decomposition Regularization. To promote the discriminability of  $\mathbf{z}_{i,unk}^{t}$  for identifying private data, we impose a feature decomposition regularizer. Concretely,
+
+$$
+\begin{array}{l} p _ {i} = \frac {\exp \left(\left\| \mathbf {z} _ {i , u n k} ^ {t} \right\| _ {2}\right)}{\exp \left(\left\| \mathbf {z} _ {i , u n k} ^ {t} \right\| _ {2}\right) + \exp \left(\left\| \mathbf {z} _ {i , k n w} ^ {t} \right\| _ {2}\right)}, \tag {6} \\ \mathcal {L} _ {r e g} = - \frac {1}{N} \sum_ {i = 1} ^ {N} \tau_ {i} ^ {t} \cdot \left(\hat {y} _ {i} ^ {t} \log \left(p _ {i}\right) + \left(1 - \hat {y} _ {i} ^ {t}\right) \log \left(1 - p _ {i}\right)\right) \\ \end{array}
+$$
+
+$\hat{y}_i^t = 1$  or 0 means pseudo-labeled as private/common data.
+
+Feature Consensus Regularization. Recent studies [41, 52, 53] in SFDA and SF-UniDA observe that incorporating consensus regularization with nearest neighbors in feature space could assist models in achieving more stable performance. Following them, we integrate the objective  $\mathcal{L}_{con}$  into LEAD. More details are included in the supplementary.
+
+Overall Optimization Objective. Taking into account the discussions above, the eventual loss function is defined as:
+
+$$
+\mathcal {L} = \lambda \cdot \mathcal {L} _ {c e} + \mathcal {L} _ {r e g} + \mathcal {L} _ {c o n} \tag {7}
+$$
+
+where  $\lambda > 0$  is a trade-off hyper-parameter.
+
+# 4. Experiments
+
+# 4.1. Experimental Setup
+
+Dataset. We empirically verify the effectiveness of our LEAD on four datasets, including Office-31 [43], OfficeHome [49], VisDA [36], and DomainNet [37]. For a
+
+Table 2. H-score (\%) comparison in OPDA scenario on Office-Home. U denotes methods applicable for all potential label-shift scenarios (i.e., OPDA, OSDA, and PDA). SF represents source data-free. CF indicates model adaptation without time-consuming K-means clustering.  
+
+<table><tr><td>Methods</td><td>U</td><td>SF</td><td>CF</td><td>Ar2Cl</td><td>Ar2Pr</td><td>Ar2Re</td><td>Cl2Ar</td><td>Cl2Pr</td><td>Cl2Re</td><td>Pr2Ar</td><td>Pr2Cl</td><td>Pr2Re</td><td>Re2Ar</td><td>Re2Cl</td><td>Re2Pr</td><td>Avg</td></tr><tr><td>CMU [15]</td><td>✘</td><td>✘</td><td>✓</td><td>56.0</td><td>56.9</td><td>59.2</td><td>67.0</td><td>64.3</td><td>67.8</td><td>54.7</td><td>51.1</td><td>66.4</td><td>68.2</td><td>57.9</td><td>69.7</td><td>61.6</td></tr><tr><td>DANCE [47]</td><td>✓</td><td>✘</td><td>✓</td><td>61.0</td><td>60.4</td><td>64.9</td><td>65.7</td><td>58.8</td><td>61.8</td><td>73.1</td><td>61.2</td><td>66.6</td><td>67.7</td><td>62.4</td><td>63.7</td><td>63.9</td></tr><tr><td>DCC [25]</td><td>✓</td><td>✘</td><td>✘</td><td>58.0</td><td>54.1</td><td>58.0</td><td>74.6</td><td>70.6</td><td>77.5</td><td>64.3</td><td>73.6</td><td>74.9</td><td>81.0</td><td>75.1</td><td>80.4</td><td>70.2</td></tr><tr><td>OVANet [44]</td><td>✘</td><td>✘</td><td>✓</td><td>62.8</td><td>75.6</td><td>78.6</td><td>70.7</td><td>68.8</td><td>75.0</td><td>71.3</td><td>58.6</td><td>80.5</td><td>76.1</td><td>64.1</td><td>78.9</td><td>71.8</td></tr><tr><td>GATE [7]</td><td>✓</td><td>✘</td><td>✓</td><td>63.8</td><td>75.9</td><td>81.4</td><td>74.0</td><td>72.1</td><td>79.8</td><td>74.7</td><td>70.3</td><td>82.7</td><td>79.1</td><td>71.5</td><td>81.7</td><td>75.6</td></tr><tr><td>UniOT [5]</td><td>✘</td><td>✘</td><td>✓</td><td>67.3</td><td>80.5</td><td>86.0</td><td>73.5</td><td>77.3</td><td>84.3</td><td>75.5</td><td>63.3</td><td>86.0</td><td>77.8</td><td>65.4</td><td>81.9</td><td>76.6</td></tr><tr><td>Source-only</td><td>-</td><td>-</td><td>-</td><td>47.3</td><td>71.6</td><td>81.9</td><td>51.5</td><td>57.2</td><td>69.4</td><td>56.0</td><td>40.3</td><td>76.6</td><td>61.4</td><td>44.2</td><td>73.5</td><td>60.9</td></tr><tr><td>SHOT-O [27]</td><td>✘</td><td>✓</td><td>✓</td><td>32.9</td><td>29.5</td><td>39.6</td><td>56.8</td><td>30.1</td><td>41.1</td><td>54.9</td><td>35.4</td><td>42.3</td><td>58.5</td><td>33.5</td><td>33.3</td><td>40.7</td></tr><tr><td>LEAD</td><td>✓</td><td>✓</td><td>✓</td><td>62.7</td><td>78.1</td><td>86.4</td><td>70.6</td><td>76.3</td><td>83.4</td><td>75.3</td><td>60.6</td><td>86.2</td><td>75.4</td><td>60.7</td><td>83.7</td><td>75.0</td></tr><tr><td>UMAD [28]</td><td>✘</td><td>✓</td><td>✓</td><td>61.1</td><td>76.3</td><td>82.7</td><td>70.7</td><td>67.7</td><td>75.7</td><td>64.4</td><td>55.7</td><td>76.3</td><td>73.2</td><td>60.4</td><td>77.2</td><td>70.1</td></tr><tr><td>+ LEAD</td><td>✓</td><td>✓</td><td>✓</td><td>65.2</td><td>82.6</td><td>87.4</td><td>78.0</td><td>76.5</td><td>87.5</td><td>79.8</td><td>65.0</td><td>88.4</td><td>79.4</td><td>63.0</td><td>83.5</td><td>78.0 (+7.9)</td></tr><tr><td>GLC [41]</td><td>✓</td><td>✓</td><td>✘</td><td>64.3</td><td>78.2</td><td>89.8</td><td>63.1</td><td>81.7</td><td>89.1</td><td>77.6</td><td>54.2</td><td>88.9</td><td>80.7</td><td>54.2</td><td>85.9</td><td>75.6</td></tr><tr><td>+ LEAD</td><td>✓</td><td>✓</td><td>✘</td><td>65.7</td><td>79.7</td><td>88.7</td><td>65.0</td><td>80.3</td><td>88.5</td><td>77.6</td><td>57.4</td><td>88.9</td><td>78.9</td><td>57.8</td><td>85.5</td><td>76.2 (+0.6)</td></tr></table>
+
+Table 3. H-score (\%) comparison in OPDA scenario on Office-31, VisDA, and DomainNet. Some results are cited from UMAD [28].  
+
+<table><tr><td rowspan="2">Methods</td><td rowspan="2">U</td><td rowspan="2">SF</td><td rowspan="2">CF</td><td colspan="7">Office-31</td><td colspan="7">DomainNet</td><td>VisDA</td></tr><tr><td>A2D</td><td>A2W</td><td>D2A</td><td>D2W</td><td>W2A</td><td>W2D</td><td>Avg</td><td>P2R</td><td>P2S</td><td>R2P</td><td>R2S</td><td>S2P</td><td>S2R</td><td>Avg</td><td>S2R</td></tr><tr><td>CMU [15]</td><td>X</td><td>X</td><td>✓</td><td>68.1</td><td>67.3</td><td>71.4</td><td>79.3</td><td>72.2</td><td>80.4</td><td>73.1</td><td>50.8</td><td>45.1</td><td>52.2</td><td>45.6</td><td>44.8</td><td>51.0</td><td>48.3</td><td>32.9</td></tr><tr><td>DANCE [47]</td><td>✓</td><td>X</td><td>✓</td><td>78.6</td><td>71.5</td><td>79.9</td><td>91.4</td><td>72.2</td><td>87.9</td><td>80.3</td><td>21.0</td><td>37.0</td><td>47.3</td><td>46.7</td><td>27.7</td><td>21.0</td><td>33.5</td><td>42.8</td></tr><tr><td>DCC [25]</td><td>✓</td><td>X</td><td>X</td><td>88.5</td><td>78.5</td><td>70.2</td><td>79.3</td><td>75.9</td><td>88.6</td><td>80.2</td><td>56.9</td><td>43.7</td><td>50.3</td><td>43.3</td><td>44.9</td><td>56.2</td><td>49.2</td><td>43.0</td></tr><tr><td>OVANet [44]</td><td>X</td><td>X</td><td>✓</td><td>85.8</td><td>79.4</td><td>80.1</td><td>95.4</td><td>84.0</td><td>94.3</td><td>86.5</td><td>56.0</td><td>47.1</td><td>51.7</td><td>44.9</td><td>47.4</td><td>57.2</td><td>50.7</td><td>53.1</td></tr><tr><td>GATE [7]</td><td>✓</td><td>X</td><td>✓</td><td>87.7</td><td>81.6</td><td>84.2</td><td>94.8</td><td>83.4</td><td>94.1</td><td>87.6</td><td>57.4</td><td>48.7</td><td>52.8</td><td>47.6</td><td>49.5</td><td>56.3</td><td>52.1</td><td>56.4</td></tr><tr><td>UniOT [5]</td><td>X</td><td>X</td><td>✓</td><td>87.0</td><td>88.5</td><td>88.4</td><td>98.8</td><td>87.6</td><td>96.6</td><td>91.1</td><td>59.3</td><td>51.8</td><td>47.8</td><td>48.3</td><td>46.8</td><td>58.3</td><td>52.0</td><td>57.3</td></tr><tr><td>Source-only</td><td>-</td><td>-</td><td>-</td><td>70.9</td><td>63.2</td><td>39.6</td><td>77.3</td><td>52.2</td><td>86.4</td><td>64.9</td><td>57.3</td><td>38.2</td><td>47.8</td><td>38.4</td><td>32.2</td><td>48.2</td><td>43.7</td><td>25.7</td></tr><tr><td>SHOT-O [27]</td><td>X</td><td>✓</td><td>✓</td><td>73.5</td><td>67.2</td><td>59.3</td><td>88.3</td><td>77.1</td><td>84.4</td><td>75.0</td><td>35.0</td><td>30.8</td><td>37.2</td><td>28.3</td><td>31.9</td><td>32.2</td><td>32.6</td><td>44.0</td></tr><tr><td>LEAD</td><td>✓</td><td>✓</td><td>✓</td><td>85.4</td><td>85.0</td><td>86.3</td><td>90.9</td><td>86.2</td><td>93.1</td><td>87.8</td><td>59.9</td><td>46.1</td><td>51.3</td><td>45.0</td><td>45.9</td><td>56.3</td><td>50.8</td><td>76.6</td></tr><tr><td>UMAD [28]</td><td>X</td><td>✓</td><td>✓</td><td>79.1</td><td>77.4</td><td>87.4</td><td>90.7</td><td>90.4</td><td>97.2</td><td>87.0</td><td>59.0</td><td>44.3</td><td>50.1</td><td>42.1</td><td>32.0</td><td>55.3</td><td>47.1</td><td>58.3</td></tr><tr><td>+ LEAD</td><td>✓</td><td>✓</td><td>✓</td><td>88.7</td><td>89.2</td><td>90.8</td><td>95.8</td><td>90.4</td><td>97.1</td><td>92.0 (+5.0)</td><td>59.3</td><td>46.0</td><td>49.8</td><td>43.8</td><td>43.9</td><td>56.0</td><td>49.8 (+2.7)</td><td>67.2 (+8.9)</td></tr><tr><td>GLC [41]</td><td>✓</td><td>✓</td><td>X</td><td>81.5</td><td>84.5</td><td>89.8</td><td>90.4</td><td>88.4</td><td>92.3</td><td>87.8</td><td>63.3</td><td>50.5</td><td>54.9</td><td>50.9</td><td>49.6</td><td>61.3</td><td>55.1</td><td>73.1</td></tr><tr><td>+ LEAD</td><td>✓</td><td>✓</td><td>X</td><td>83.0</td><td>86.8</td><td>87.6</td><td>92.0</td><td>87.1</td><td>93.2</td><td>88.3 (+0.5)</td><td>63.5</td><td>50.7</td><td>55.1</td><td>51.6</td><td>49.9</td><td>61.3</td><td>55.4 (+0.3)</td><td>76.8 (+3.7)</td></tr></table>
+
+fair comparison, we evaluate LEAD on partial-set domain adaptation (PDA), open-set domain adaptation (OSDA), and open-partial-set domain adaptation (OPDA). Details of classes split are summarized in Table 1.
+
+Evaluation. We utilize the same evaluation metric as previous works. In PDA scenarios, we report the classification accuracy for evaluation. In OSDA and OPDA scenarios, we report the H-score for performance comparison, which is a harmonic mean of accuracy over common data and accuracy over private data. It is worth noting that LEAD can be incorporated effortlessly into most existing SF-UniDA methods, for potential performance improvement. To demonstrate this merit, we integrate LEAD with two representative methods: UMAD [28] and GLC [41].
+
+Implementation Details. All the experiments are conducted on a single RTX-3090 GPU with PyTorch-1.10. We adopt the same network architecture as existing baseline methods. During target model adaptation, we apply the SGD optimizer with momentum 0.9. The batch size is set to 64 for all experiments. The learning rate is set to 1e-3 for Office-31 and Office-Home, and 1e-4 for VisDA and DomainNet. As for  $\lambda$ , it is set to 0.3 for Office-31, 1.0 for VisDA, and 2.0 for Office-Home and DomainNet. During inference, we adopt the same protocol like [41]. More details are presented in the supplementary.
+
+# 4.2. Experimental Results
+
+Results for OPDA Scenarios. To verify the effectiveness of LEAD, we first conduct experiments in the most challenging OPDA scenarios, where both source and target domains contain private data. Table 2 summarizes the results on Office-Home, and Table 3 details the results on Office-31, DomainNet, and VisDA. These results demonstrate that LEAD achieves performance surpassing or comparable to existing methods based on K-means clustering for segregating common and private data. In comparison with methods without clustering, LEAD achieves significantly superior performance. For instance, on Office-Home, DomainNet, and VisDA datasets, LEAD outperforms UMAD by  $4.9\%$ ,  $3.7\%$ , and  $18.3\%$ , respectively. We attribute this to our instance-level adaptive decision strategy, which effectively circumvents the limitations imposed by a fixed threshold. While GLC achieves commendable performance on its own, the integration with LEAD further amplifies its effectiveness. For example, LEAD improves GLC in the H-score on VisDA from  $73.1\%$  to  $76.8\%$ . The integration with LEAD proves even more significant against UMAD, with the H-score on Office-Home and VisDA boosting from  $70.1\% /58.3\%$  to  $78.0\% /67.2\%$ , respectively.
+
+Results for OSDA Scenarios. We then conduct experiments in OSDA scenarios, where only the target domain
+
+Table 4. H-score (%) comparison in OSDA scenario on Office-Home, Office-31, and VisDA.  
+
+<table><tr><td rowspan="2">Methods</td><td rowspan="2">U SF CF</td><td colspan="15">Office-Home</td><td colspan="7">Office-31</td><td>VisDA</td></tr><tr><td>Ar2Cl</td><td>Ar2Pr</td><td>Ar2Re</td><td>Cl2Ar</td><td>Cl2Pr</td><td>Cl2Re</td><td>Pr2Ar</td><td>Pr2Cl</td><td>Pr2Re</td><td>Re2Ar</td><td>Re2Cl</td><td>Re2Pr</td><td>Avg</td><td>A2D</td><td>A2W</td><td>D2A</td><td>D2W</td><td>W2A</td><td>W2D</td><td>Avg</td><td>S2R</td><td></td><td></td></tr><tr><td>CMU [15]</td><td>X X Y</td><td>55.0</td><td>57.0</td><td>59.0</td><td>59.3</td><td>58.2</td><td>60.6</td><td>59.2</td><td>51.3</td><td>61.2</td><td>61.9</td><td>53.5</td><td>55.3</td><td>57.6</td><td>52.6</td><td>55.7</td><td>76.5</td><td>75.9</td><td>65.8</td><td>64.7</td><td>65.2</td><td>54.2</td><td></td><td></td></tr><tr><td>DANCE [47]</td><td>✓ X Y</td><td>6.5</td><td>9.0</td><td>9.9</td><td>20.4</td><td>10.4</td><td>9.2</td><td>28.4</td><td>12.8</td><td>12.6</td><td>14.2</td><td>7.9</td><td>13.2</td><td>12.9</td><td>84.9</td><td>78.8</td><td>79.1</td><td>78.8</td><td>68.3</td><td>78.8</td><td>79.8</td><td>67.5</td><td></td><td></td></tr><tr><td>DCC [25]</td><td>✓ X X</td><td>56.1</td><td>67.5</td><td>66.7</td><td>49.6</td><td>66.5</td><td>64.0</td><td>55.8</td><td>53.0</td><td>70.5</td><td>61.6</td><td>57.2</td><td>71.9</td><td>61.7</td><td>58.3</td><td>54.8</td><td>67.2</td><td>89.4</td><td>85.3</td><td>80.9</td><td>72.7</td><td>59.6</td><td></td><td></td></tr><tr><td>OVANet [44]</td><td>X X Y</td><td>58.6</td><td>66.3</td><td>69.9</td><td>62.0</td><td>65.2</td><td>68.6</td><td>59.8</td><td>53.4</td><td>69.3</td><td>68.7</td><td>59.6</td><td>66.7</td><td>64.0</td><td>90.5</td><td>88.3</td><td>86.7</td><td>98.2</td><td>88.3</td><td>98.4</td><td>91.7</td><td>66.1</td><td></td><td></td></tr><tr><td>GATE [7]</td><td>✓ X Y</td><td>63.8</td><td>70.5</td><td>75.8</td><td>66.4</td><td>67.9</td><td>71.7</td><td>67.3</td><td>61.5</td><td>76.0</td><td>70.4</td><td>61.8</td><td>75.1</td><td>69.0</td><td>88.4</td><td>86.5</td><td>84.2</td><td>95.0</td><td>86.1</td><td>96.7</td><td>89.5</td><td>70.8</td><td></td><td></td></tr><tr><td>Source-only</td><td>- - -</td><td>46.1</td><td>63.3</td><td>72.9</td><td>42.8</td><td>54.0</td><td>58.7</td><td>47.8</td><td>36.1</td><td>66.2</td><td>60.8</td><td>45.3</td><td>68.2</td><td>55.2</td><td>78.2</td><td>72.1</td><td>44.2</td><td>82.2</td><td>52.1</td><td>88.8</td><td>69.6</td><td>29.1</td><td></td><td></td></tr><tr><td>SHOT-O [27]</td><td>X Y Y</td><td>37.7</td><td>41.8</td><td>48.4</td><td>56.4</td><td>39.8</td><td>40.9</td><td>60.0</td><td>41.5</td><td>49.7</td><td>61.8</td><td>41.4</td><td>43.6</td><td>46.9</td><td>80.2</td><td>71.6</td><td>64.3</td><td>93.1</td><td>64.0</td><td>91.8</td><td>77.5</td><td>28.1</td><td></td><td></td></tr><tr><td>LEAD</td><td>✓ Y Y</td><td>60.7</td><td>70.8</td><td>76.5</td><td>61.0</td><td>68.6</td><td>70.8</td><td>65.5</td><td>59.8</td><td>74.2</td><td>64.8</td><td>57.7</td><td>75.8</td><td>67.2</td><td>84.9</td><td>85.1</td><td>90.2</td><td>94.8</td><td>90.3</td><td>96.5</td><td>90.3</td><td>74.2</td><td></td><td></td></tr><tr><td>UMAD [28]</td><td>X Y Y</td><td>59.2</td><td>71.8</td><td>76.6</td><td>63.5</td><td>69.0</td><td>71.9</td><td>62.5</td><td>54.6</td><td>72.8</td><td>66.5</td><td>57.9</td><td>70.7</td><td>66.4</td><td>88.5</td><td>84.4</td><td>86.8</td><td>95.0</td><td>88.2</td><td>95.9</td><td>89.8</td><td>66.8</td><td></td><td></td></tr><tr><td>+ LEAD</td><td>✓ Y Y</td><td>62.6</td><td>73.6</td><td>77.3</td><td>61.3</td><td>66.2</td><td>70.7</td><td>63.3</td><td>54.6</td><td>75.1</td><td>66.7</td><td>63.5</td><td>75.6</td><td>67.6</td><td>90.4</td><td>89.6</td><td>90.3</td><td>95.4</td><td>90.7</td><td>97.3</td><td>92.3</td><td>70.2</td><td></td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>+2.5</td><td></td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr></table>
+
+Table 5. Accuracy comparison (%) in PDA scenario on Office-Home, Office-31, and VisDA.  
+
+<table><tr><td rowspan="2">Methods</td><td rowspan="2">U SF CF</td><td colspan="15">Office-Home</td><td colspan="7">Office-31</td><td>VisDA</td></tr><tr><td>Ar2Cl</td><td>Ar2Pr</td><td>Ar2Re</td><td>Cl2Ar</td><td>Cl2Pr</td><td>Cl2Re</td><td>Pr2Ar</td><td>Pr2Cl</td><td>Pr2Re</td><td>Re2Ar</td><td>Re2Cl</td><td>Re2Pr</td><td colspan="2">Avg</td><td>A2D</td><td>A2W</td><td>D2A</td><td>D2W</td><td>W2A</td><td>W2D</td><td>Avg</td><td>S2R</td><td></td></tr><tr><td>CMU [15]</td><td>X X X</td><td>50.9</td><td>74.2</td><td>78.4</td><td>62.2</td><td>64.1</td><td>72.5</td><td>63.5</td><td>47.9</td><td>78.3</td><td>72.4</td><td>54.7</td><td>78.9</td><td colspan="2">66.5</td><td>84.1</td><td>84.2</td><td>69.2</td><td>97.2</td><td>66.8</td><td>98.8</td><td>83.4</td><td>65.5</td><td></td></tr><tr><td>DANCE [47]</td><td>✓ X X</td><td>53.6</td><td>73.2</td><td>84.9</td><td>70.8</td><td>67.3</td><td>82.6</td><td>70.0</td><td>50.9</td><td>84.8</td><td>77.0</td><td>55.9</td><td>81.8</td><td colspan="2">71.1</td><td>77.1</td><td>71.2</td><td>83.7</td><td>94.6</td><td>92.6</td><td>96.8</td><td>86.0</td><td>73.7</td><td></td></tr><tr><td>DCC [25]</td><td>✓ X X</td><td>54.2</td><td>47.5</td><td>57.5</td><td>83.8</td><td>71.6</td><td>86.2</td><td>63.7</td><td>65.0</td><td>75.2</td><td>85.5</td><td>78.2</td><td>82.6</td><td colspan="2">70.9</td><td>87.3</td><td>81.3</td><td>95.4</td><td>100.0</td><td>95.5</td><td>100.0</td><td>93.3</td><td>72.4</td><td></td></tr><tr><td>OVANet [44]</td><td>X X X</td><td>34.1</td><td>54.6</td><td>72.1</td><td>42.4</td><td>47.3</td><td>55.9</td><td>38.2</td><td>26.2</td><td>61.7</td><td>56.7</td><td>35.8</td><td>68.9</td><td colspan="2">49.5</td><td>69.4</td><td>61.7</td><td>61.4</td><td>90.2</td><td>66.4</td><td>98.7</td><td>74.6</td><td>34.3</td><td></td></tr><tr><td>GATE [7]</td><td>✓ X X</td><td>55.8</td><td>75.9</td><td>85.3</td><td>73.6</td><td>70.2</td><td>83.0</td><td>72.1</td><td>59.5</td><td>84.7</td><td>79.6</td><td>63.9</td><td>83.8</td><td colspan="2">74.0</td><td>89.5</td><td>86.2</td><td>93.5</td><td>100.0</td><td>94.4</td><td>98.6</td><td>93.7</td><td>75.6</td><td></td></tr><tr><td>Source-only</td><td>- - -</td><td>45.9</td><td>69.2</td><td>81.1</td><td>55.7</td><td>61.2</td><td>64.8</td><td>60.7</td><td>41.1</td><td>75.8</td><td>70.5</td><td>49.9</td><td>78.4</td><td colspan="2">62.9</td><td>90.4</td><td>79.3</td><td>79.3</td><td>95.9</td><td>84.3</td><td>98.1</td><td>87.8</td><td>42.8</td><td></td></tr><tr><td>SHOT-P [27]</td><td>X X Y</td><td>64.7</td><td>85.1</td><td>90.1</td><td>75.1</td><td>73.9</td><td>84.2</td><td>76.4</td><td>64.1</td><td>90.3</td><td>80.7</td><td>63.3</td><td>85.5</td><td colspan="2">77.8</td><td>89.8</td><td>84.4</td><td>92.2</td><td>96.6</td><td>92.2</td><td>99.4</td><td>92.4</td><td>74.2</td><td></td></tr><tr><td>LEAD</td><td>✓ Y Y</td><td>58.2</td><td>83.1</td><td>87.0</td><td>70.5</td><td>75.4</td><td>83.3</td><td>73.7</td><td>50.4</td><td>83.7</td><td>78.3</td><td>58.7</td><td>83.2</td><td colspan="2">73.8</td><td>89.8</td><td>93.9</td><td>95.6</td><td>98.6</td><td>96.0</td><td>99.4</td><td>95.5</td><td>75.3</td><td></td></tr><tr><td>UMAD [28]</td><td>X Y Y</td><td>51.2</td><td>66.5</td><td>79.2</td><td>63.1</td><td>62.9</td><td>68.2</td><td>63.3</td><td>56.4</td><td>75.9</td><td>74.5</td><td>55.9</td><td>78.3</td><td colspan="2">66.3</td><td>85.4</td><td>85.1</td><td>83.5</td><td>97.6</td><td>86.2</td><td>99.4</td><td>89.5</td><td>68.5</td><td></td></tr><tr><td>+ LEAD</td><td>✓ Y Y</td><td>61.1</td><td>78.2</td><td>87.5</td><td>70.5</td><td>78.5</td><td>81.8</td><td>74.1</td><td>60.4</td><td>83.3</td><td>78.8</td><td>63.2</td><td>82.1</td><td colspan="2">75.0</td><td>89.2</td><td>90.8</td><td>90.6</td><td>98.0</td><td>93.0</td><td>100.0</td><td>93.6</td><td>78.1</td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td colspan="2">+8.7</td><td></td><td></td><td></td><td></td><td></td><td>+4.1</td><td>+9.6</td><td></td><td></td></tr><tr><td>GLC [41]</td><td>✓ Y X</td><td>55.9</td><td>79.0</td><td>87.5</td><td>72.5</td><td>71.8</td><td>82.7</td><td>74.9</td><td>41.7</td><td>82.4</td><td>77.3</td><td>60.4</td><td>84.3</td><td colspan="2">72.5</td><td>89.8</td><td>89.8</td><td>92.8</td><td>96.6</td><td>96.1</td><td>99.4</td><td>94.1</td><td>76.2</td><td></td></tr><tr><td>+ LEAD</td><td>✓ Y X</td><td>56.6</td><td>81.2</td><td>88.1</td><td>72.5</td><td>72.2</td><td>83.2</td><td>75.3</td><td>43.6</td><td>83.4</td><td>78.2</td><td>59.7</td><td>84.2</td><td colspan="2">73.2</td><td>89.8</td><td>93.2</td><td>95.6</td><td>96.9</td><td>96.0</td><td>99.4</td><td>95.1</td><td>75.5</td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td colspan="2">+0.7</td><td></td><td></td><td></td><td></td><td></td><td>+1.0</td><td>-0.7</td><td></td><td></td></tr></table>
+
+involves private data. Table 4 lists the results, demonstrating the superiority of LEAD against baselines. Specifically, LEAD obtains the H-score of  $67.2\%$ ,  $90.3\%$ , and  $74.2\%$  on Office-Home, Office-31, and VisDA datasets, respectively. Similar to the observations in OPDA scenarios, LEAD also exhibits performance improvement to existing methods. LEAD improves the H-score of UMAD by  $1.2\%$ ,  $2.5\%$ , and  $3.4\%$  across the Office-Home, Office-31, and VisDA datasets, respectively. The results again verify the merit of LEAD when incorporated with existing methods.
+
+Results for PDA Scenarios. Finally, we verify the effectiveness of LEAD in PDA scenarios, where the target domain's label sets are subsets of those in the source domain. Results presented in Table 5 show that LEAD achieves superior performance even compared to methods tailored for PDA. In particular, LEAD attains the overall accuracy of  $73.8\%$ ,  $95.5\%$ , and  $75.3\%$  on Office-Home, Office-31, and VisDA datasets, individually. LEAD contributes the accuracy increase of  $8.7\%$ ,  $4.1\%$ , and  $9.6\%$  to UMAD on these datasets. Note that, there is a slight degradation  $(-0.7\%)$  for GLC w/ LEAD. It may arise from gradient conflict, causing the optimization process to inadvertently compromise one objective in favor of improving the overall objective. We will pursue better integration strategies in future work.
+
+Table 6. Ablation studies of LEAD in OPDA scenarios.  
+
+<table><tr><td>Lce</td><td>Lreg</td><td>Lcon</td><td>Office-31</td><td>Office-Home</td><td>VisDA</td></tr><tr><td>-</td><td>-</td><td>-</td><td>64.9</td><td>60.9</td><td>25.7</td></tr><tr><td>✓</td><td>-</td><td>-</td><td>82.0</td><td>73.6</td><td>61.5</td></tr><tr><td>✓</td><td>✓</td><td>-</td><td>84.5</td><td>74.5</td><td>67.3</td></tr><tr><td>✓</td><td>-</td><td>✓</td><td>87.2</td><td>74.5</td><td>75.7</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>87.8</td><td>75.0</td><td>76.6</td></tr></table>
+
+# 4.3. Experimental Analysis
+
+Ablation Study. To assess the contribution of different components within LEAD, we carry out extensive ablation studies in OPDA scenarios. The results, detailed in Table 6, confirm that each component is not only effective but also complementary to the others.
+
+Efficiency Comparison. As previously stated, LEAD employs the distance to target prototypes and source anchors for adaptive pseudo-labeling. This design, in contrast to clustering-based methods, notably reduces the need for computational resources. Table 7 juxtaposes the runtime of GLC [41] and LEAD in OPDA scenarios. It is clear that LEAD requires minimal resources for deriving decision boundaries, whereas GLC's resource demands escalate dramatically with data scale. In particular, on DomainNet, with about 0.6 million images across 345 categories, GLC averages 897.65 seconds, while LEAD takes only 0.29 sec
+
+![](images/272dc3cb2d8c736b11cf92868aefcd5a1556bce19c89b588cbf4274e63087ebf.jpg)  
+(a) Sensitivity to  $\lambda$
+
+![](images/039a3a74b32629a546ea44434469cf1ba504d2e9fc48a5d3968bb893703994ba.jpg)  
+(b) H-score convergence
+
+![](images/5adf2f4b6957ee926f84826bf54253e771ca8d412b05a8741ebed93b861bb315.jpg)  
+(c)  $\mathrm{Ar}\rightarrow \mathrm{Pr}$  in OPDA
+
+![](images/a3f8ae72befbceebaf4610de0e38520614dac47bcf9abf0b8500ba7a595ff590.jpg)  
+(d)  $\mathrm{Re}\rightarrow \mathrm{Cl}$  in OPDA
+
+Table 7. Runtime (s) to derive pseudo-label decision boundaries.  
+
+<table><tr><td></td><td>Office-31</td><td>Office-Home</td><td>VisDA</td><td>DomainNet</td></tr><tr><td>GLC [41]</td><td>0.19</td><td>0.51</td><td>0.46</td><td>897.65</td></tr><tr><td>LEAD</td><td>0.02</td><td>0.02</td><td>0.11</td><td>0.29</td></tr></table>
+
+onds on the same platform. Moreover, LEAD also shows substantial resource savings even on normal-scale datasets, e.g., on VisDA with over  $75\%$  reduction.
+
+Parameter Sensitivity. We investigate the parameter sensitivity of  $\lambda$  on Office-31 in OPDA scenarios, where the range of  $\lambda$  is set to [0.1, 0.2, 0.3, 0.4, 0.5]. Figure 3 (a) illustrates that the results are stable around the selected parameter  $\lambda = 0.3$ . Through oracle validation, we may find the optimal parameter configuration for this setting is  $\lambda = 0.1$ .
+
+Training Stability. Figure 3 (b) visualizes the training curves of our LEAD on VisDA in OPDA scenarios. Generally, the training procedure of LEAD is stable and effective.
+
+Varying Unknown Classes. With the rise in unknown private classes, accurately distinguishing common from private data becomes more challenging. To examine the robustness of our LEAD, we compared it with GLC and UMAD in OPDA scenarios using the Office-Home dataset. The results in Figure 3 (c-d) show that LEAD achieves stable results and consistently boosts existing methods.
+
+Effect of Instance-level Decision Boundary. To evaluate the contribution of our instance-level pseudo-labeling strategy, we conduct a comparison against the intuitive design, which uses the average of  $\mu_{\text{com}}$  and  $\mu_{\text{pri}}$  as the threshold. As depicted in Figure 4 (a), instance-level decision boundary strategy significantly outperforms the vanilla global decision design (75.0% vs 63.1% on Office-Home in OPDA scenarios). We attribute this to that vanilla design discounts the inconsistency of covariate shifts across categories, and also the variability among samples from the same category.
+
+Exploration with Entropy as the Indicator. Contrasting with existing threshold-based methods that utilize Entropy as the indicator for differentiating common and private data, we propose decomposing the feature and using the projection  $\mathbf{z}_{i,unk}^{t}$  on the source-unknown space as an alternative indicator. To empirically substantiate the superiority, we remold our framework to incorporate Entropy as the indicator. Figure 4 (b) depicts the results. An observation is that while employing entropy as the indicator within our framework is
+
+![](images/3f2ae93e6a3123e54df700f932bcee05fe553c6c6eeed04979dfea9a7f441902.jpg)  
+Figure 3. Robustness analysis. (a) shows the sensitivity to  $\lambda$  on Office-31. (b) presents the H-score curves on VisDA. (c-d) present robustness analysis when varying the unknown private categories.  
+(a) Effect of Instance-level Decision Boundary  
+Figure 4. Methodology analysis. (a) compares the effectiveness of our instance-level decision strategy against the vanilla global decision strategy. (b) examines the efficacy of using Entropy as the indicator for private data.
+
+![](images/862ba535973c6ca976f54376d3e3fe936843dd25a2033bfb58ea613f8a1c298d.jpg)  
+(b) Exploration with Entropy as the Indicator
+
+feasible, its performance is inferior compared to  $\mathbf{z}_{i,unk}^{t}$ . We speculate that this inferiority might result from entropy's limited capacity to distinguish between common samples with high uncertainty and private unknown samples.
+
+# 5. Conclusion
+
+In this paper, we delve into source-free universal domain adaptation (SF-UniDA). Different from existing methods that leverage hand-crafted thresholding strategies or feature-clustering algorithms, we propose a novel idea of LEArning Decomposition (LEAD) tailored for SF-UniDA. Technically, LEAD first decomposes features into source-known and -unknown two parts, then establishes instance-level decision boundaries for pseudo-labeling. It offers an elegant view to identify target-private unknown data without tedious tuning a threshold or relying on unstable clustering. Extensive experiments across various scenarios have verified the effectiveness of our LEAD. Besides, it is appealing in view that LEAD can be seamlessly incorporated into existing methods to further boost performance. Remarkably, LEAD improves UMAC by  $7.9\%$  overall H-score in the OPDA scenario on Office-Home dataset.
+
+Acknowledgment: This work is supported by the National Natural Science Foundation of China (No. 62372329), in part by the National Key Research and Development Program of China (No. 2021YFB2501104), in part by Shanghai Rising Star Program (No.21QC1400900), in part by Tongji-Qomolo Autonomous Driving Commercial Vehicle Joint Lab Project, and in part by Xiaomi Young Talents Program, and in part by the International Exchange Program for Graduate Students, Tongji University (No.2023020053).
+
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2024/LEAP-VO_ Long-term Effective Any Point Tracking for Visual Odometry/03c2e012-3152-4602-8d61-0831334e6fb6_content_list.json

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+        "type": "text",
+        "text": "LEAP-VO: Long-term Effective Any Point Tracking for Visual Odometry",
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+        "type": "text",
+        "text": "Weirong Chen $^{1,2*}$  Le Chen $^{3}$  Rui Wang $^{4}$  Marc Pollefeys $^{4}$",
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+        "text": "$^{1}$ TU Munich  $^{2}$ Munich Center for Machine Learning  $^{3}$ MPI for Intelligent Systems  $^{4}$ Microsoft",
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+        "text": "Abstract",
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+    {
+        "type": "text",
+        "text": "Visual odometry estimates the motion of a moving camera based on visual input. Existing methods, mostly focusing on two-view point tracking, often ignore the rich temporal context in the image sequence, thereby overlooking the global motion patterns and providing no assessment of the full trajectory reliability. These shortcomings hinder performance in scenarios with occlusion, dynamic objects, and low-texture areas. To address these challenges, we present the Long-term Effective Any Point Tracking (LEAP) module. LEAP innovatively combines visual, inter-track, and temporal cues with mindfully selected anchors for dynamic track estimation. Moreover, LEAP's temporal probabilistic formulation integrates distribution updates into a learnable iterative refinement module to reason about point-wise uncertainty. Based on these traits, we develop LEAP-VO, a robust visual odometry system adept at handling occlusions and dynamic scenes. Our mindful integration showcases a novel practice by employing long-term point tracking as the front-end. Extensive experiments demonstrate that the proposed pipeline significantly outperforms existing baselines across various visual odometry benchmarks.",
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+        "type": "text",
+        "text": "1. Introduction",
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+        "type": "text",
+        "text": "Visual odometry (VO) calculates the camera's position and movement from an image sequence. It is widely used in various fields including robotics [46], mixed reality [23], and autonomous driving [15]. The performance of VO highly depends on the accuracy of its point tracking front-end, which recovers relative camera motion between consecutive frames using projective geometry. It further requires the point correspondences to be static, as dynamic points can lead to inaccurate motion estimation and pose recovery.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Despite significant advances in feature tracking and optical flow estimation, most existing VO methods mainly focus on the two-view case, i.e., computing feature correspondences between a pair of images. However, these methods",
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+        "image_caption": [
+            "Visual Odometry",
+            "Figure 1. Comparison between two-view approach and multi-view approach for visual odometry. (a) In the two-view approach, correspondences are derived for every image pair and concatenated. Managing occlusion becomes challenging without the temporal context. (b) In the multi-view approach, long-term point trajectories can be obtained all at once, enabling the detection of occlusion and tracking points under partial occlusions."
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "are limited as they rely solely on pairwise relative motion, thus neglecting the valuable temporal information in image sequences. Consequently, they often struggle with capturing dynamic motion patterns in tracks. Another challenge arises from the need to handle occlusions. In two-view scenarios, occlusion is not explicitly modeled, leading to misidentification of occluded points as incorrect matches. To address these challenges effectively, we propose to introduce a long-term point tracker, which can recover the trajectories of specific points across the image sequence given a sparse set of these query points. Its capability of leveraging temporal context and reliably tracking queries over multiple frames even under occlusion, makes it highly suitable for VO applications (refer to Figure 1).",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Recently, Persistent Independent Particles (PIPs) [16] proposes a novel pipeline that brings the idea of iterative refinement into the long-term point tracking task, with the local correlation evidence to maintain feasible computation. While it is proficient in leveraging the temporal context present in the image sequence, it ignores the inter-track information in the image sequence and processes each query point independently. Consequently, PIPs struggles to cap",
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+    {
+        "type": "header",
+        "text": "CVF",
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+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
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+    {
+        "type": "page_footnote",
+        "text": "*Work done at Microsoft Mixed Reality & AI Lab Zurich for a Master's degree.",
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+        "page_idx": 0
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+    {
+        "type": "page_number",
+        "text": "19844",
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "ture the global motion patterns from the image sequence. Additionally, it lacks a reliability metric for its trajectory estimates, hindering its application in quality-sensitive tasks like video segmentation and visual odometry. To mitigate the aforementioned issues, we propose a pipeline that explores dynamic track estimation and temporal probabilistic formulation for long-term point tracking.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we present Long-term Effective Point Tracking (LEAP), aiming to estimate the reliability of predicted correspondences and track moving object trajectories in dynamic scenes. To achieve this, we harness the global motion patterns—often overlooked in existing methods—through an anchor-based dynamic track estimation module, leveraging visual, temporal, and inter-track information to differentiate between the static and dynamic elements. We also incorporate a temporal probabilistic approach into our LEAP pipeline to handle uncertainties and refine the distribution of point correspondences iteratively, showcasing superior performance in complex real-world situations. More importantly, we pioneer the usage of continuous motion estimation from long-term point tracking to construct a robust visual odometry system. Our LEAP-VO distinguishes itself through its thoughtful integration of visual features, track distribution, and global motion patterns, significantly enhancing both the performance and robustness of visual odometry in dynamic environments.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Long-term Point Tracking. In the realm of long-term point tracking or Tracking Any Point (TAP), various methods have been introduced recently. PIPs [16] reframes pixel tracking as a long-term motion estimation with local information and improves tracking accuracy by associating each pixel with a trajectory that spans multiple image frames. The subsequent works enhance performance by integrating spatial context features [2], tracking multiple queries concurrently [18], and extending temporal fields and templates [49]. TAP-Net [9] adopts a different method by locating candidate correspondences through a global cost volume, improved by TAPIR's trajectory refinement [10] and BootsTAP's semi-supervised training [11]. Other approaches explore self-supervision targets to learn visual correspondence via powerful feature representation [5, 17, 36]. Recently, OmniMotion [37] provides a pure test-time optimization method that infers the point trajectory and occlusion directly from videos with optical flow predictions. However, its slow inference speed makes it unsuitable for real-time applications such as visual odometry.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Monocular Visual Odometry. Visual Odometry (VO) can be categorized into indirect (feature-based) and direct methods. Indirect methods, such as MonoSLAM [8] and ORB-SLAM [25], mostly rely on feature extraction and",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "matching to estimate the camera pose. Direct methods, conversely, skip feature extraction and matching and utilize intensity to optimize camera pose and 3D scene point positions based on photometric errors [12, 13, 38], showing better performance on low-texture regions where keypoint tracking can easily fail. However, they are more vulnerable to illumination changes and issues with rolling shutter cameras. Advancements in deep learning have spawned end-to-end monocular VO methods in supervised [3, 28, 30, 33, 39, 40, 43, 44] and unsupervised [21, 27, 45, 51] settings. DeepVO [39] utilizes Recurrent Neural Networks to model sequential data, while SfMLearner [51] develops an unsupervised framework to learn the depth and camera motion from unlabeled monocular videos. TartanVO [40] proposes a VO model that generalizes to multiple datasets and real-world scenarios. DROID-SLAM [32] follows learning-based optimization from RAFT [31] and proposes an end-to-end system, integrating flow, confidence, and geometric optimization via iterative GRU updates. The followed-up work DPVO [33] further cuts computational complexity by replacing dense feature tracking with sparse patch tracking.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Dynamic Track Estimation. In addition to enhancing accuracy, numerous studies have focused on the detection of dynamic objects within videos. Methods based on segmentation, such as DynaSLAM [1] and RCVD [20], employ semantic cues from pre-trained models to exclude dynamic regions. However, these segmentation-based methods are constrained to predefined object categories and struggle to capture real-world motion (for example, differentiating between a stationary and a moving car). Alternatively, DyanVO [28] and ParticleSfM [48] adopt a trajectory-based motion detection approach. This method addresses dynamic scenes using estimated point track information, thereby generating reliable camera trajectories in complex motion scenarios. Nonetheless, they depend on dense optical flow estimation to capture global motion patterns. Furthermore, dynamic tracks can be detected using additional depth information for a 3D consistency check [7, 47], or by optimization based on photo consistency [35, 41, 42].",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "3. Method",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Our goal is to tackle the aforementioned challenges in VO systems, particularly in handling dynamic environments, temporal occlusions, and low-texture regions. To this end, we introduce our LEAP module, which incorporates dynamic track estimation and temporal probabilistic formulation. Furthermore, we illustrate how this module serves as the cornerstone for constructing our advanced VO system.",
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+        "type": "text",
+        "text": "3.1. Preliminary: Tracking Any Point",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Tracking arbitrary pixels in an image sequence is traditionally akin to estimating optical flow, where each pixel",
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+    {
+        "type": "page_number",
+        "text": "19845",
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+    },
+    {
+        "type": "text",
+        "text": "is mapped to a corresponding location in a subsequent frame. However, two-view approaches often overlook the rich temporal context within the image sequence, leading to suboptimal outcomes. Recent advancements address this by revisiting the particle video concept and improving long-term point tracking through learning-based techniques [10, 16, 18]. These TAP methods can track points over multiple frames and detect occlusions, significantly boosting tracking robustness under challenging scenarios.",
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+    {
+        "type": "text",
+        "text": "**Formulation.** Given a sequence of  $S$  consecutive RGB images  $\\mathbf{I} = [\\mathbf{I}_1, \\dots, \\mathbf{I}_S]$ ,  $\\mathbf{I}_s \\in \\mathbb{R}^{3 \\times H \\times W}$  as input, the goal of TAP is to track a set of query points across these frames. For a specific query point with the 2D pixel coordinate  $\\mathbf{x}_q \\in \\mathbb{R}^2$  in frame  $s_q$ , TAP predicts its trajectory across all  $S$  images as  $\\mathbf{X} = [\\mathbf{x}_1, \\dots, \\mathbf{x}_S]$ ,  $\\mathbf{x}_s \\in \\mathbb{R}^2$ , given  $\\mathbf{x}_{s_q} = \\mathbf{x}_q$ . Additionally, TAP estimates the visibility of each point throughout the sequence as  $\\mathbf{V} = [v_1, \\dots, v_S]$ , where  $v_s \\in \\{0, 1\\}$  is a binary label of point visibility indicating whether a point in frame  $s$  is visible or occluded. The TAP formulation for a single query can be described as",
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\left(\\mathbf {X}, \\mathbf {V}\\right) = \\operatorname {T A P} \\left(\\mathbf {I}, \\mathbf {x} _ {q}, s _ {q}\\right). \\tag {1}\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "PIPs [16], a notable learning-based TAP method, offers a promising solution featuring local cost volumes and iterative refinement. Initially, each image  $\\mathbf{I}_s\\in \\mathbf{I}$  is processed through a CNN feature extractor  $\\mathcal{F}$  to extract the feature map  $\\mathbf{Y}_{\\mathbf{s}} = \\mathcal{F}(\\mathbf{I}_{s})$ . Point features  $\\mathbf{f}_q$  are computed by bilinear sampling at the query positions  $\\mathbf{x_s}$  on  $\\mathbf{Y}_s$ . These point features from each image are then concatenated to form a point feature tensor  $\\mathbf{F} = [\\mathbf{f}_1,\\dots ,\\mathbf{f}_S]$ . PIPs approaches the TAP problem by iteratively updating the state variables  $(\\mathbf{X},\\mathbf{F})$ , with the initial states obtained by duplicating the query positions and features. During the  $k$ -th iterative refinement, PIPs computes a multi-scale local cost volume  $\\mathbf{C}[\\mathbf{X}^k ]$  centered around the current estimated point position  $\\mathbf{X}^k$ . Utilizing this local evidence, PIPs predicts updates for the state variables via",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{r} \\left(\\Delta \\mathbf {X}, \\Delta \\mathbf {F}\\right) = \\operatorname {R e f i n e r} \\left(\\mathbf {F} ^ {k}, \\operatorname {p o s} \\left(\\mathbf {X} ^ {k} - \\mathbf {x} _ {\\mathbf {q}}\\right), \\mathbf {C} ^ {k} \\left[ \\mathbf {X} ^ {k} \\right]\\right), \\\\ \\mathbf {X} ^ {k + 1} \\leftarrow \\mathbf {X} ^ {k} + \\Delta \\mathbf {X}, \\quad \\mathbf {F} ^ {k + 1} \\leftarrow \\mathbf {F} ^ {k} + \\Delta \\mathbf {F}, \\end{array} \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathrm{pos}(\\cdot)$  refers to the positional embedding. The final point feature  $\\mathbf{F}^K$  is used to predict point visibility with a simple linear projection layer  $\\mathcal{G}_v$ , yielding  $\\mathbf{V} = \\mathcal{G}_v(\\mathbf{F}^K)$ . Recent advances extend PIPs by replacing the MLP-based refiner with an attention-based refiner and adding spatial feature aggregation to track multiple queries together [18].",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.2. Anchor-based Dynamic Track Estimation",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The established TAP model enables us to extract long-term point trajectories and thereby recover camera motion from an image sequence. However, dynamic environments",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/f9a4b8f0c4199ea8b8569721db074c6591697e11ec43d5bbfbe71c1e30542119.jpg",
+        "image_caption": [
+            "Figure 2. Distributed image gradient-based sampling with  $k = 8$ ,  $N_{a} = 64$ . After computing the image gradient and pooling, we split the gradient map into  $8 \\times 8$  grids and select the point with the maximum gradient in each grid."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "pose extra challenges for VO systems that rely on static 3D point correspondences linked to unchanging scene locations. Therefore, integrating dynamic track estimation into the VO system is crucial for real-world applications.",
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "We propose an innovative method for dynamic track estimation that leverages visual, temporal, and inter-track information. While common techniques like monocular segmentation [20] excel at identifying moving objects using visual cues but can erroneously label static objects, like parked cars, as dynamic. Trajectory-based methods [48], utilizing optical flows from two or multiple frames, can differentiate static and moving objects apart but tend to ignore visual information and can be inefficient due to dense trajectories computation. Merging these two distinct methods is nontrivial; however, the formulation of the TAP pipeline, enhanced with inter-track attention, offers a viable solution.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Our method smartly integrates visual appearance, long-term motion, and inter-track cues, combining the strengths of segmentation and trajectory-based techniques. Utilizing TAP, we extract point features  $\\mathbf{F}$  and long-term trajectories  $\\mathbf{X}$  from the video input. These features capture visual information and the iterative refinement module exchanges information across tracks over time for accurate labeling. However, such a method depends on the query distribution and quantities. With only one query during inference time, it cannot utilize inter-track information. Likewise, if the queries focus on a single object, the system may overlook the motions of other objects due to similar motion patterns.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Anchor-based Inter-track Attention. To better capture global motion patterns, we introduce additional anchors alongside the given queries, denoted as  $\\mathcal{A}$ ,  $|\\mathcal{A}| = N_{a}$ . Ideally, the anchor set should exhibit two characteristics: (1) the anchors should be easy to track, and (2) they should be well-distributed to encapsulate global motion patterns. Given the image  $\\mathbf{I}_{s_q}$  from which the queries  $\\mathbf{x}_q$  are extracted (we maintain the same notations for both single and multiple queries for simplicity), we first employ the Sobel Kernel to derive the image gradient  $(\\mathbf{G}_x,\\mathbf{G}_y)$  for image  $\\mathbf{I}_{s_q}$ . We then apply an average pooling layer on gradient maps for smoothing and downscaling feature maps. Subsequently, we divide the gradient map into  $k\\times k$  sub-regions and select top  $\\frac{N_a}{k^2}$  pixels with the highest image gradient magnitude in",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "19846",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "each local grid. The process is demonstrated in Figure 2.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "To predict the dynamic label of a trajectory, we track queries with additional anchors and concatenate the original query features  $\\mathbf{X}$  and query trajectories  $\\mathbf{F}$  with anchor features  $\\mathbf{X}_A$  and anchor trajectories  $\\mathbf{F}_A$ . We apply a shallow MLP layer  $\\mathcal{G}_d$  with average pooling over the temporal dimension. The dynamic track label  $\\mathbf{m}_d$  is estimated as",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {m} _ {d} = \\operatorname {a v g p o o l} \\left(\\mathcal {G} _ {d} \\left(\\left[ \\mathbf {X} ^ {K}; \\mathbf {X} _ {A} ^ {K} \\right], \\left[ \\mathbf {F} ^ {K}; \\mathbf {F} _ {A} ^ {K} \\right]\\right)\\right). \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Since newly added anchors often lack ground truth information, we employ a semi-supervised training scheme that tracks queries and anchors together to leverage inter-track attention but only calculates losses based on query predictions. This approach prevents the network from developing bias towards specific query sampling methods while learning dynamic track labels effectively.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.3. Temporal Probability Modeling",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Supervised learning applied to large-scale datasets has yielded notable advancements in learning-based point tracking methods. Nonetheless, trajectory estimation errors remain a concern, especially under challenging conditions like occlusions, motion blur, or textureless regions. Recognizing the varying reliability of trajectories, integrating an uncertainty estimation mechanism into the correspondence estimation process is beneficial [6]. This is particularly crucial for quality-sensitive tasks such as visual odometry.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "To evaluate the reliability of point correspondences, we incorporate a probabilistic formulation into the TAP pipeline. Given an image sequence  $\\mathbf{I}$  and a single query point  $\\mathbf{x}_q$ , our objective is to compute the conditional probability density of point trajectory as  $p(\\mathbf{X}|\\mathbf{I},\\mathbf{x}_q)$ . Recognizing the strong correlation between points within the same track, treating each point in the track as independent becomes suboptimal. Therefore, we propose to model the distribution of point trajectories by applying two multivariate distributions, respectively for the 2D coordinates. Let  $\\mathbf{X} = [\\mathbf{a};\\mathbf{b}]$ , where  $\\mathbf{a}\\in \\mathbb{R}^S$  and  $\\mathbf{b}\\in \\mathbb{R}^{S}$  represent the  $\\mathbf{X}$  and  $\\mathbf{Y}$  coordinate of all points in  $\\mathbf{X}$ , respectively. Assuming independence between these two coordinates, the joint probability distribution can be expressed as  $p(\\mathbf{X}|\\mathbf{I},\\mathbf{x}_q) = p(\\mathbf{a}|\\mathbf{I},\\mathbf{x}_q)\\cdot p(\\mathbf{b}|\\mathbf{I},\\mathbf{x}_q)$ . We adopt the multivariate Cauchy distribution, which is associated with its heavy tails distribution and is more stable for optimization. The probability density function (PDF) of a single coordinate is given by",
+        "bbox": [
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+            470,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\np (\\mathbf {a} | \\mathbf {I}, \\mathbf {x} _ {q}) = \\frac {\\Gamma \\left(\\frac {1 + S}{2}\\right)}{\\Gamma \\left(\\frac {1}{2}\\right) \\pi^ {\\frac {S}{2}} \\left| \\boldsymbol {\\Sigma} _ {a} \\right| ^ {\\frac {1}{2}} \\left[ 1 + \\left(\\mathbf {a} - \\boldsymbol {\\mu} _ {a}\\right) ^ {T} \\boldsymbol {\\Sigma} _ {a} ^ {- 1} \\left(\\mathbf {a} - \\boldsymbol {\\mu} _ {a}\\right) \\right] ^ {\\frac {1 + S}{2}}} \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            76,
+            787,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "and a similar expression is applicable for  $p(\\mathbf{b}|\\mathbf{I},\\mathbf{x}_q)$ .  $\\Gamma$  is the Gamma function. The parameters  $(\\boldsymbol{\\mu}_a,\\boldsymbol{\\Sigma}_a,\\boldsymbol{\\mu}_b,\\boldsymbol{\\Sigma}_b)$  represent the location and scale matrices for the respective coordinates. During inference, the uncertainty associated",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/a70127acf14c96950f4d02f1fdf61d4ad2cb1f4fc795d5e9f3b2983140ece6d1.jpg",
+        "image_caption": [
+            "Figure 3. LEAP Front-end. Once image feature maps are obtained, selected anchors aid in tracking. The queries and anchors are processed by a refiner to iteratively update states. The model outputs trajectory distribution, visibility, and dynamic track label."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "with each point is quantified by the sum of diagonal scale estimates at position  $(s,s)$  as  $\\phi (\\mathbf{x}_s) = \\pmb {\\Sigma}_a[s,s] + \\pmb {\\Sigma}_b[s,s]$",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Kernel-based Estimation. Rather than just predicting the positions of points within a trajectory, our model focuses on recovering the distribution of point trajectories by estimating its parameters. The location parameter predictions can be associated with the previous point trajectory as  $[\\pmb{\\mu}_a; \\pmb{\\mu}_b] = \\mathbf{X}$ . However, directly deriving a symmetric and positive definite scale matrix from model outputs is challenging. To address this, we employ a kernel-based approach with the linear kernel  $K(\\mathbf{x}, \\mathbf{y}) = \\mathbf{x}^T \\mathbf{y}$ . During each iteration, two scale matrices  $(\\pmb{\\Sigma}_a, \\pmb{\\Sigma}_b)$  are constructed by first applying two linear projection layers to the point features, represented as  $\\mathbf{F}_a^k = \\mathcal{G}_a(\\mathbf{F}^k)$  and  $\\mathbf{F}_b^k = \\mathcal{G}_b(\\mathbf{F}^k)$ . We then compute the scale matrices as  $\\pmb{\\Sigma}_a = K(\\mathbf{F}_a, \\mathbf{F}_a) + \\sigma \\mathbf{I}$ , and  $\\pmb{\\Sigma}_b = K(\\mathbf{F}_b, \\mathbf{F}_b) + \\sigma \\mathbf{I}$ , where  $\\sigma$  is a small positive value and  $\\mathbf{I}$  is the identity matrix. The model parameters are refined through Maximum Likelihood Estimation (MLE) using a negative log-likelihood (NLL) loss function.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Loss Functions. We supervise the point trajectory mainly with the NLL loss, which is based on the predicted distribution parameters and the ground-truth point trajectory. The main point trajectory loss is given as",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\text {m a i n}} = \\sum_ {k} ^ {K} \\gamma^ {K - k} \\mathcal {L} _ {N L L} \\left(\\mathbf {X} ^ {k}, \\mathbf {X} ^ {*}, \\boldsymbol {\\Sigma} _ {a} ^ {k}, \\boldsymbol {\\Sigma} _ {b} ^ {k}\\right), \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            542,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $K$  is the number of iteration and  $\\gamma = 0.8$ .",
+        "bbox": [
+            500,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "For the visibility and dynamic track label supervision, we use the cross entropy loss with the estimates  $\\mathbf{V},\\mathbf{m}_d$  and ground truth  $\\mathbf{V}^{*},\\mathbf{m}_{d}^{*}$  as",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\text {v i s}} = \\left(1 - \\mathbf {V} ^ {*}\\right) \\log \\left(1 - \\mathbf {V}\\right) + \\mathbf {V} ^ {*} \\log \\mathbf {V}. \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {d y n} = \\left(1 - \\mathbf {m} _ {d} ^ {*}\\right) \\log \\left(1 - \\mathbf {m} _ {d}\\right) + \\mathbf {m} _ {d} ^ {*} \\log \\mathbf {m} _ {d}. \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            540,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The total loss is a weighted sum of three losses:",
+        "bbox": [
+            500,
+            859,
+            815,
+            875
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\text {t o t a l}} = w _ {1} \\mathcal {L} _ {\\text {m a i n}} + w _ {2} \\mathcal {L} _ {\\text {v i s}} + w _ {3} \\mathcal {L} _ {\\text {d y n}}. \\tag {8}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "19847",
+        "bbox": [
+            480,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/005c323b67834729f12b46342f226d06e34bd05848cbaea2bb4db7b3f676de27.jpg",
+        "image_caption": [
+            "Figure 4. LEAP-VO pipeline. Given a new image  $\\mathbf{I}_t$  received at time  $t$ , the keypoint extractor extracts new keypoints from  $\\mathbf{I}_t$ . Then, all the keypoints from the latest  $S_{LP}$ -frame  $\\mathbf{I}_{t - S_{LP} + 1:t}$  are tracked across all other frames within the current LEAP window, followed by a track filtering step to remove outliers. Finally, the local BA module is used on the current BA window to update the camera poses and 3D positions of the extracted keypoints. The colored arrows denote the moving direction of each module when a new image is received."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            119,
+            85,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/bffe5d79cb06a7a1728eda2276e66086b413c42983dcc93b2df1db81da7e0b08.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.4. LEAP-VO",
+        "text_level": 1,
+        "bbox": [
+            76,
+            361,
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+            376
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Leveraging the anchor-based dynamic track estimations and temporal probabilistic formulation, we develop our Long-term Effective Point Tracking (LEAP) pipeline, boosting the accuracy of point tracking and simultaneously capturing global motion patterns and uncertainties of the tracks (refer to Figure 3). In this section, we demonstrate how we can build visual odometry for dynamic scenes based on the long-term tracking capabilities of LEAP. Our LEAP-VO pipeline is illustrated in Figure 4.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Keypoint Extraction and Tracking. In our VO system, the LEAP model serves as the front-end. When a new image frame  $\\mathbf{I}_t$  is captured at time  $t$ , we sample  $N$  new keypoints from this image to initiate point tracking. We consistently employ the distributed image gradient-based sampling method (refer to Section 3.2) for keypoint selection due to its favorable properties in feature distinctiveness and distribution. This approach also obviates the need for additional anchors during tracking. The LEAP model then tracks these keypoints across the last  $S_{LP}$  frames, performing bidirectional tracking (both forward and backward in time). Notably,  $S_{LP}$  can exceed the model window  $S$ , thus enabling more expansive tracking capabilities through sequential prediction [16, 18].",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Track Filtering. Theoretically, precise camera pose estimation between two images can be attained with just a few accurate correspondences under certain conditions. However, the quality of correspondences obtained from feature matching or optical flow can vary. Traditional VO pipelines often use RANSAC [14] to filter out incorrect matches, but their efficiency decreases with more keypoints and views. Our approach, in contrast, bypasses the sampling-based method and uses trajectory quality assessments from LEAP",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "for more efficient and informative track filtering.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "(i) Visibility and Dynamic Track Label: The LEAP model has the capability to estimate not only the 2D point positions within a trajectory but also the visibility of each point and the dynamic track label of the entire trajectory. Thresholds  $\\gamma_v$  for visibility and  $\\gamma_d$  for dynamic track labels are set to ensure that only visible and static points are utilized in the bundle adjustment process.",
+            "(ii) Track Uncertainty: In Section 3.3, we introduce probabilistic modeling to LEAP, allowing us to gauge confidence via distribution measurements. We select only high-confidence points, which correspond to low uncertainty measurements. Denoting our model's uncertainty estimation as  $\\Phi$ , we retain points that exhibit high confidence using the criterion  $\\Phi \\leq Q(\\gamma_u)$ , where  $\\gamma_u$  is the uncertainty quantile and  $Q:[0,1] \\to \\mathbb{R}$  is the quantile function.",
+            "(iii) Track Length: After filtering, we evaluate and remove tracks with insufficient observations, as bundle adjustment is more reliable with increased observations and wider baselines. Tracks with fewer than  $\\gamma_{\\text{track}}$  valid points are excluded from optimization cost computation due to their potential unreliability."
+        ],
+        "bbox": [
+            496,
+            378,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Sliding-window Optimization. With the point validation mask established, we proceed to define the optimization cost function for our sliding window bundle adjustment. The window size for local bundle adjustment, denoted as  $S_{BA}$ , may differ from the point tracking window size  $S_{LP}$ . Our geometric bundle adjustment aims to optimize camera poses  $\\mathbf{T}$  and 3D scene point positions  $\\mathbf{Q}$  by aligning the induced point trajectory from the projective relationship, with the estimated point trajectory from LEAP. We parameterize a 3D scene point  $\\mathbf{Q}_i$  by its 2D keypoint location  $\\mathbf{x}_i$  in image  $\\mathbf{I}_i$  and depth  $d_i$ . Let  $\\mathrm{LEAP}_{i\\rightarrow j}$  denote the mapping of tracking keypoint from  $\\mathbf{I}_i$  to  $\\mathbf{I}_j$  using LEAP model. The",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "19848",
+        "bbox": [
+            480,
+            944,
+            517,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "reprojection cost is formulated as:",
+        "bbox": [
+            76,
+            90,
+            307,
+            107
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\sum_ {i} \\sum_ {j \\in | i - j | \\leq S _ {B A}} \\sum_ {n} w _ {i \\rightarrow j, n} \\| \\mathcal {P} (\\mathbf {T} _ {i}, \\mathbf {T} _ {j}, \\mathbf {K}, d _ {i, n}) - \\\\ \\operatorname {L E A P} _ {i \\rightarrow j} (\\mathbf {x} _ {i, n}) \\| _ {\\rho}, \\tag {9} \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            94,
+            118,
+            468,
+            174
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where  $\\| \\cdot \\|_{\\rho}$  is the distance metric, and the weight  $w_{i\\rightarrow j,n}$  is derived from the track filtering results. We use the GaussNewton method [34] to optimize Eq. (9) for  $K_{BA}$  iterations. At each iteration, we compute the camera poses update  $\\Delta \\xi^{(k)}\\in \\mathfrak{se}(3)$  (lie-algebra corresponding to  $\\mathbf{T}$ ), and the depth update  $\\Delta \\mathbf{D}^{(k)}$  for each point. The optimization can be solved efficiently with the Schur decomposition. We use the robust Huber loss function for the distance metric.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4. Experiment",
+        "text_level": 1,
+        "bbox": [
+            76,
+            324,
+            200,
+            340
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.1. Datasets and Metrics",
+        "text_level": 1,
+        "bbox": [
+            76,
+            349,
+            274,
+            364
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Replica. Replica [29] provides synthetic indoor environments for simulating the image-capturing process with a moving camera. We use the camera trajectories provided by [50] for the localization task, resulting in 16 camera trajectories derived from 8 static scenes. Each sequence comprises 900 frames with rendered RGB images. We use \"Sequence 1\" for the visual odometry evaluation.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "MPI Sintel. The MPI Sintel [4] dataset contains dynamic image sequences from open-source 3D animated short films. These sequences consist of large and complex object motion, along with other imaging effects such as motion blur and defocus blur. Following prior works [20, 48], we assess dynamic VO performance on the MPI Sintel dataset, with each sequence containing 20 to 50 image frames.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "TartanAir Shibuya. The TartanAir Shibuya dataset [26] features dynamic scenes from two scenarios: \"Standing Humans\" and \"Road Crossing\". The majority of the humans remain stationary in \"Standing Humans\" sequences, while \"Road Crossing\" sequences provide a more challenging setting where multiple humans are moving in different directions. Each sequence in the dataset includes 100 frames with more than 30 tracked moving humans.",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Metrics. For visual odometry, we compare the Absolute Translation Error (ATE), Relative Translation Error (RPE trans), and Relative Rotation Error (RPE rot) following [33, 47, 48]. ATE measures how much the estimated trajectory deviated from the ground truth trajectory, which is calculated as the root mean square error (RMSE) overall all pose transformations after scaling and alignment. \"RPE trans\" computes translation errors made over a certain distance (meter), and \"RPE rot\" computes the estimated rotation over a certain distance (degree). Both \"RPE trans\" and \"RPE rot\" are calculated on all poses and then averaged.",
+        "bbox": [
+            75,
+            737,
+            470,
+            905
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/9faf726c5e5fb61c91080f585bbf38c00eb5c872769d353a44f2b26fadf5eaf6.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"3\">Replica</td></tr><tr><td>ATE (m)</td><td>RPE trans (m)</td><td>RPE rot (deg)</td></tr><tr><td>ORB-SLAM2 [24]</td><td>0.086</td><td>0.030</td><td>0.650</td></tr><tr><td>DynaSLAM [1]</td><td>0.039</td><td>0.017</td><td>0.366</td></tr><tr><td>DROID-SLAM [32]</td><td>0.267</td><td>0.036</td><td>2.631</td></tr><tr><td>TartanVO [40]</td><td>0.406</td><td>0.036</td><td>2.063</td></tr><tr><td>DytanVO [28]</td><td>0.289</td><td>0.035</td><td>2.146</td></tr><tr><td>DPVO [33]</td><td>0.257</td><td>0.036</td><td>2.635</td></tr><tr><td>LEAP-VO (Ours)</td><td>0.204</td><td>0.030</td><td>1.992</td></tr></table>",
+        "bbox": [
+            504,
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+            224
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/0740f1e91760ce2e792e2709686305b58406ec0e90f256e01d9deb71f739d8d8.jpg",
+        "table_caption": [
+            "Table 1. Camera tracking results on Replica [29]. The statistics demonstrate that our method achieves better results than other competitive baselines."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"3\">MPI Sintel</td></tr><tr><td>ATE (m)</td><td>RPE trans (m)</td><td>RPE rot (deg)</td></tr><tr><td>ORB-SLAM2 [24]</td><td>X</td><td>X</td><td>X</td></tr><tr><td>DynaSLAM [1]</td><td>X</td><td>X</td><td>X</td></tr><tr><td>DROID-SLAM [32]</td><td>0.175</td><td>0.084</td><td>1.912</td></tr><tr><td>TartanVO [40]</td><td>0.238</td><td>0.093</td><td>1.305</td></tr><tr><td>DytanVO [28]</td><td>0.131</td><td>0.097</td><td>1.538</td></tr><tr><td>DPVO [33]</td><td>0.076</td><td>0.078</td><td>1.722</td></tr><tr><td>LEAP-VO (Ours)</td><td>0.037</td><td>0.055</td><td>1.263</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Table 2. Camera tracking results on MPI Sintel [4]. The statistics show that our method outperforms other competitive baselines. 'X' denotes the tracking failure case.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.2. Implementation details",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We employ CoTracker [18], a recent PIPs variant, as our base TAP model. We train our model on the TAP-Vid-Kubric [9] training set, following [18]. We load the pretrained CoTracker weights for the image feature extractor and train LEAP for 100,000 steps using 4 NVIDIA A100 GPUs in parallel. During training, we use  $K = 4$  steps for iterative refinements,  $N = 256$  for the number of queries,  $S = 8$  for the model window, and  $S_{LP} = 12$  for the tracking window. For inter-track anchor-based attention, the number of anchors is 64. The loss weights are set to  $w_{1} = 1.0, w_{2} = 0.5, w_{3} = 0.5$ . In LEAP-VO, we perform 4 steps for each bundle adjustment with the Huber Loss for distance metric. The bundle adjustment window size  $S_{BA}$  is set to 15. Track filtering parameters are set at  $\\gamma_v = 0.9, \\gamma_d = 0.9, \\gamma_u = 0.8, \\gamma_{track} = 3$ . Please refer to our supplementary materials for more details.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.3. Visual Odometry Results",
+        "text_level": 1,
+        "bbox": [
+            500,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We compare our methods against the state-of-the-art SLAM and VO approaches, including ORB-SLAM2 [24], DynaSLAM [1], DROID-SLAM [32], TartanVO [40], DytanVO [28], and DPVO [33]. Evaluations are conducted on the static Replica dataset [29] as well as on the dynamic datasets MPI-Sintel [4] and TartanAir-Shibuya [26].",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Replica. We compare our method with other baselines on the Replica dataset, which contains eight static scenes",
+        "bbox": [
+            498,
+            869,
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+            901
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "19849",
+        "bbox": [
+            480,
+            944,
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+            955
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/88ddaacfec9a855b6b763fd39bd052dacd1e76b1bf07559f5abfc40ca0b7d100.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"2\">StandingHuman</td><td colspan=\"3\">RoadCrossing (Easy)</td><td colspan=\"2\">RoadCrossing (Hard)</td><td rowspan=\"2\">Average</td></tr><tr><td>01</td><td>02</td><td>03</td><td>04</td><td>05</td><td>06</td><td>07</td></tr><tr><td>ORB-SLAM2 [24] w/ mask</td><td>0.0788</td><td>0.0060</td><td>0.0657</td><td>0.0196</td><td>0.0148</td><td>1.0984</td><td>0.8476</td><td>0.3044</td></tr><tr><td>DynaSLAM [1]</td><td>X</td><td>0.8836</td><td>0.3907</td><td>0.4196</td><td>0.4925</td><td>0.6446</td><td>0.6539</td><td>(0.5808)</td></tr><tr><td>AirDOS [26] w/ mask</td><td>0.0606</td><td>0.0193</td><td>0.0951</td><td>0.0331</td><td>0.0206</td><td>0.2230</td><td>0.5625</td><td>0.1449</td></tr><tr><td>DROID-SLAM [32]</td><td>0.0051</td><td>0.0073</td><td>0.0103</td><td>0.0120</td><td>0.2278</td><td>0.0253</td><td>0.5788</td><td>0.1238</td></tr><tr><td>TartanVO [40]</td><td>0.0600</td><td>0.1605</td><td>0.2762</td><td>0.1814</td><td>0.2174</td><td>0.3228</td><td>0.5009</td><td>0.2456</td></tr><tr><td>DytanVO [28]</td><td>0.0327</td><td>0.1017</td><td>0.0608</td><td>0.0516</td><td>0.0755</td><td>0.0365</td><td>0.0660</td><td>0.0607</td></tr><tr><td>DPVO [39]</td><td>0.0539</td><td>0.1603</td><td>0.1788</td><td>0.2858</td><td>0.1196</td><td>0.1119</td><td>0.1498</td><td>0.1514</td></tr><tr><td>LEAP-VO (Ours)</td><td>0.0081</td><td>0.0185</td><td>0.0399</td><td>0.0317</td><td>0.0113</td><td>0.0689</td><td>0.0246</td><td>0.0290</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Table 3. ATE (m) results on TartanAir-Shibuya Sequences [26]. ( $\\cdot$ ) denotes averaging on valid scenes only. We can observe that our method shows better results for ATE on most sequences, outperforming all SLAM and VO baselines on average ATE.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/0c9be0f3fcfc59cefc63ad77edac4adc0e039eefe5b343e437c31e099d237ab9.jpg",
+        "image_caption": [
+            "(a) RoadCrossing 04"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            84,
+            273,
+            279,
+            421
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/f5a4197b9fd43580001e00f745e1a2cbf7cc380b0001405e7443351579a9253f.jpg",
+        "image_caption": [
+            "(b) RoadCrossing 05"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            287,
+            272,
+            480,
+            421
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/422bd73a1d36da5ecdab37f323089a41085702b01500552c15b23bbc9e085202.jpg",
+        "image_caption": [
+            "(c) RoadCrossing 06",
+            "Figure 5. Qualitative results of camera trajectory estimation on TartanAir-Shibuya [26]. The visualizations show that our method provides more robust and accurate camera pose trajectories, especially in hard cases (RoadCrossing 06 and RoadCrossing 07)."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            491,
+            272,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/500f27a167516833358616cab081a003fdad56f68b6e256912b551c566d37440.jpg",
+        "image_caption": [
+            "(d) RoadCrossing 07"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            692,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "without any moving objects. Challenges arise in two test sequences that contain prolonged occlusions, leading to the potential camera tracking loss. As illustrated in Table 1, our approach outperforms other VO methods on all three metrics, showing effectiveness under static environments and the capability to handle occlusions. Further insights are available in Section 4.5. For classical methods, ORBSLAM2 [24] and DynaSLAM [1], we observe tracking loss and resuming via re-localization, which reduces long-term drift and shows high accuracy for camera pose tracking.",
+        "bbox": [
+            75,
+            477,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "MPI-Sintel. We also evaluate our VO camera trajectory accuracy on 14 dynamic scenes from the MPI Sintel dataset, following the setting of [48]. As shown in Table 2, our method substantially surpasses other VO baselines in dynamic scenes, thanks to our temporal uncertainty estimation and dynamic track detection. Traditional feature-based methods like ORB-SLAM2 [24] and DynaSLAM [1] sometimes fail to track camera movements in highly dynamic sequences, primarily due to outliers from dynamic object correspondences and segmentation-based only dynamic track estimation. In contrast, our approach, which considers visual, temporal, and inter-track information, demonstrates notable improvements in dynamic scene tracking accuracy.",
+        "bbox": [
+            75,
+            635,
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+            833
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "TartanAir-Shibuya. Following DytanVO [28], we further evaluate the VO performance using the dynamic TartanAir-Shibuya dataset. We assess the Average Trajectory Error (ATE) across seven diverse scenes, ranging from simple to",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "challenging. As depicted in Table 3, our method consistently outperforms all other SLAM and VO baselines in the majority of these scenes. Moreover, trajectory visualizations in Figure 5 also highlight the robust camera tracking capabilities of our method in dynamic environments.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.4. Dynamic Track Estimation Results",
+        "text_level": 1,
+        "bbox": [
+            498,
+            559,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "In our LEAP formulation, we have introduced the anchor-based dynamic track estimation module to distinguish between static and dynamic point trajectories, which provides valuable information for handling dynamic scenes in visual odometry. Our method leverages both point feature information and inter-track relations to predict the dynamic track label for each trajectory. To demonstrate the performance of the proposed dynamic track estimation module, we take the LEAP model and evaluate it on novel image sequences from diverse datasets. For a comprehensive demonstration, we uniformly sample  $16 \\times 16$  queries among the images and track them for  $T = 8$  frames. The results, shown in Figure 6, illustrate that LEAP can effectively handle various scenarios, including single-object motion, complex and rapid motion, and multi-object motion with occlusion.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.5. Ablation Study",
+        "text_level": 1,
+        "bbox": [
+            500,
+            816,
+            653,
+            832
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Track Filtering. To highlight the efficacy of our track filtering module in LEAP-VO, we conduct an ablation study on different masks used in track filtering. We study three types of filtering criteria: visibility, dynamic",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "19850",
+        "bbox": [
+            480,
+            944,
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+            955
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/781af32895b8c1318275094eab868761f2d0179d29830e8800be855692ef374b.jpg",
+        "image_caption": [
+            "Figure 6. Visualization of dynamic track estimation on DAVIS [19], MPI-Sintel [4], and TartanAir-Shibuya [26]. Odd columns: all point trajectories. Even columns: estimated dynamic point trajectories."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            83,
+            90,
+            462,
+            319
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/849ddeb126a9119bf85089fee5033115a331c32107fbd180edaeec2c0c8ce3b9.jpg",
+        "image_caption": [
+            "Figure 7. Visualization of point-wise uncertainty measurements. Keypoints with the lowest  $20\\%$  (left) and highest  $20\\%$  (right) uncertainty are shown in green and yellow, respectively."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            81,
+            383,
+            465,
+            525
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "track, and confidence filtering. Table 4 shows the impact of applying various filtering types on the dynamic MPI Sintel benchmark. Without dynamic filtering or confidence filtering, the ATE increases by  $46\\%$  and  $130\\%$ , respectively. Combining all three types of filtering methods altogether, we achieve the best results in all three metrics.",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/1ee9533292ee09daae5704bd49dc27defff0357868632af005d5f5d707109e22.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"3\">Track Filtering</td><td colspan=\"3\">MPI Sintel</td></tr><tr><td>Vis.</td><td>Dyn.</td><td>Conf.</td><td>ATE</td><td>RPE trans</td><td>RPE rot</td></tr><tr><td rowspan=\"4\">LEAP-VO</td><td>✓</td><td>-</td><td>-</td><td>0.118</td><td>0.078</td><td>1.340</td></tr><tr><td>✓</td><td>✓</td><td>-</td><td>0.085</td><td>0.062</td><td>1.281</td></tr><tr><td>✓</td><td>-</td><td>✓</td><td>0.054</td><td>0.058</td><td>1.274</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>0.037</td><td>0.055</td><td>1.263</td></tr></table>",
+        "bbox": [
+            84,
+            678,
+            460,
+            772
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Uncertainty Estimation. As illustrated in Figure 7, we demonstrate the LEAP's capability to provide meaningful per-point uncertainty. It models the uncertainty as distribution parameters for both the entire track and individual points. Two key observations can be found from Figure 7. Firstly, our model reliably identifies high-uncertainty",
+        "bbox": [
+            75,
+            809,
+            468,
+            902
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "points, typically located in low-texture areas or in regions with repetitive patterns. Secondly, although not explicitly supervised, the model tends to assign higher uncertainty to dynamic objects, which are inherently more challenging to track. These findings highlight the efficacy of LEAP's probabilistic formulation in handling uncertainty.",
+        "bbox": [
+            496,
+            90,
+            890,
+            181
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Keypoint Extraction. Table 5 showcases the effectiveness of various keypoint extraction strategies for VO performance. Despite its distinctive features, SIFT extraction provides inferior performance due to its unpredictable keypoint distribution. In contrast, the random sampling tends to generate well-separated keypoints, leading to a performance similar to SIFT's. Our distributed image gradient-based sampling shows the best performance, underscoring the significance of feature distribution and distinctiveness.",
+        "bbox": [
+            496,
+            191,
+            890,
+            325
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/97c60765d761296eda93eb56bac7175dba27f1dda620d9805ab0652b917566aa.jpg",
+        "table_caption": [
+            "Table 4. Effect of the proposed track filtering method on MPI-Sintel [4]. Tracking using all criteria yields the best results."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Policy:</td><td>Uniform</td><td>Random</td><td>SIFT [22]</td><td>Ours</td></tr><tr><td>ATE (m):</td><td>0.1511</td><td>0.0366</td><td>0.0355</td><td>0.0290</td></tr></table>",
+        "bbox": [
+            547,
+            327,
+            844,
+            367
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Baseline comparison. We evaluate the pretrained CoTracker [18] for the end VO performance. Table 6 shows that LEAP front-end outperforms CoTracker on all datasets, demonstrating the effectiveness of the proposed dynamic track estimation and temporal probability modeling.",
+        "bbox": [
+            496,
+            414,
+            890,
+            491
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/8efc96d69cf79bff7d4790d40d3929500fccf9ebdc1a343f9fdf266338968788.jpg",
+        "table_caption": [
+            "Table 5. Comparison of keypoint extraction policies ( $N_{a} = 64$ ) on TartanAir-Shibuya [26]. Our distributed image-gradient sampling method achieves better results compared to other policies."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Front-end</td><td colspan=\"3\">Replica</td><td colspan=\"3\">MPI Sintel</td><td>Shibuya</td></tr><tr><td>ATE</td><td>RPE trans</td><td>RPE rot</td><td>ATE</td><td>RPE trans</td><td>RPE rot</td><td>ATE</td></tr><tr><td>CoTracker</td><td>0.301</td><td>0.031</td><td>2.043</td><td>0.126</td><td>0.071</td><td>1.366</td><td>0.160</td></tr><tr><td>LEAP</td><td>0.204</td><td>0.030</td><td>1.992</td><td>0.037</td><td>0.055</td><td>1.263</td><td>0.029</td></tr></table>",
+        "bbox": [
+            506,
+            496,
+            880,
+            566
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Table 6. Baseline comparison with CoTracker front-end [18]. Our LEAP front-end achieves better results on all datasets.",
+        "bbox": [
+            500,
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+            593
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5. Conclusion",
+        "text_level": 1,
+        "bbox": [
+            500,
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+            618
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "We introduce Long-term Effective Any Point Tracking (LEAP), designed to tackle the limitations of previous point-tracking methods. By leveraging visual, inter-track, and temporal cues within an anchor-based dynamic track estimation module, LEAP captures global motion patterns and effectively discriminates between static and dynamic elements. Moreover, our approach incorporates a temporal probabilistic formulation into the point-tracking pipeline, emulating recursive Bayesian filtering through a learning-based refinement module. This enables our model to accurately assess the reliability of point trajectory estimates. Using LEAP as the front-end, we then develop the LEAP-VO system, featuring novel integration of visual information, global motion patterns, and track distribution for handling dynamic scenes. Additionally, our takes for LEAP-VO can be integrated with other TAP-based front-ends, offering the potential to markedly improve camera-tracking accuracy and robustness.",
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2024/LEAP-VO_ Long-term Effective Any Point Tracking for Visual Odometry/03c2e012-3152-4602-8d61-0831334e6fb6_origin.pdf

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2024/LEAP-VO_ Long-term Effective Any Point Tracking for Visual Odometry/full.md

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+# LEAP-VO: Long-term Effective Any Point Tracking for Visual Odometry
+
+Weirong Chen $^{1,2*}$  Le Chen $^{3}$  Rui Wang $^{4}$  Marc Pollefeys $^{4}$
+
+$^{1}$ TU Munich  $^{2}$ Munich Center for Machine Learning  $^{3}$ MPI for Intelligent Systems  $^{4}$ Microsoft
+
+# Abstract
+
+Visual odometry estimates the motion of a moving camera based on visual input. Existing methods, mostly focusing on two-view point tracking, often ignore the rich temporal context in the image sequence, thereby overlooking the global motion patterns and providing no assessment of the full trajectory reliability. These shortcomings hinder performance in scenarios with occlusion, dynamic objects, and low-texture areas. To address these challenges, we present the Long-term Effective Any Point Tracking (LEAP) module. LEAP innovatively combines visual, inter-track, and temporal cues with mindfully selected anchors for dynamic track estimation. Moreover, LEAP's temporal probabilistic formulation integrates distribution updates into a learnable iterative refinement module to reason about point-wise uncertainty. Based on these traits, we develop LEAP-VO, a robust visual odometry system adept at handling occlusions and dynamic scenes. Our mindful integration showcases a novel practice by employing long-term point tracking as the front-end. Extensive experiments demonstrate that the proposed pipeline significantly outperforms existing baselines across various visual odometry benchmarks.
+
+# 1. Introduction
+
+Visual odometry (VO) calculates the camera's position and movement from an image sequence. It is widely used in various fields including robotics [46], mixed reality [23], and autonomous driving [15]. The performance of VO highly depends on the accuracy of its point tracking front-end, which recovers relative camera motion between consecutive frames using projective geometry. It further requires the point correspondences to be static, as dynamic points can lead to inaccurate motion estimation and pose recovery.
+
+Despite significant advances in feature tracking and optical flow estimation, most existing VO methods mainly focus on the two-view case, i.e., computing feature correspondences between a pair of images. However, these methods
+
+![](images/7a76ff2249955c9c8077c455b55618895587c7dd0639e49aad6be7800470b4de.jpg)
+
+![](images/070ad67c83554f8e25cf7cd79e091da3bce520463dff2693730f48a768a657d4.jpg)
+
+![](images/faed9191be70cfa06e13b268052bd065dc87863b05880998ec81b4c6d869c1b0.jpg)  
+Visual Odometry  
+Figure 1. Comparison between two-view approach and multi-view approach for visual odometry. (a) In the two-view approach, correspondences are derived for every image pair and concatenated. Managing occlusion becomes challenging without the temporal context. (b) In the multi-view approach, long-term point trajectories can be obtained all at once, enabling the detection of occlusion and tracking points under partial occlusions.
+
+are limited as they rely solely on pairwise relative motion, thus neglecting the valuable temporal information in image sequences. Consequently, they often struggle with capturing dynamic motion patterns in tracks. Another challenge arises from the need to handle occlusions. In two-view scenarios, occlusion is not explicitly modeled, leading to misidentification of occluded points as incorrect matches. To address these challenges effectively, we propose to introduce a long-term point tracker, which can recover the trajectories of specific points across the image sequence given a sparse set of these query points. Its capability of leveraging temporal context and reliably tracking queries over multiple frames even under occlusion, makes it highly suitable for VO applications (refer to Figure 1).
+
+Recently, Persistent Independent Particles (PIPs) [16] proposes a novel pipeline that brings the idea of iterative refinement into the long-term point tracking task, with the local correlation evidence to maintain feasible computation. While it is proficient in leveraging the temporal context present in the image sequence, it ignores the inter-track information in the image sequence and processes each query point independently. Consequently, PIPs struggles to cap
+
+ture the global motion patterns from the image sequence. Additionally, it lacks a reliability metric for its trajectory estimates, hindering its application in quality-sensitive tasks like video segmentation and visual odometry. To mitigate the aforementioned issues, we propose a pipeline that explores dynamic track estimation and temporal probabilistic formulation for long-term point tracking.
+
+In this paper, we present Long-term Effective Point Tracking (LEAP), aiming to estimate the reliability of predicted correspondences and track moving object trajectories in dynamic scenes. To achieve this, we harness the global motion patterns—often overlooked in existing methods—through an anchor-based dynamic track estimation module, leveraging visual, temporal, and inter-track information to differentiate between the static and dynamic elements. We also incorporate a temporal probabilistic approach into our LEAP pipeline to handle uncertainties and refine the distribution of point correspondences iteratively, showcasing superior performance in complex real-world situations. More importantly, we pioneer the usage of continuous motion estimation from long-term point tracking to construct a robust visual odometry system. Our LEAP-VO distinguishes itself through its thoughtful integration of visual features, track distribution, and global motion patterns, significantly enhancing both the performance and robustness of visual odometry in dynamic environments.
+
+# 2. Related Work
+
+Long-term Point Tracking. In the realm of long-term point tracking or Tracking Any Point (TAP), various methods have been introduced recently. PIPs [16] reframes pixel tracking as a long-term motion estimation with local information and improves tracking accuracy by associating each pixel with a trajectory that spans multiple image frames. The subsequent works enhance performance by integrating spatial context features [2], tracking multiple queries concurrently [18], and extending temporal fields and templates [49]. TAP-Net [9] adopts a different method by locating candidate correspondences through a global cost volume, improved by TAPIR's trajectory refinement [10] and BootsTAP's semi-supervised training [11]. Other approaches explore self-supervision targets to learn visual correspondence via powerful feature representation [5, 17, 36]. Recently, OmniMotion [37] provides a pure test-time optimization method that infers the point trajectory and occlusion directly from videos with optical flow predictions. However, its slow inference speed makes it unsuitable for real-time applications such as visual odometry.
+
+Monocular Visual Odometry. Visual Odometry (VO) can be categorized into indirect (feature-based) and direct methods. Indirect methods, such as MonoSLAM [8] and ORB-SLAM [25], mostly rely on feature extraction and
+
+matching to estimate the camera pose. Direct methods, conversely, skip feature extraction and matching and utilize intensity to optimize camera pose and 3D scene point positions based on photometric errors [12, 13, 38], showing better performance on low-texture regions where keypoint tracking can easily fail. However, they are more vulnerable to illumination changes and issues with rolling shutter cameras. Advancements in deep learning have spawned end-to-end monocular VO methods in supervised [3, 28, 30, 33, 39, 40, 43, 44] and unsupervised [21, 27, 45, 51] settings. DeepVO [39] utilizes Recurrent Neural Networks to model sequential data, while SfMLearner [51] develops an unsupervised framework to learn the depth and camera motion from unlabeled monocular videos. TartanVO [40] proposes a VO model that generalizes to multiple datasets and real-world scenarios. DROID-SLAM [32] follows learning-based optimization from RAFT [31] and proposes an end-to-end system, integrating flow, confidence, and geometric optimization via iterative GRU updates. The followed-up work DPVO [33] further cuts computational complexity by replacing dense feature tracking with sparse patch tracking.
+
+Dynamic Track Estimation. In addition to enhancing accuracy, numerous studies have focused on the detection of dynamic objects within videos. Methods based on segmentation, such as DynaSLAM [1] and RCVD [20], employ semantic cues from pre-trained models to exclude dynamic regions. However, these segmentation-based methods are constrained to predefined object categories and struggle to capture real-world motion (for example, differentiating between a stationary and a moving car). Alternatively, DyanVO [28] and ParticleSfM [48] adopt a trajectory-based motion detection approach. This method addresses dynamic scenes using estimated point track information, thereby generating reliable camera trajectories in complex motion scenarios. Nonetheless, they depend on dense optical flow estimation to capture global motion patterns. Furthermore, dynamic tracks can be detected using additional depth information for a 3D consistency check [7, 47], or by optimization based on photo consistency [35, 41, 42].
+
+# 3. Method
+
+Our goal is to tackle the aforementioned challenges in VO systems, particularly in handling dynamic environments, temporal occlusions, and low-texture regions. To this end, we introduce our LEAP module, which incorporates dynamic track estimation and temporal probabilistic formulation. Furthermore, we illustrate how this module serves as the cornerstone for constructing our advanced VO system.
+
+# 3.1. Preliminary: Tracking Any Point
+
+Tracking arbitrary pixels in an image sequence is traditionally akin to estimating optical flow, where each pixel
+
+is mapped to a corresponding location in a subsequent frame. However, two-view approaches often overlook the rich temporal context within the image sequence, leading to suboptimal outcomes. Recent advancements address this by revisiting the particle video concept and improving long-term point tracking through learning-based techniques [10, 16, 18]. These TAP methods can track points over multiple frames and detect occlusions, significantly boosting tracking robustness under challenging scenarios.
+
+**Formulation.** Given a sequence of  $S$  consecutive RGB images  $\mathbf{I} = [\mathbf{I}_1, \dots, \mathbf{I}_S]$ ,  $\mathbf{I}_s \in \mathbb{R}^{3 \times H \times W}$  as input, the goal of TAP is to track a set of query points across these frames. For a specific query point with the 2D pixel coordinate  $\mathbf{x}_q \in \mathbb{R}^2$  in frame  $s_q$ , TAP predicts its trajectory across all  $S$  images as  $\mathbf{X} = [\mathbf{x}_1, \dots, \mathbf{x}_S]$ ,  $\mathbf{x}_s \in \mathbb{R}^2$ , given  $\mathbf{x}_{s_q} = \mathbf{x}_q$ . Additionally, TAP estimates the visibility of each point throughout the sequence as  $\mathbf{V} = [v_1, \dots, v_S]$ , where  $v_s \in \{0, 1\}$  is a binary label of point visibility indicating whether a point in frame  $s$  is visible or occluded. The TAP formulation for a single query can be described as
+
+$$
+\left(\mathbf {X}, \mathbf {V}\right) = \operatorname {T A P} \left(\mathbf {I}, \mathbf {x} _ {q}, s _ {q}\right). \tag {1}
+$$
+
+PIPs [16], a notable learning-based TAP method, offers a promising solution featuring local cost volumes and iterative refinement. Initially, each image  $\mathbf{I}_s\in \mathbf{I}$  is processed through a CNN feature extractor  $\mathcal{F}$  to extract the feature map  $\mathbf{Y}_{\mathbf{s}} = \mathcal{F}(\mathbf{I}_{s})$ . Point features  $\mathbf{f}_q$  are computed by bilinear sampling at the query positions  $\mathbf{x_s}$  on  $\mathbf{Y}_s$ . These point features from each image are then concatenated to form a point feature tensor  $\mathbf{F} = [\mathbf{f}_1,\dots ,\mathbf{f}_S]$ . PIPs approaches the TAP problem by iteratively updating the state variables  $(\mathbf{X},\mathbf{F})$ , with the initial states obtained by duplicating the query positions and features. During the  $k$ -th iterative refinement, PIPs computes a multi-scale local cost volume  $\mathbf{C}[\mathbf{X}^k ]$  centered around the current estimated point position  $\mathbf{X}^k$ . Utilizing this local evidence, PIPs predicts updates for the state variables via
+
+$$
+\begin{array}{r} \left(\Delta \mathbf {X}, \Delta \mathbf {F}\right) = \operatorname {R e f i n e r} \left(\mathbf {F} ^ {k}, \operatorname {p o s} \left(\mathbf {X} ^ {k} - \mathbf {x} _ {\mathbf {q}}\right), \mathbf {C} ^ {k} \left[ \mathbf {X} ^ {k} \right]\right), \\ \mathbf {X} ^ {k + 1} \leftarrow \mathbf {X} ^ {k} + \Delta \mathbf {X}, \quad \mathbf {F} ^ {k + 1} \leftarrow \mathbf {F} ^ {k} + \Delta \mathbf {F}, \end{array} \tag {2}
+$$
+
+where  $\mathrm{pos}(\cdot)$  refers to the positional embedding. The final point feature  $\mathbf{F}^K$  is used to predict point visibility with a simple linear projection layer  $\mathcal{G}_v$ , yielding  $\mathbf{V} = \mathcal{G}_v(\mathbf{F}^K)$ . Recent advances extend PIPs by replacing the MLP-based refiner with an attention-based refiner and adding spatial feature aggregation to track multiple queries together [18].
+
+# 3.2. Anchor-based Dynamic Track Estimation
+
+The established TAP model enables us to extract long-term point trajectories and thereby recover camera motion from an image sequence. However, dynamic environments
+
+![](images/f9a4b8f0c4199ea8b8569721db074c6591697e11ec43d5bbfbe71c1e30542119.jpg)  
+Figure 2. Distributed image gradient-based sampling with  $k = 8$ ,  $N_{a} = 64$ . After computing the image gradient and pooling, we split the gradient map into  $8 \times 8$  grids and select the point with the maximum gradient in each grid.
+
+pose extra challenges for VO systems that rely on static 3D point correspondences linked to unchanging scene locations. Therefore, integrating dynamic track estimation into the VO system is crucial for real-world applications.
+
+We propose an innovative method for dynamic track estimation that leverages visual, temporal, and inter-track information. While common techniques like monocular segmentation [20] excel at identifying moving objects using visual cues but can erroneously label static objects, like parked cars, as dynamic. Trajectory-based methods [48], utilizing optical flows from two or multiple frames, can differentiate static and moving objects apart but tend to ignore visual information and can be inefficient due to dense trajectories computation. Merging these two distinct methods is nontrivial; however, the formulation of the TAP pipeline, enhanced with inter-track attention, offers a viable solution.
+
+Our method smartly integrates visual appearance, long-term motion, and inter-track cues, combining the strengths of segmentation and trajectory-based techniques. Utilizing TAP, we extract point features  $\mathbf{F}$  and long-term trajectories  $\mathbf{X}$  from the video input. These features capture visual information and the iterative refinement module exchanges information across tracks over time for accurate labeling. However, such a method depends on the query distribution and quantities. With only one query during inference time, it cannot utilize inter-track information. Likewise, if the queries focus on a single object, the system may overlook the motions of other objects due to similar motion patterns.
+
+Anchor-based Inter-track Attention. To better capture global motion patterns, we introduce additional anchors alongside the given queries, denoted as  $\mathcal{A}$ ,  $|\mathcal{A}| = N_{a}$ . Ideally, the anchor set should exhibit two characteristics: (1) the anchors should be easy to track, and (2) they should be well-distributed to encapsulate global motion patterns. Given the image  $\mathbf{I}_{s_q}$  from which the queries  $\mathbf{x}_q$  are extracted (we maintain the same notations for both single and multiple queries for simplicity), we first employ the Sobel Kernel to derive the image gradient  $(\mathbf{G}_x,\mathbf{G}_y)$  for image  $\mathbf{I}_{s_q}$ . We then apply an average pooling layer on gradient maps for smoothing and downscaling feature maps. Subsequently, we divide the gradient map into  $k\times k$  sub-regions and select top  $\frac{N_a}{k^2}$  pixels with the highest image gradient magnitude in
+
+each local grid. The process is demonstrated in Figure 2.
+
+To predict the dynamic label of a trajectory, we track queries with additional anchors and concatenate the original query features  $\mathbf{X}$  and query trajectories  $\mathbf{F}$  with anchor features  $\mathbf{X}_A$  and anchor trajectories  $\mathbf{F}_A$ . We apply a shallow MLP layer  $\mathcal{G}_d$  with average pooling over the temporal dimension. The dynamic track label  $\mathbf{m}_d$  is estimated as
+
+$$
+\mathbf {m} _ {d} = \operatorname {a v g p o o l} \left(\mathcal {G} _ {d} \left(\left[ \mathbf {X} ^ {K}; \mathbf {X} _ {A} ^ {K} \right], \left[ \mathbf {F} ^ {K}; \mathbf {F} _ {A} ^ {K} \right]\right)\right). \tag {3}
+$$
+
+Since newly added anchors often lack ground truth information, we employ a semi-supervised training scheme that tracks queries and anchors together to leverage inter-track attention but only calculates losses based on query predictions. This approach prevents the network from developing bias towards specific query sampling methods while learning dynamic track labels effectively.
+
+# 3.3. Temporal Probability Modeling
+
+Supervised learning applied to large-scale datasets has yielded notable advancements in learning-based point tracking methods. Nonetheless, trajectory estimation errors remain a concern, especially under challenging conditions like occlusions, motion blur, or textureless regions. Recognizing the varying reliability of trajectories, integrating an uncertainty estimation mechanism into the correspondence estimation process is beneficial [6]. This is particularly crucial for quality-sensitive tasks such as visual odometry.
+
+To evaluate the reliability of point correspondences, we incorporate a probabilistic formulation into the TAP pipeline. Given an image sequence  $\mathbf{I}$  and a single query point  $\mathbf{x}_q$ , our objective is to compute the conditional probability density of point trajectory as  $p(\mathbf{X}|\mathbf{I},\mathbf{x}_q)$ . Recognizing the strong correlation between points within the same track, treating each point in the track as independent becomes suboptimal. Therefore, we propose to model the distribution of point trajectories by applying two multivariate distributions, respectively for the 2D coordinates. Let  $\mathbf{X} = [\mathbf{a};\mathbf{b}]$ , where  $\mathbf{a}\in \mathbb{R}^S$  and  $\mathbf{b}\in \mathbb{R}^{S}$  represent the  $\mathbf{X}$  and  $\mathbf{Y}$  coordinate of all points in  $\mathbf{X}$ , respectively. Assuming independence between these two coordinates, the joint probability distribution can be expressed as  $p(\mathbf{X}|\mathbf{I},\mathbf{x}_q) = p(\mathbf{a}|\mathbf{I},\mathbf{x}_q)\cdot p(\mathbf{b}|\mathbf{I},\mathbf{x}_q)$ . We adopt the multivariate Cauchy distribution, which is associated with its heavy tails distribution and is more stable for optimization. The probability density function (PDF) of a single coordinate is given by
+
+$$
+p (\mathbf {a} | \mathbf {I}, \mathbf {x} _ {q}) = \frac {\Gamma \left(\frac {1 + S}{2}\right)}{\Gamma \left(\frac {1}{2}\right) \pi^ {\frac {S}{2}} \left| \boldsymbol {\Sigma} _ {a} \right| ^ {\frac {1}{2}} \left[ 1 + \left(\mathbf {a} - \boldsymbol {\mu} _ {a}\right) ^ {T} \boldsymbol {\Sigma} _ {a} ^ {- 1} \left(\mathbf {a} - \boldsymbol {\mu} _ {a}\right) \right] ^ {\frac {1 + S}{2}}} \tag {4}
+$$
+
+and a similar expression is applicable for  $p(\mathbf{b}|\mathbf{I},\mathbf{x}_q)$ .  $\Gamma$  is the Gamma function. The parameters  $(\boldsymbol{\mu}_a,\boldsymbol{\Sigma}_a,\boldsymbol{\mu}_b,\boldsymbol{\Sigma}_b)$  represent the location and scale matrices for the respective coordinates. During inference, the uncertainty associated
+
+![](images/a70127acf14c96950f4d02f1fdf61d4ad2cb1f4fc795d5e9f3b2983140ece6d1.jpg)  
+Figure 3. LEAP Front-end. Once image feature maps are obtained, selected anchors aid in tracking. The queries and anchors are processed by a refiner to iteratively update states. The model outputs trajectory distribution, visibility, and dynamic track label.
+
+with each point is quantified by the sum of diagonal scale estimates at position  $(s,s)$  as  $\phi (\mathbf{x}_s) = \pmb {\Sigma}_a[s,s] + \pmb {\Sigma}_b[s,s]$
+
+Kernel-based Estimation. Rather than just predicting the positions of points within a trajectory, our model focuses on recovering the distribution of point trajectories by estimating its parameters. The location parameter predictions can be associated with the previous point trajectory as  $[\pmb{\mu}_a; \pmb{\mu}_b] = \mathbf{X}$ . However, directly deriving a symmetric and positive definite scale matrix from model outputs is challenging. To address this, we employ a kernel-based approach with the linear kernel  $K(\mathbf{x}, \mathbf{y}) = \mathbf{x}^T \mathbf{y}$ . During each iteration, two scale matrices  $(\pmb{\Sigma}_a, \pmb{\Sigma}_b)$  are constructed by first applying two linear projection layers to the point features, represented as  $\mathbf{F}_a^k = \mathcal{G}_a(\mathbf{F}^k)$  and  $\mathbf{F}_b^k = \mathcal{G}_b(\mathbf{F}^k)$ . We then compute the scale matrices as  $\pmb{\Sigma}_a = K(\mathbf{F}_a, \mathbf{F}_a) + \sigma \mathbf{I}$ , and  $\pmb{\Sigma}_b = K(\mathbf{F}_b, \mathbf{F}_b) + \sigma \mathbf{I}$ , where  $\sigma$  is a small positive value and  $\mathbf{I}$  is the identity matrix. The model parameters are refined through Maximum Likelihood Estimation (MLE) using a negative log-likelihood (NLL) loss function.
+
+Loss Functions. We supervise the point trajectory mainly with the NLL loss, which is based on the predicted distribution parameters and the ground-truth point trajectory. The main point trajectory loss is given as
+
+$$
+\mathcal {L} _ {\text {m a i n}} = \sum_ {k} ^ {K} \gamma^ {K - k} \mathcal {L} _ {N L L} \left(\mathbf {X} ^ {k}, \mathbf {X} ^ {*}, \boldsymbol {\Sigma} _ {a} ^ {k}, \boldsymbol {\Sigma} _ {b} ^ {k}\right), \tag {5}
+$$
+
+where  $K$  is the number of iteration and  $\gamma = 0.8$ .
+
+For the visibility and dynamic track label supervision, we use the cross entropy loss with the estimates  $\mathbf{V},\mathbf{m}_d$  and ground truth  $\mathbf{V}^{*},\mathbf{m}_{d}^{*}$  as
+
+$$
+\mathcal {L} _ {\text {v i s}} = \left(1 - \mathbf {V} ^ {*}\right) \log \left(1 - \mathbf {V}\right) + \mathbf {V} ^ {*} \log \mathbf {V}. \tag {6}
+$$
+
+$$
+\mathcal {L} _ {d y n} = \left(1 - \mathbf {m} _ {d} ^ {*}\right) \log \left(1 - \mathbf {m} _ {d}\right) + \mathbf {m} _ {d} ^ {*} \log \mathbf {m} _ {d}. \tag {7}
+$$
+
+The total loss is a weighted sum of three losses:
+
+$$
+\mathcal {L} _ {\text {t o t a l}} = w _ {1} \mathcal {L} _ {\text {m a i n}} + w _ {2} \mathcal {L} _ {\text {v i s}} + w _ {3} \mathcal {L} _ {\text {d y n}}. \tag {8}
+$$
+
+![](images/005c323b67834729f12b46342f226d06e34bd05848cbaea2bb4db7b3f676de27.jpg)  
+Figure 4. LEAP-VO pipeline. Given a new image  $\mathbf{I}_t$  received at time  $t$ , the keypoint extractor extracts new keypoints from  $\mathbf{I}_t$ . Then, all the keypoints from the latest  $S_{LP}$ -frame  $\mathbf{I}_{t - S_{LP} + 1:t}$  are tracked across all other frames within the current LEAP window, followed by a track filtering step to remove outliers. Finally, the local BA module is used on the current BA window to update the camera poses and 3D positions of the extracted keypoints. The colored arrows denote the moving direction of each module when a new image is received.
+
+![](images/bffe5d79cb06a7a1728eda2276e66086b413c42983dcc93b2df1db81da7e0b08.jpg)
+
+# 3.4. LEAP-VO
+
+Leveraging the anchor-based dynamic track estimations and temporal probabilistic formulation, we develop our Long-term Effective Point Tracking (LEAP) pipeline, boosting the accuracy of point tracking and simultaneously capturing global motion patterns and uncertainties of the tracks (refer to Figure 3). In this section, we demonstrate how we can build visual odometry for dynamic scenes based on the long-term tracking capabilities of LEAP. Our LEAP-VO pipeline is illustrated in Figure 4.
+
+Keypoint Extraction and Tracking. In our VO system, the LEAP model serves as the front-end. When a new image frame  $\mathbf{I}_t$  is captured at time  $t$ , we sample  $N$  new keypoints from this image to initiate point tracking. We consistently employ the distributed image gradient-based sampling method (refer to Section 3.2) for keypoint selection due to its favorable properties in feature distinctiveness and distribution. This approach also obviates the need for additional anchors during tracking. The LEAP model then tracks these keypoints across the last  $S_{LP}$  frames, performing bidirectional tracking (both forward and backward in time). Notably,  $S_{LP}$  can exceed the model window  $S$ , thus enabling more expansive tracking capabilities through sequential prediction [16, 18].
+
+Track Filtering. Theoretically, precise camera pose estimation between two images can be attained with just a few accurate correspondences under certain conditions. However, the quality of correspondences obtained from feature matching or optical flow can vary. Traditional VO pipelines often use RANSAC [14] to filter out incorrect matches, but their efficiency decreases with more keypoints and views. Our approach, in contrast, bypasses the sampling-based method and uses trajectory quality assessments from LEAP
+
+for more efficient and informative track filtering.
+
+(i) Visibility and Dynamic Track Label: The LEAP model has the capability to estimate not only the 2D point positions within a trajectory but also the visibility of each point and the dynamic track label of the entire trajectory. Thresholds  $\gamma_v$  for visibility and  $\gamma_d$  for dynamic track labels are set to ensure that only visible and static points are utilized in the bundle adjustment process.  
+(ii) Track Uncertainty: In Section 3.3, we introduce probabilistic modeling to LEAP, allowing us to gauge confidence via distribution measurements. We select only high-confidence points, which correspond to low uncertainty measurements. Denoting our model's uncertainty estimation as  $\Phi$ , we retain points that exhibit high confidence using the criterion  $\Phi \leq Q(\gamma_u)$ , where  $\gamma_u$  is the uncertainty quantile and  $Q:[0,1] \to \mathbb{R}$  is the quantile function.  
+(iii) Track Length: After filtering, we evaluate and remove tracks with insufficient observations, as bundle adjustment is more reliable with increased observations and wider baselines. Tracks with fewer than  $\gamma_{\text{track}}$  valid points are excluded from optimization cost computation due to their potential unreliability.
+
+Sliding-window Optimization. With the point validation mask established, we proceed to define the optimization cost function for our sliding window bundle adjustment. The window size for local bundle adjustment, denoted as  $S_{BA}$ , may differ from the point tracking window size  $S_{LP}$ . Our geometric bundle adjustment aims to optimize camera poses  $\mathbf{T}$  and 3D scene point positions  $\mathbf{Q}$  by aligning the induced point trajectory from the projective relationship, with the estimated point trajectory from LEAP. We parameterize a 3D scene point  $\mathbf{Q}_i$  by its 2D keypoint location  $\mathbf{x}_i$  in image  $\mathbf{I}_i$  and depth  $d_i$ . Let  $\mathrm{LEAP}_{i\rightarrow j}$  denote the mapping of tracking keypoint from  $\mathbf{I}_i$  to  $\mathbf{I}_j$  using LEAP model. The
+
+reprojection cost is formulated as:
+
+$$
+\begin{array}{l} \sum_ {i} \sum_ {j \in | i - j | \leq S _ {B A}} \sum_ {n} w _ {i \rightarrow j, n} \| \mathcal {P} (\mathbf {T} _ {i}, \mathbf {T} _ {j}, \mathbf {K}, d _ {i, n}) - \\ \operatorname {L E A P} _ {i \rightarrow j} (\mathbf {x} _ {i, n}) \| _ {\rho}, \tag {9} \\ \end{array}
+$$
+
+where  $\| \cdot \|_{\rho}$  is the distance metric, and the weight  $w_{i\rightarrow j,n}$  is derived from the track filtering results. We use the GaussNewton method [34] to optimize Eq. (9) for  $K_{BA}$  iterations. At each iteration, we compute the camera poses update  $\Delta \xi^{(k)}\in \mathfrak{se}(3)$  (lie-algebra corresponding to  $\mathbf{T}$ ), and the depth update  $\Delta \mathbf{D}^{(k)}$  for each point. The optimization can be solved efficiently with the Schur decomposition. We use the robust Huber loss function for the distance metric.
+
+# 4. Experiment
+
+# 4.1. Datasets and Metrics
+
+Replica. Replica [29] provides synthetic indoor environments for simulating the image-capturing process with a moving camera. We use the camera trajectories provided by [50] for the localization task, resulting in 16 camera trajectories derived from 8 static scenes. Each sequence comprises 900 frames with rendered RGB images. We use "Sequence 1" for the visual odometry evaluation.
+
+MPI Sintel. The MPI Sintel [4] dataset contains dynamic image sequences from open-source 3D animated short films. These sequences consist of large and complex object motion, along with other imaging effects such as motion blur and defocus blur. Following prior works [20, 48], we assess dynamic VO performance on the MPI Sintel dataset, with each sequence containing 20 to 50 image frames.
+
+TartanAir Shibuya. The TartanAir Shibuya dataset [26] features dynamic scenes from two scenarios: "Standing Humans" and "Road Crossing". The majority of the humans remain stationary in "Standing Humans" sequences, while "Road Crossing" sequences provide a more challenging setting where multiple humans are moving in different directions. Each sequence in the dataset includes 100 frames with more than 30 tracked moving humans.
+
+Metrics. For visual odometry, we compare the Absolute Translation Error (ATE), Relative Translation Error (RPE trans), and Relative Rotation Error (RPE rot) following [33, 47, 48]. ATE measures how much the estimated trajectory deviated from the ground truth trajectory, which is calculated as the root mean square error (RMSE) overall all pose transformations after scaling and alignment. "RPE trans" computes translation errors made over a certain distance (meter), and "RPE rot" computes the estimated rotation over a certain distance (degree). Both "RPE trans" and "RPE rot" are calculated on all poses and then averaged.
+
+<table><tr><td rowspan="2">Method</td><td colspan="3">Replica</td></tr><tr><td>ATE (m)</td><td>RPE trans (m)</td><td>RPE rot (deg)</td></tr><tr><td>ORB-SLAM2 [24]</td><td>0.086</td><td>0.030</td><td>0.650</td></tr><tr><td>DynaSLAM [1]</td><td>0.039</td><td>0.017</td><td>0.366</td></tr><tr><td>DROID-SLAM [32]</td><td>0.267</td><td>0.036</td><td>2.631</td></tr><tr><td>TartanVO [40]</td><td>0.406</td><td>0.036</td><td>2.063</td></tr><tr><td>DytanVO [28]</td><td>0.289</td><td>0.035</td><td>2.146</td></tr><tr><td>DPVO [33]</td><td>0.257</td><td>0.036</td><td>2.635</td></tr><tr><td>LEAP-VO (Ours)</td><td>0.204</td><td>0.030</td><td>1.992</td></tr></table>
+
+Table 1. Camera tracking results on Replica [29]. The statistics demonstrate that our method achieves better results than other competitive baselines.  
+
+<table><tr><td rowspan="2">Method</td><td colspan="3">MPI Sintel</td></tr><tr><td>ATE (m)</td><td>RPE trans (m)</td><td>RPE rot (deg)</td></tr><tr><td>ORB-SLAM2 [24]</td><td>X</td><td>X</td><td>X</td></tr><tr><td>DynaSLAM [1]</td><td>X</td><td>X</td><td>X</td></tr><tr><td>DROID-SLAM [32]</td><td>0.175</td><td>0.084</td><td>1.912</td></tr><tr><td>TartanVO [40]</td><td>0.238</td><td>0.093</td><td>1.305</td></tr><tr><td>DytanVO [28]</td><td>0.131</td><td>0.097</td><td>1.538</td></tr><tr><td>DPVO [33]</td><td>0.076</td><td>0.078</td><td>1.722</td></tr><tr><td>LEAP-VO (Ours)</td><td>0.037</td><td>0.055</td><td>1.263</td></tr></table>
+
+Table 2. Camera tracking results on MPI Sintel [4]. The statistics show that our method outperforms other competitive baselines. 'X' denotes the tracking failure case.
+
+# 4.2. Implementation details
+
+We employ CoTracker [18], a recent PIPs variant, as our base TAP model. We train our model on the TAP-Vid-Kubric [9] training set, following [18]. We load the pretrained CoTracker weights for the image feature extractor and train LEAP for 100,000 steps using 4 NVIDIA A100 GPUs in parallel. During training, we use  $K = 4$  steps for iterative refinements,  $N = 256$  for the number of queries,  $S = 8$  for the model window, and  $S_{LP} = 12$  for the tracking window. For inter-track anchor-based attention, the number of anchors is 64. The loss weights are set to  $w_{1} = 1.0, w_{2} = 0.5, w_{3} = 0.5$ . In LEAP-VO, we perform 4 steps for each bundle adjustment with the Huber Loss for distance metric. The bundle adjustment window size  $S_{BA}$  is set to 15. Track filtering parameters are set at  $\gamma_v = 0.9, \gamma_d = 0.9, \gamma_u = 0.8, \gamma_{track} = 3$ . Please refer to our supplementary materials for more details.
+
+# 4.3. Visual Odometry Results
+
+We compare our methods against the state-of-the-art SLAM and VO approaches, including ORB-SLAM2 [24], DynaSLAM [1], DROID-SLAM [32], TartanVO [40], DytanVO [28], and DPVO [33]. Evaluations are conducted on the static Replica dataset [29] as well as on the dynamic datasets MPI-Sintel [4] and TartanAir-Shibuya [26].
+
+Replica. We compare our method with other baselines on the Replica dataset, which contains eight static scenes
+
+<table><tr><td rowspan="2">Method</td><td colspan="2">StandingHuman</td><td colspan="3">RoadCrossing (Easy)</td><td colspan="2">RoadCrossing (Hard)</td><td rowspan="2">Average</td></tr><tr><td>01</td><td>02</td><td>03</td><td>04</td><td>05</td><td>06</td><td>07</td></tr><tr><td>ORB-SLAM2 [24] w/ mask</td><td>0.0788</td><td>0.0060</td><td>0.0657</td><td>0.0196</td><td>0.0148</td><td>1.0984</td><td>0.8476</td><td>0.3044</td></tr><tr><td>DynaSLAM [1]</td><td>X</td><td>0.8836</td><td>0.3907</td><td>0.4196</td><td>0.4925</td><td>0.6446</td><td>0.6539</td><td>(0.5808)</td></tr><tr><td>AirDOS [26] w/ mask</td><td>0.0606</td><td>0.0193</td><td>0.0951</td><td>0.0331</td><td>0.0206</td><td>0.2230</td><td>0.5625</td><td>0.1449</td></tr><tr><td>DROID-SLAM [32]</td><td>0.0051</td><td>0.0073</td><td>0.0103</td><td>0.0120</td><td>0.2278</td><td>0.0253</td><td>0.5788</td><td>0.1238</td></tr><tr><td>TartanVO [40]</td><td>0.0600</td><td>0.1605</td><td>0.2762</td><td>0.1814</td><td>0.2174</td><td>0.3228</td><td>0.5009</td><td>0.2456</td></tr><tr><td>DytanVO [28]</td><td>0.0327</td><td>0.1017</td><td>0.0608</td><td>0.0516</td><td>0.0755</td><td>0.0365</td><td>0.0660</td><td>0.0607</td></tr><tr><td>DPVO [39]</td><td>0.0539</td><td>0.1603</td><td>0.1788</td><td>0.2858</td><td>0.1196</td><td>0.1119</td><td>0.1498</td><td>0.1514</td></tr><tr><td>LEAP-VO (Ours)</td><td>0.0081</td><td>0.0185</td><td>0.0399</td><td>0.0317</td><td>0.0113</td><td>0.0689</td><td>0.0246</td><td>0.0290</td></tr></table>
+
+Table 3. ATE (m) results on TartanAir-Shibuya Sequences [26]. ( $\cdot$ ) denotes averaging on valid scenes only. We can observe that our method shows better results for ATE on most sequences, outperforming all SLAM and VO baselines on average ATE.
+
+![](images/0c9be0f3fcfc59cefc63ad77edac4adc0e039eefe5b343e437c31e099d237ab9.jpg)  
+(a) RoadCrossing 04
+
+![](images/f5a4197b9fd43580001e00f745e1a2cbf7cc380b0001405e7443351579a9253f.jpg)  
+(b) RoadCrossing 05
+
+![](images/422bd73a1d36da5ecdab37f323089a41085702b01500552c15b23bbc9e085202.jpg)  
+(c) RoadCrossing 06  
+Figure 5. Qualitative results of camera trajectory estimation on TartanAir-Shibuya [26]. The visualizations show that our method provides more robust and accurate camera pose trajectories, especially in hard cases (RoadCrossing 06 and RoadCrossing 07).
+
+![](images/500f27a167516833358616cab081a003fdad56f68b6e256912b551c566d37440.jpg)  
+(d) RoadCrossing 07
+
+without any moving objects. Challenges arise in two test sequences that contain prolonged occlusions, leading to the potential camera tracking loss. As illustrated in Table 1, our approach outperforms other VO methods on all three metrics, showing effectiveness under static environments and the capability to handle occlusions. Further insights are available in Section 4.5. For classical methods, ORBSLAM2 [24] and DynaSLAM [1], we observe tracking loss and resuming via re-localization, which reduces long-term drift and shows high accuracy for camera pose tracking.
+
+MPI-Sintel. We also evaluate our VO camera trajectory accuracy on 14 dynamic scenes from the MPI Sintel dataset, following the setting of [48]. As shown in Table 2, our method substantially surpasses other VO baselines in dynamic scenes, thanks to our temporal uncertainty estimation and dynamic track detection. Traditional feature-based methods like ORB-SLAM2 [24] and DynaSLAM [1] sometimes fail to track camera movements in highly dynamic sequences, primarily due to outliers from dynamic object correspondences and segmentation-based only dynamic track estimation. In contrast, our approach, which considers visual, temporal, and inter-track information, demonstrates notable improvements in dynamic scene tracking accuracy.
+
+TartanAir-Shibuya. Following DytanVO [28], we further evaluate the VO performance using the dynamic TartanAir-Shibuya dataset. We assess the Average Trajectory Error (ATE) across seven diverse scenes, ranging from simple to
+
+challenging. As depicted in Table 3, our method consistently outperforms all other SLAM and VO baselines in the majority of these scenes. Moreover, trajectory visualizations in Figure 5 also highlight the robust camera tracking capabilities of our method in dynamic environments.
+
+# 4.4. Dynamic Track Estimation Results
+
+In our LEAP formulation, we have introduced the anchor-based dynamic track estimation module to distinguish between static and dynamic point trajectories, which provides valuable information for handling dynamic scenes in visual odometry. Our method leverages both point feature information and inter-track relations to predict the dynamic track label for each trajectory. To demonstrate the performance of the proposed dynamic track estimation module, we take the LEAP model and evaluate it on novel image sequences from diverse datasets. For a comprehensive demonstration, we uniformly sample  $16 \times 16$  queries among the images and track them for  $T = 8$  frames. The results, shown in Figure 6, illustrate that LEAP can effectively handle various scenarios, including single-object motion, complex and rapid motion, and multi-object motion with occlusion.
+
+# 4.5. Ablation Study
+
+Track Filtering. To highlight the efficacy of our track filtering module in LEAP-VO, we conduct an ablation study on different masks used in track filtering. We study three types of filtering criteria: visibility, dynamic
+
+![](images/781af32895b8c1318275094eab868761f2d0179d29830e8800be855692ef374b.jpg)  
+Figure 6. Visualization of dynamic track estimation on DAVIS [19], MPI-Sintel [4], and TartanAir-Shibuya [26]. Odd columns: all point trajectories. Even columns: estimated dynamic point trajectories.
+
+![](images/849ddeb126a9119bf85089fee5033115a331c32107fbd180edaeec2c0c8ce3b9.jpg)  
+Figure 7. Visualization of point-wise uncertainty measurements. Keypoints with the lowest  $20\%$  (left) and highest  $20\%$  (right) uncertainty are shown in green and yellow, respectively.
+
+track, and confidence filtering. Table 4 shows the impact of applying various filtering types on the dynamic MPI Sintel benchmark. Without dynamic filtering or confidence filtering, the ATE increases by  $46\%$  and  $130\%$ , respectively. Combining all three types of filtering methods altogether, we achieve the best results in all three metrics.
+
+<table><tr><td rowspan="2">Method</td><td colspan="3">Track Filtering</td><td colspan="3">MPI Sintel</td></tr><tr><td>Vis.</td><td>Dyn.</td><td>Conf.</td><td>ATE</td><td>RPE trans</td><td>RPE rot</td></tr><tr><td rowspan="4">LEAP-VO</td><td>✓</td><td>-</td><td>-</td><td>0.118</td><td>0.078</td><td>1.340</td></tr><tr><td>✓</td><td>✓</td><td>-</td><td>0.085</td><td>0.062</td><td>1.281</td></tr><tr><td>✓</td><td>-</td><td>✓</td><td>0.054</td><td>0.058</td><td>1.274</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>0.037</td><td>0.055</td><td>1.263</td></tr></table>
+
+Uncertainty Estimation. As illustrated in Figure 7, we demonstrate the LEAP's capability to provide meaningful per-point uncertainty. It models the uncertainty as distribution parameters for both the entire track and individual points. Two key observations can be found from Figure 7. Firstly, our model reliably identifies high-uncertainty
+
+points, typically located in low-texture areas or in regions with repetitive patterns. Secondly, although not explicitly supervised, the model tends to assign higher uncertainty to dynamic objects, which are inherently more challenging to track. These findings highlight the efficacy of LEAP's probabilistic formulation in handling uncertainty.
+
+Keypoint Extraction. Table 5 showcases the effectiveness of various keypoint extraction strategies for VO performance. Despite its distinctive features, SIFT extraction provides inferior performance due to its unpredictable keypoint distribution. In contrast, the random sampling tends to generate well-separated keypoints, leading to a performance similar to SIFT's. Our distributed image gradient-based sampling shows the best performance, underscoring the significance of feature distribution and distinctiveness.
+
+Table 4. Effect of the proposed track filtering method on MPI-Sintel [4]. Tracking using all criteria yields the best results.  
+
+<table><tr><td>Policy:</td><td>Uniform</td><td>Random</td><td>SIFT [22]</td><td>Ours</td></tr><tr><td>ATE (m):</td><td>0.1511</td><td>0.0366</td><td>0.0355</td><td>0.0290</td></tr></table>
+
+Baseline comparison. We evaluate the pretrained CoTracker [18] for the end VO performance. Table 6 shows that LEAP front-end outperforms CoTracker on all datasets, demonstrating the effectiveness of the proposed dynamic track estimation and temporal probability modeling.
+
+Table 5. Comparison of keypoint extraction policies ( $N_{a} = 64$ ) on TartanAir-Shibuya [26]. Our distributed image-gradient sampling method achieves better results compared to other policies.  
+
+<table><tr><td rowspan="2">Front-end</td><td colspan="3">Replica</td><td colspan="3">MPI Sintel</td><td>Shibuya</td></tr><tr><td>ATE</td><td>RPE trans</td><td>RPE rot</td><td>ATE</td><td>RPE trans</td><td>RPE rot</td><td>ATE</td></tr><tr><td>CoTracker</td><td>0.301</td><td>0.031</td><td>2.043</td><td>0.126</td><td>0.071</td><td>1.366</td><td>0.160</td></tr><tr><td>LEAP</td><td>0.204</td><td>0.030</td><td>1.992</td><td>0.037</td><td>0.055</td><td>1.263</td><td>0.029</td></tr></table>
+
+Table 6. Baseline comparison with CoTracker front-end [18]. Our LEAP front-end achieves better results on all datasets.
+
+# 5. Conclusion
+
+We introduce Long-term Effective Any Point Tracking (LEAP), designed to tackle the limitations of previous point-tracking methods. By leveraging visual, inter-track, and temporal cues within an anchor-based dynamic track estimation module, LEAP captures global motion patterns and effectively discriminates between static and dynamic elements. Moreover, our approach incorporates a temporal probabilistic formulation into the point-tracking pipeline, emulating recursive Bayesian filtering through a learning-based refinement module. This enables our model to accurately assess the reliability of point trajectory estimates. Using LEAP as the front-end, we then develop the LEAP-VO system, featuring novel integration of visual information, global motion patterns, and track distribution for handling dynamic scenes. Additionally, our takes for LEAP-VO can be integrated with other TAP-based front-ends, offering the potential to markedly improve camera-tracking accuracy and robustness.
+
+# References
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+    {
+        "type": "text",
+        "text": "LEDS: Limitless Image Editing using Text-to-Image Models",
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+        "image_caption": [
+            "Figure 1. LEDs++ facilitates versatile image-to-image editing. Several complex cases are available now."
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Text-to-image diffusion models have recently received increasing interest for their astonishing ability to produce high-fidelity images from solely text inputs. Subsequent research efforts aim to exploit and apply their capabilities to real image editing. However, existing image-to-image methods are often inefficient, imprecise, and of limited versatility. They either require time-consuming fine-tuning, deviate unnecessarily strongly from the input image, and/or lack support for multiple, simultaneous edits. To address these issues, we introduce LEDs++, an efficient yet versatile and precise textual image manipulation technique. LEDs++'s novel inversion approach requires no tuning nor optimization and produces high-fidelity results with a few diffusion steps. Second, our methodology supports multiple simultaneous edits and is architecture-agnostic. Third, we use a novel implicit masking technique that limits changes to relevant image regions. We propose the novel TEdBench++ benchmark as part of our exhaustive evaluation. Our results demonstrate the capabilities of LEDs++ and its improvements over previous methods.",
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+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Text-to-image diffusion models (DM) have garnered recognition for their ability to generate high-quality images from",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "textual descriptions. A growing body of research has recently been dedicated to utilizing these models for manipulating real images. However, several barriers prevent many real-world applications of diffusion-based image editing. Current methods often entail computationally expensive model tuning or other optimization, presenting practical challenges [6, 18, 28, 30, 44]. Additionally, existing techniques have the proclivity to induce profound changes to the original image [17, 26], often resulting in completely different images. Lastly, all these approaches are inherently constrained when editing multiple (arbitrary) concepts simultaneously. We tackle these problems by introducing LEDs++ $^{1}$ , a diffusion-based image editing technique addressing these limitations.",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "LEDITS++<sup>2</sup> offers a streamlined approach for textual image editing, eliminating the need for extensive parameter tuning. To this end, we derive image inversion for a more efficient diffusion sampling algorithm to a) drastically reduce computational resources and b) guarantee perfect image reconstruction. Thus, we overcome computational obstacles and avoid changes in the edited image in the first place. Furthermore, we use a novel implicit masking approach to semantically ground each edit instruction to its relevant image region. This further optimizes changes to the image by retaining the overall image composition and object identity.",
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+        "list_items": [
+            "*Equal contribution †Partially as research intern at Adobe",
+            "1LEDITS++ stands for Limitless Edits with sde-dpm-solver++.",
+            "2https://huggingface.co/spaces/leditsplusplus/project"
+        ],
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+        "text": "CVF",
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+    {
+        "type": "header",
+        "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
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+        "text": "8861",
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+    {
+        "type": "text",
+        "text": "Additionally, LEDs++ is the only method to date to facilitate easy and versatile image editing by supporting multiple simultaneous instructions without causing undue interference. Finally, its lightweight architecture-agnostic nature ensures compatibility with both latent and pixel-based diffusion models, providing high accessibility.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In this work, we establish the methodical benefits of LEDs++ and demonstrate that this intuitive, lightweight approach offers sophisticated semantic control for image editing. Specifically, we contribute by (i) devising a formal definition of LEDs++ while (ii) deriving perfect inversion for a more efficient diffusion sampling method, (iii) qualitatively and empirically demonstrating its efficiency, versatility, and precision, (iv) providing an exhaustive empirical comparison to concurrent works with automatic and human user metrics, and thereby (v) introducing Textual Editing Benchmark++ (TEdBench++, a more holistic and coherent testbed for evaluating textual image manipulation.",
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+    {
+        "type": "text",
+        "text": "2. Background",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Recently, large-scale, text-guided DMs have enabled versatile applications in image generation [3, 33, 37]. Especially latent diffusion models [31, 34] have gained attention for their computational efficiency. Below, we discuss related work for efficient, versatile image manipulation with DMs.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Diffusion Sampling. Generating outputs with DMs requires multiple iterative denoising steps that constitute the main bottleneck at inference. Commonly used sampling methods such as DDPM [15] or DDIM [42] require tens or hundreds of steps to produce high-quality samples. Consequently, numerous works have been dedicated to speeding up the sampling process without loss in quality. Distillation efforts progressively reduce the number of required steps through further training [25, 27]. Other works focus on improving the sampling itself, e.g. using high-order ODE-solvers [22, 23, 46]. Such solvers can be readily combined with pre-trained DMs at inference to lower the number of denoising steps. With LEDs++, we derive perfect image inversion with the DPM-Solver++, allowing image editing in as few as 20 total steps.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Semantic Control during Diffusion. While text-to-image DMs generate new, astonishing images, fine-grained control over the generative process remains challenging. Minor changes to the text prompt lead to entirely different outputs. Wu et al. [45] studied concept disentanglement using linear combinations of text embeddings to gain semantic control. Methods like Prompt-to-Prompt [14] and other works [8, 30] utilize the DM's attention layers to attribute pixels to tokens from the text prompt. Dedicated operations on the attention maps enable more control over the generated images. Other works have focused on the noise estimates of DMs [5, 20] providing semantic control over the generation process. With LEDs++, we now enable",
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+    {
+        "type": "text",
+        "text": "fine-grained semantic control for manipulating real images, going beyond purely generative applications.",
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+    {
+        "type": "text",
+        "text": "Real Image Editing. Since DMs' rise in popularity for text-to-image generation, they have also been explored for (real) image-to-image editing. As a first, simple approach, SDEdit added noise to the image for an intermediate step in the diffusion process [26]. While lightweight, the resulting image diverges substantially from the input as it is (partially) regenerated. Inpainting allows to keep the change small by having a user provide additional masks to restrict changes to certain image regions [2, 29]. Yet, user masks are costly or often simply unavailable. Other works have thus explored semantically grounded approaches using cross-attention instead to better control image manipulation [7, 28, 30]. In contrast, LEDs++ leverages both attention-and noise-based masking to obtain fine-grained masks, enabling strong semantic control over real images.",
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+    {
+        "type": "text",
+        "text": "Another important aspect of image manipulation methods is the required tuning and overall runtime. Instruct-Pix2Pix continues training a DM at scale to enable image editing capabilities [6]. Finetuning instead on each individual input to constrain the generation on the real image has shown helpful [18, 44] but not computationally efficient. Consequently, recent works have largely relied on inverting the deterministic DDIM sampling process [42] to save computational resources. DDIM inversion identifies an initial noise vector that results in the input image when denoised again. However, faithful reconstructions are only obtained in the limit of small steps, thus requiring large numbers of inversion steps. Moreover, small errors will still incur at each timestep, often accumulating into meaningful deviations from the input, requiring costly error correction through optimization [28, 30]. Recently, Huberman-Spiegelglas et al. proposed an inversion technique [17] for the DDPM sampler [15] to address the limitations of DDIM inversion. LEDs++ provides the same guarantees of perfect inversion with even further reduced runtime alongside an edit-friendly latent space, enabling more versatility.",
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+        "type": "text",
+        "text": "3. Image Editing with Text-to-Image Models",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "Before devising the methodology of LEDs++, let us first motivate the desired features and use cases. Specifically, we aim for efficiency, versatility, and precision. The goal is to provide a method that enables a fast exploratory workflow for image editing in which a user can iteratively interact with the model and explore various edits. Consequently, LEDs++ produces outputs quickly with no tuning or optimization to not disrupt the creative process. Further, arbitrary editing instructions and combinations thereof are supported to facilitate a wide range of image manipulations (e.g., complex multi-editing). Lastly, we provide precise and sophisticated semantic control over the image editing. Each of the (potentially multiple) edit instruc",
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+    {
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+        "text": "8862",
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+    {
+        "type": "text",
+        "text": "tions can be steered individually, and changes are automatically restricted to relevant image regions. Importantly, with LEDs++ we prioritize compositional robustness.",
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+    {
+        "type": "text",
+        "text": "3.1. Guided Diffusion Models",
+        "text_level": 1,
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Let us first define some general background for diffusion models. DMs iteratively denoise a Gaussian distributed variable to produce samples of a learned data distribution. Let's consider a diffusion process that gradually turns an image  $x_0$  into Gaussian noise.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nx _ {t} = \\sqrt {1 - \\beta_ {t}} x _ {t - 1} + \\sqrt {\\beta_ {t}} n _ {t}, \\quad t = 1, \\dots , T \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            114,
+            253,
+            468,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $n_t$  are iid normal distributed vectors and  $\\beta_t$  a variance schedule. The diffusion process is equivalently expressed as",
+        "bbox": [
+            76,
+            281,
+            468,
+            311
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nx _ {t} = \\sqrt {\\bar {\\alpha} _ {t}} x _ {0} + \\sqrt {1 - \\bar {\\alpha} _ {t}} \\epsilon_ {t} \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            181,
+            320,
+            468,
+            338
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $\\alpha_{t} = 1 - \\beta_{t}$ ,  $\\bar{\\alpha}_{t} = \\Pi_{s=1}^{t} \\alpha_{s}$  and  $\\epsilon_{t} \\sim \\mathcal{N}(0, \\mathbf{I})$ . Importantly, all  $\\epsilon_{t}$  are not statistically independent. Instead, consecutive pairs  $\\epsilon_{t}, \\epsilon_{t-1}$  are strongly dependent, which will be relevant later. To generate an (new) image  $\\hat{x}_{0}$  the reverse diffusion process starts from random noise  $x_{T} \\sim \\mathcal{N}(0, \\mathbf{I})$  which can be iteratively denoised as",
+        "bbox": [
+            76,
+            347,
+            468,
+            436
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nx _ {t - 1} = \\hat {\\mu} _ {t} \\left(x _ {t}\\right) + \\sigma_ {t} z _ {t}, \\quad t = T, \\dots , 1 \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            138,
+            448,
+            468,
+            464
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Here  $z_{t}$  are iid standard normal vectors, and common variance schedulers  $\\sigma_{t}$  can be expressed in the general form",
+        "bbox": [
+            76,
+            474,
+            468,
+            503
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\sigma_ {t} = \\eta \\beta_ {t} \\frac {1 - \\bar {\\alpha} _ {t - 1}}{1 - \\bar {\\alpha} _ {t}}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            205,
+            512,
+            338,
+            542
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $\\eta \\in [0,1]$ . In this formulation,  $\\eta = 0$  corresponds to the deterministic DDIM [42] and  $\\eta = 1$  to the DDPM scheme [15]. Lastly, in theses cases, we have  $\\hat{\\mu}_t(x_t) =$",
+        "bbox": [
+            76,
+            551,
+            468,
+            598
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\sqrt {\\bar {\\alpha} _ {t - 1}} \\frac {x _ {t} - \\sqrt {1 - \\bar {\\alpha} _ {t}} \\hat {\\epsilon} _ {\\theta} (x _ {t})}{\\sqrt {\\bar {\\alpha} _ {t}}} + \\sqrt {1 - \\bar {\\alpha} _ {t - 1} - \\sigma_ {t} ^ {2}} \\hat {\\epsilon} _ {\\theta} (x _ {t})\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            89,
+            606,
+            454,
+            640
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Here  $\\hat{\\epsilon}_{\\theta}(x_{t})$  is an estimate of  $\\epsilon_{t}$  produced by our neural network DM with learned parameters  $\\theta$ , commonly implemented as a U-Net [35]. For text-to-image generation, the model is conditioned on a text prompt  $p$  to produce images faithful to that prompt. The DM is trained to produce the noise estimate  $\\hat{\\epsilon}_{\\theta}(x_{t})$  needed for iteratively sampling  $\\hat{x}_0$  (Eq. 3). For text-conditioned DMs,  $\\hat{\\epsilon}_{\\theta}$  is calculated using specific guidance techniques.",
+        "bbox": [
+            76,
+            648,
+            468,
+            768
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Most DMs rely on classifier-free guidance [16], a conditioning method using a purely generative diffusion model, eliminating the need for an additional classifier. During training, the text conditioning  $c_{p}$  is randomly dropped with a fixed probability, resulting in a joint model for unconditional and conditional objectives. During inference, the score estimates for the  $\\epsilon$ -prediction are adjusted so that:",
+        "bbox": [
+            76,
+            768,
+            468,
+            875
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\hat {\\epsilon} _ {\\theta} \\left(x _ {t}, c _ {p}\\right) := \\hat {\\epsilon} _ {\\theta} \\left(x _ {t}\\right) + s _ {g} \\left(\\hat {\\epsilon} _ {\\theta} \\left(x _ {t}, c _ {p}\\right) - \\hat {\\epsilon} _ {\\theta} \\left(x _ {t}\\right)\\right) \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            116,
+            883,
+            468,
+            902
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "with guidance scale  $s_g$  and  $\\hat{\\epsilon}_{\\theta}$  defining the noise estimate with parameters  $\\theta$ . Intuitively, the unconditioned  $\\epsilon$ -prediction is pushed in the direction of the conditioned one, with  $s_g$  determining the extent of the adjustment.",
+        "bbox": [
+            498,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.2.LEDITS++",
+        "text_level": 1,
+        "bbox": [
+            500,
+            160,
+            612,
+            174
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "With the fundamentals established, the methodology of LEDs++ can now be broken down into three components: (1) efficient image inversion, (2) versatile textual editing, and (3) semantic grounding of image changes.",
+        "bbox": [
+            498,
+            183,
+            890,
+            243
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Component 1: Perfect Inversion. Utilizing text-to-image models for editing real images requires conditioning the generation on the input image. Recent works have largely relied on inverting the sampling process to identify  $x_{T}$  that will be denoised to the input image  $x_{0}$  [28, 30]. Inverting the DDPM scheduler is generally preferred over DDIM inversion since the former can be achieved in fewer timesteps and with no reconstruction error [17].",
+        "bbox": [
+            498,
+            244,
+            890,
+            364
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "However, there exist more efficient schemes than DDPM for sampling DMs that greatly reduce the required number of steps and consequently DM evaluations. We here propose a more efficient inversion method by deriving the desired inversion properties for such a scheme. As demonstrated by Song et al.[43], DDPM can be viewed as a first-order stochastic differential equation (SDE) solver when formulating the reverse diffusion process as an SDE. This SDE can be solved more efficiently—in fewer steps—using a higher-order differential equation solver, here dpmsolver++ [23]. The reverse diffusion process from Eq. 3 for the second-order sde-dpm-solver++ can be written as",
+        "bbox": [
+            498,
+            364,
+            890,
+            546
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nx _ {t - 1} = \\hat {\\mu} _ {t} \\left(x _ {t}, x _ {t + 1}\\right) + \\sigma_ {t} z _ {t}, \\quad t = T, \\dots , 1 \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            542,
+            556,
+            890,
+            571
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where now",
+        "bbox": [
+            500,
+            584,
+            576,
+            595
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\sigma_ {t} = \\sqrt {1 - \\bar {\\alpha} _ {t - 1}} \\sqrt {1 - e ^ {- 2 h _ {t - 1}}}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            586,
+            604,
+            803,
+            625
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "and higher-order  $\\hat{\\mu}_t$  depends now on  $x$  from two timesteps,  $x_t$  and  $x_{t + 1}$ . Such that  $\\hat{\\mu}_t(x_t,x_{t + 1}) =$",
+        "bbox": [
+            498,
+            635,
+            888,
+            666
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\frac {\\sqrt {1 - \\bar {\\alpha} _ {t - 1}}}{\\sqrt {1 - \\bar {\\alpha} _ {t}}} e ^ {- h _ {t - 1}} x _ {t} + \\sqrt {\\bar {\\alpha} _ {t - 1}} \\left(1 - e ^ {- 2 h _ {t - 1}}\\right) \\hat {\\epsilon} _ {\\theta} (x _ {t}) \\\\ + 0. 5 \\sqrt {\\bar {\\alpha} _ {t - 1}} \\left(1 - e ^ {- 2 h _ {t - 1}}\\right) \\frac {- h _ {t}}{h _ {t - 1}} \\left(\\hat {\\epsilon} _ {\\theta} \\left(x _ {t + 1}\\right) - \\hat {\\epsilon} _ {\\theta} \\left(x _ {t}\\right)\\right) \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            517,
+            675,
+            872,
+            742
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "with",
+        "bbox": [
+            500,
+            750,
+            534,
+            763
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nh _ {t} = \\frac {\\ln (\\sqrt {\\bar {\\alpha} _ {t}})}{\\ln (\\sqrt {1 - \\bar {\\alpha} _ {t}})} - \\frac {\\ln (\\sqrt {\\bar {\\alpha} _ {t + 1}})}{\\ln (\\sqrt {1 - \\bar {\\alpha} _ {t + 1}})}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            566,
+            761,
+            823,
+            795
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "For the detailed derivation of the solver and proof of faster convergence, we refer the reader to the relevant literature [22, 23]. Based on the above, we now devise our inversion process. Given an input image  $x_0$  we construct an auxiliary reconstruction sequence of noise images  $x_1, \\ldots, x_T$  as",
+        "bbox": [
+            498,
+            799,
+            890,
+            875
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nx _ {t} = \\sqrt {\\bar {\\alpha} _ {t}} x _ {0} + \\sqrt {1 - \\bar {\\alpha} _ {t}} \\tilde {\\varepsilon} _ {t} \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            604,
+            883,
+            890,
+            900
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "8863",
+        "bbox": [
+            482,
+            944,
+            514,
+            955
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $\\tilde{\\epsilon}_t\\sim \\mathcal{N}(0,\\mathbf{I})$ . Contrary to Eq. 2, the  $\\tilde{\\epsilon}_t$  are now statistically independent, which is a desirable property for image editing [17]. Lastly, the respective  $z_{t}$  for the inversion can be derived from Eq. 5 as",
+        "bbox": [
+            75,
+            90,
+            468,
+            151
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nz _ {t} = \\frac {x _ {t - 1} - \\hat {\\mu} _ {t} \\left(x _ {t} , x _ {t + 1}\\right)}{\\sigma_ {t}}, \\quad t = T,.., 1 \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            127,
+            161,
+            468,
+            193
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "with  $\\hat{\\mu}$  and  $\\sigma_{t}$  as defined above. We base our implementation on the multistep variant of sde-dpm-solver++, which only requires one evaluation of the DM at each diffusion timestep by reusing the estimates from the previous step. The number of timesteps can be reduced further by stopping the inversion at an intermediate step  $t < T$  and starting the generation at that step. Empirically, we observed that  $t\\in [0.9T,0.8T]$  usually produces edits of the same fidelity as  $t = T$ , supporting observations in previous work [17, 26] that earlier timesteps are less relevant to the edit.",
+        "bbox": [
+            75,
+            202,
+            468,
+            353
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Component 2: Textual Editing. After creating our reconstruction sequence  $x_{1}, \\ldots, x_{T}$  and calculating the respective  $z_{t}$ , we now edit the image by manipulating the noise estimate  $\\hat{\\epsilon}_{\\theta}$  based on a set of edit instructions  $\\{e_i\\}_{i \\in I}$ . We devise a dedicated guidance term for each concept  $e_{i}$  based on conditioned and unconditioned estimates. Let us formally define LEDs++'s guidance by starting with a single editing prompt  $e$ . We compute",
+        "bbox": [
+            75,
+            354,
+            468,
+            474
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\hat {\\epsilon} _ {\\theta} \\left(x _ {t}, c _ {e}\\right) := \\hat {\\epsilon} _ {\\theta} \\left(x _ {t}\\right) + \\gamma \\left(x _ {t}, c _ {e}\\right) \\tag {8}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            165,
+            486,
+            468,
+            502
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "with guidance term  $\\gamma$ . Consequently, setting  $\\gamma = 0$  will reconstruct the input image  $x_0$ . We construct  $\\gamma$  to push the unconditioned score estimate  $\\hat{\\epsilon}_{\\theta}(x_t)$  —i.e. the input image reconstruction—away from/towards the edit concept estimate  $\\hat{\\epsilon}_{\\theta}(x_t, c_e)$ , depending on the guidance direction:",
+        "bbox": [
+            75,
+            513,
+            468,
+            589
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\gamma \\left(x _ {t}, c _ {e}\\right) = \\phi (\\psi ; s _ {e}, \\lambda) \\psi \\left(x _ {t}, c _ {e}\\right) \\tag {9}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            163,
+            601,
+            468,
+            617
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\phi$  applies an edit guidance scale  $s_e$  element-wise, and  $\\psi$  depends on the edit direction:  $\\psi(x_t, c_e) =$",
+        "bbox": [
+            76,
+            628,
+            468,
+            659
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\left\\{ \\begin{array}{l} \\hat {\\epsilon} _ {\\theta} \\left(x _ {t}, c _ {e}\\right) - \\hat {\\epsilon} _ {\\theta} \\left(x _ {t}\\right) \\quad \\text {i f p o s . g u i d a n c e} \\\\ - \\left(\\hat {\\epsilon} _ {\\theta} \\left(x _ {t}, c _ {e}\\right) - \\hat {\\epsilon} _ {\\theta} \\left(x _ {t}\\right)\\right) \\quad \\text {i f n e g . g u i d a n c e} \\end{array} \\right. \\tag {10}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            104,
+            670,
+            468,
+            709
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Thus, changing the guidance direction is reflected by the direction between  $\\hat{\\epsilon}_{\\theta}(x_t,c_e)$  and  $\\hat{\\epsilon}_{\\theta}(x_t)$ . The term  $\\phi$  identifies those dimensions of the image and respective  $\\hat{\\epsilon}_{\\theta}$  that are relevant to a prompt  $e$ . Consequently,  $\\phi$  returns 0 for all irrelevant dimensions and a scaling factor  $s_e$  for the others. We describe the construction of  $\\phi$  in detail below. Larger  $s_e$  will increase the effect of the edit, and  $\\lambda \\in (0,1)$  reflects the percentage of the pixels selected as relevant by  $\\phi$ . Notably, for a single concept  $e$  and uniform  $\\phi = s_e$ , Eq. 8 generalizes to the classifier-free guidance term in Eq. 4.",
+        "bbox": [
+            75,
+            719,
+            468,
+            869
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "For multiple  $e_i$ , we calculate  $\\gamma_t^i$  as described above, with each defining their own hyperparameter values  $\\lambda^i$ ,  $s_e^i$ . The",
+        "bbox": [
+            75,
+            869,
+            468,
+            901
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "sum of all  $\\gamma_t^i$  results in",
+        "bbox": [
+            500,
+            90,
+            653,
+            106
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\hat {\\gamma} _ {t} \\left(x _ {t}, c _ {e _ {i}}\\right) = \\sum_ {i \\in I} \\gamma_ {t} ^ {i} \\left(x _ {t}, c _ {e _ {i}}\\right) \\tag {11}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            589,
+            114,
+            890,
+            140
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Component 3: Semantic Grounding. The masking term  $\\phi$  (Eq. 9) is the intersection (pointwise product) of binary masks  $M^1$  and  $M^2$  combined with scaling factor  $s_e$ :",
+        "bbox": [
+            498,
+            146,
+            890,
+            191
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\phi (\\psi ; s _ {e _ {i}}, \\lambda) = s _ {e _ {i}} M _ {i} ^ {1} M _ {i} ^ {2} \\tag {12}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            607,
+            200,
+            890,
+            217
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $M_{i}^{1}$  is a binary mask generated from the U-Net's cross-attention layers and  $M_{i}^{2}$  is a binary mask derived from the noise estimate. Intuitively, each mask is an importance map, where  $M_{i}^{1}$  is more strongly grounded than  $M_{i}^{2}$ , but of significantly coarser granularity. Therefore, the intersection of the two yields a mask both focused on relevant image regions and of fine granularity. With LEDs++, we empirically demonstrate that these maps can also capture regions of an image relevant to an editing concept that is not already present. Specifically for multiple edits, calculating a dedicated mask for each edit prompt ensures that the corresponding guidance terms remain largely isolated, limiting interference between them.",
+        "bbox": [
+            496,
+            226,
+            890,
+            421
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Formally, at each time step  $t$ , a U-Net forward pass with editing prompt  $e_i$  is performed to generate cross-attention maps for each token of the editing prompt. All cross-attention maps of the smallest resolution (e.g.,  $16 \\times 16$  for SD) are averaged over all heads and layers, and the resulting maps are summed over all editing tokens, resulting in a single map  $A_t^{e_i} \\in R^{16 \\times 16}$ . Importantly, we utilize the same U-Net evaluation  $\\hat{\\epsilon}_{\\theta}(x_t, c_e)$  already performed in Eq. 10 to produce  $M^1$  with minimal overhead. Each map  $A_t^{e_i}$  is up-sampled to match the size of  $x_t$ . Cross-attention mask  $M^1$  is derived by calculating the  $\\lambda$ -th percentile of up-sampled  $A_t^{e_i}$  and",
+        "bbox": [
+            496,
+            422,
+            890,
+            604
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nM _ {i} ^ {1} = \\left\\{ \\begin{array}{l l} 1 & \\text {i f} \\left| A _ {t} ^ {e _ {i}} \\right| \\geq \\eta_ {\\lambda} \\left(\\left| A _ {t} ^ {e _ {i}} \\right|\\right) \\\\ 0 & \\text {e l s e} \\end{array} \\right. \\tag {13}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            575,
+            613,
+            890,
+            654
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\eta_{\\lambda}(|\\cdot|)$  is the  $\\lambda$ -th percentile. By definition,  $M^1$  only selects image regions that correlate strongly with the editing prompt, and  $\\lambda$  determines the size of this selected region.",
+        "bbox": [
+            496,
+            662,
+            890,
+            707
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The fine-grained mask  $M^2$  is calculated based on the guidance vector  $\\psi$  of noise estimates derived in Eq. 10. The difference between unconditioned and conditioned  $\\hat{\\epsilon}_{\\theta}$ , generally captures outlines and object edges of  $x_{t}$ . Consequently, the largest absolute values of  $\\psi$  provide meaningful segmentation information of fine granularity for  $M^2$",
+        "bbox": [
+            496,
+            708,
+            890,
+            799
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nM ^ {2} = \\left\\{ \\begin{array}{l l} 1 & \\text {i f} | \\psi | \\geq \\eta_ {\\lambda} (| \\psi |) \\\\ 0 & \\text {e l s e} \\end{array} \\right. \\tag {14}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In general, threshold  $\\lambda$  should correspond to the performed edit. Changes affecting the entire image, such as style transfer, should choose smaller  $\\lambda (\\rightarrow 0)$ , whereas edits targeting",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "8864",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/aa8709af9cdd4c546356fdd95823f9d774fb44ad62023ae5dae09689d981550b.jpg",
+        "image_caption": [
+            "Figure 2. Comparison of image editing methods. (top) LEDs++ is the only method to restrict edits to the tree leaves and position of the car. (bottom) Ours is the only approach faithfully executing all three edits and keeping changes minimal. (Best viewed in color)"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/bd97ddbef80dd831bf1304807b0f0851b0a858012777a1cfac3695bf331144e0.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>Reconstruction \nError (RMSE) ↓</td><td>Execution \nTime (s) ↓</td><td>Variation/ \nSampling</td><td>Semantic \nGrounding</td><td>Multi- \nEditing</td></tr><tr><td>SDEdit [26]</td><td>0.81 ±0.07</td><td>2.10 ±0.02</td><td>✓</td><td>X</td><td>X</td></tr><tr><td>Imagic [18]</td><td>0.58 ±0.12</td><td>349.98 ±0.45</td><td>✓</td><td>X</td><td>X</td></tr><tr><td>Vanilla DDIM Inversion</td><td>0.22 ±0.10</td><td>37.23 ±0.04</td><td>X</td><td>X</td><td>X</td></tr><tr><td>Pix2Pix-Zero [30]</td><td>0.20 ±0.09</td><td>56.78 ±0.14</td><td>(✓)</td><td>✓</td><td>X</td></tr><tr><td>DiffEdit [9]</td><td>0.13±0.03</td><td>27.65 ±0.03</td><td>✓</td><td>✓</td><td>X</td></tr><tr><td>Edit-friendly DDPM [17]</td><td>0.00</td><td>10.36 ±0.05</td><td>✓</td><td>X</td><td>X</td></tr><tr><td>LEDSITS++ (Ours)</td><td>0.00</td><td>1.78 ±0.03</td><td>✓</td><td>✓</td><td>✓</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Table 1. Comparing key properties for diffusion-based image editing techniques, with LEDs++ offering clear methodological benefits. Due to LEDs++'s efficient perfect inversion, it is the fastest and error-free method. At the same time, its methodology is the only enabling versatility in terms of variation, semantic grounding, and multi-editing. Subscript numbers indicate standard deviation.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "specific objects or regions should use  $\\lambda$  proportional to the region's prominence in the image.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4. Properties of LEDs++",
+        "text_level": 1,
+        "bbox": [
+            76,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "With the fundamentals of LEDs++ established, we next showcase its unique properties and capabilities.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Efficiency. First off, LEDs++ offers substantial performance improvements over other image editing methods. In Tab. 1, we provide a qualitative runtime comparison, with all methods being implemented for Stable Diffusion (SD) 1.5 [34]. As a parameter-free approach, LEDs++ does not require any computationally expensive fine-tuning or optimization. Consequently, LEDs++ is orders of magnitude faster than methods like Imagic [18] or Pix2Pix-Zero [30]. Further, we only need to invert the same number of diffusion steps used at inference, which results in significant runtime improvements over the standard DDIM inversion (21x). In addition to efficient inversion, we use a recent, fast scheduler that generally requires fewer total steps, further boosting performance. This way, LEDs++ is six times faster than recent DDPM inversion [17] and on par with fast but poor-quality SDEdit [26].",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Versatility. In addition to its efficiency, LEDs++ remains versatile, enabling sheer limitless editing possibilities. In Fig. 1, we showcase a broad range of edit types.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "LEDITS++ facilitates fine-grained edits (adding/removing glasses) and holistic changes such as style transfer (painting/sketch). Furthermore, object removal and replacement facilitate even more image editing tasks. Importantly, the overall image composition is preserved in all cases. To our knowledge, LEDs++ is the only diffusion-based image editing method inherently supporting multiple edits in isolation, which allows for more complex image manipulation. Fig. 2 highlights LEDs++ benefits over previous methods. Our method produces the highest edit fidelity and is the only approach capable of faithfully executing multiple, simultaneous instructions. Moreover, LEDs++ also makes the least changes to unrelated objects and the overall background and composition of the image.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Lastly, the editing versatility benefits from the stochastic nature of the perfect but non-deterministic inversion. LEDs++ provides meaningful image variations by resampling  $\\tilde{c}_t$ . Additionally, the visual expression of each concept in the edited image scales monotonically with  $s_e$ , and the direction and magnitude of each concept can be varied freely. We present examples of both features in App. B.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Precision. Furthermore, LEDs++'s methodology keeps edits concise and avoids unnecessary deviations from the input image (Fig. 2). First, the perfect inversion will reconstruct the exact input image if no edit is applied (cf.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "8865",
+        "bbox": [
+            482,
+            944,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/65145febf9dc8f5f3ea361c981b25ba7f5ed9a8b34e59e22ec6b15377923bcfe.jpg",
+        "image_caption": [
+            "Figure 3. Exemplary edit performed with LEDs++ in only 25 diffusion steps with SD1.5. We apply a complex, compounded edit and ground each to a semantically reasonable image region."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Sec. 3.2). Consequently, we already improve on faithfulness to the input image even before applying any edits. This benefit over other methods is highlighted by the reconstruction error in Tab. 1. Second, implicit masking will semantically ground each edit to relevant image regions. This is specifically important for editing multiple concepts at the same time. While other methods only utilize one prompt for all instructions, LEDs++ isolates edits from each other (Eq. 11). Thus, we get dedicated masks for each concept as shown in Fig. 3. This design ensures that each instruction (e.g., red mask for 'cherry blossom') will be only applied where necessary. Subsequently, we provide further evidence for the efficacy of LEDs++'s masking approach.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5. Semantically Grounded Image Editing",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Cross-attention maps of DMs have been used extensively to ground regions of interest during image generation semantically [7, 8, 14, 30]. Nonetheless, these have not been combined with noise-based masks so far and thus lack fine granularity. Hence, we empirically evaluate the quality of implicit masks, i.e., attention maps  $M^1$  and noise maps  $M^2$  (Eq. 13 and 14) in the LEDs++ setup. We use a broad segmentation task for common objects as a proxy to measure the performance of implicit masks in identifying relevant image areas from edit instructions. Specifically, we utilize segmentation masks from the COCO panoptic segmentation challenge [19]. For each unique object in an image, we retrieve the masks  $M^1$ ,  $M^2$ , and their intersection per diffusion step. We use the (semantic) class label (e.g. 'person' or 'TV') as editing concept  $e$ . We consider masks at each of 50 total diffusion steps without actually editing the input image. Furthermore, we approximate mask threshold  $\\lambda$  based on the relative size of an object's bounding box.",
+        "bbox": [
+            75,
+            491,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Concise masks with LEDs++. Fig. 4 shows implicit masking as a reliable means to identify relevant image regions. Importantly, the intersection of both cross-attention masks  $M^1$  and noise maps  $M^2$  clearly outperforms each separate mask. The overall performance is even similar to a dedicated CLIPSeg model [24], despite LEDs++. masks being implicitly calculated at inference with only minimal overhead. At the same time, LEDs++.'s masking is superior to DiffEdit's [3]. Consequently, our method's inter",
+        "bbox": [
+            75,
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+            468,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/318c6382a39c079543b3cc4819e80b0f71060178d28b71ea7d436599a39f18cc.jpg",
+        "image_caption": [
+            "Figure 4. Semantic segmentation quality of LEDs++. We show the intersection over union (higher is better) for COCO panoptic segmentation. The intersection masks outperform each by a clear margin, close to the CLIPSeg reference. (Best viewed in color)"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "section of cross-attention masks and noise maps provides strong semantic grounding while being efficient during image manipulation to ensure precise editing.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "6. Image Editing Evaluation",
+        "text_level": 1,
+        "bbox": [
+            500,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Let us now compare LEDs++ to current SOTA methods for image manipulation on two benchmarks.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "6.1. Editing Multiple Concepts",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "First, we investigate the complex task of performing multiple edits simultaneously. We rely on a well-established setup for semantic image manipulation [5] to evaluate multi-conditioned attribute manipulation in facial images. In our experiment, we consider 100 images from the CelebA dataset [21]. For each image, we simultaneously edit three attributes out of a set of five, leading to ten total combinations of edit concepts. Further, we perform each edit across ten different seeds, resulting in 10,000 evaluated images for each method and hyperparameter setting, over 1M images in total. As measures for comparison, we employ CLIP and LPIPS scores. CLIP measures the text-to-image similarity of the edit instruction to the edited image, and LPIPS measures the image-to-image similarity of the real to the edited image. This way, we assess the tradeoff between the versatility of edits (CLIP) and the precision of those manipulations (LPIPS). We implement all methods based on SD1.5 and provide more details in App. C.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "LEDS++ outperforms competing methods. Fig. 5 shows the resulting CLIP vs. LPIPS plots for all methods. The top left corner represents the ideal editing method with maximum edit alignment without deviating from the initial image. Generally, one can observe a natural trade-off between versatility and precision for all methods, i.e., higher image-to-text alignment comes at the expense of lower similarity to the original image. LEDS++ is closest to the ideal region and thus clearly outperforms the other methods. In particular, the outputs remain close to the original image (low LPIPS scores), thanks to the precise implicit masking.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "8866",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/110ffe195968c3d76f23e8c672ce8b00d27b845da1c2f8bcb04eed0058e662e0.jpg",
+        "image_caption": [
+            "Figure 5. Comparison of instruction-alignment vs. image similarity trade-off for different editing methods. Results were reported for simultaneous manipulation of three facial attributes on CelebA. We plot CLIP scores (higher is better) of the target attributes against LPIPS similarity (lower is better). LEDs++ clearly outperforms all competing methods. (Best viewed in color)"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            101,
+            90,
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+            270
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "At the same time, it faithfully performs the edits (high CLIP scores) due to the dedicated, isolated editing for each concept. The depicted scores reflect our qualitative inspections for Pix2Pix-Zero and Imagic on such complex manipulations (cf. Fig. 2). We observed that these methods often break—either failing to perform all three edits and/or drastically altering the input image. Only edit-friendly DDPM [17] and LEDs++ reliably achieve the maximum average CLIP score of over 0.25. This value seems to represent an upper bound according to our manual investigations, as each attribute is edited correctly for all input images, and higher scores are not observed. Despite being computationally very efficient, LEDs++ faithfully executes each edit instruction while keeping the changes to the input low, highlighting the method's versatility and precision.",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "6.2. TEDBench  $(++)$",
+        "text_level": 1,
+        "bbox": [
+            76,
+            609,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Next, we investigate the versatility of LEDs++'s editing capabilities by running the Textual Editing Benchmark (TEDBench [18]), a collection of 100 input images paired with textual edit instructions. However, we observed a variety of inconsistencies in TEDBench and a lack of relevant editing tasks. Therefore, we propose TEDBench++ (Fig. 6a and App. D), a more challenging revised benchmark now containing 120 entries in total.<sup>3</sup> We addressed misspellings and rephrased ambiguous and inconclusive instructions. In addition to resolving these issues, we added instructions targeting challenging types of image manipulations previously not included in TEDBench: multi-conditioning, object/concept removal, style transfer, and complex replacements (Fig. 6a). We provide more details in App. D.",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We compare LEDs++ on TEdBench  $(++)$  to one of the strongest editing methods, Imagic [18] with Imagen [37].",
+        "bbox": [
+            76,
+            845,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/636c1e41362e13cfd1e413f996541c24e2fed7f5ab4e7a5f5d5480a83c80f5c6.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td colspan=\"2\">TEDBench</td><td colspan=\"2\">TEDBench++</td></tr><tr><td></td><td>SR ↑</td><td>LPIPS ↓</td><td>SR ↑</td><td>LPIPS ↓</td></tr><tr><td>Imagic w/ SD1.5</td><td>0.55</td><td>0.56</td><td>0.58</td><td>0.57</td></tr><tr><td>LEDITS++ w/ SD1.5</td><td>0.75</td><td>0.28</td><td>0.79</td><td>0.30</td></tr><tr><td>Imagic w/Imagen [18]</td><td>0.83</td><td>0.59</td><td>—</td><td>—</td></tr><tr><td>LEDITS++ w/ SD-XL</td><td>0.84</td><td>0.33</td><td>0.87</td><td>0.34</td></tr></table>",
+        "bbox": [
+            513,
+            88,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Table 2. Success rate (SR) and LPIPS scores on the original TedBench [18] and our revised version (TEDBench++) We compare Imagic to LEDs++ based on different DMs and find the latter to outperform on both metrics and benchmarks.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Since both are not publicly available, we can only compare to this specific combination of DM and editing method using Kawar et al.'s [18] curated outputs for TEdBench. Additionally, we, therefore, cannot combine LEDs++ with Imagen[37] and instead use a similarly advanced diffusion model, SD-XL [32]. However, to not only compete for the best fidelity outputs but focus the evaluation on methodological differences—not the pre-trained DM—we also compare both methods implemented with SD1.5. We provide further details in App. C.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "LEDS  $^{+ + }$  edits images reliably. We first asked users to assess the overall success of edits, i.e., if an edit instruction was faithfully realized for a given input image. The results in Tab. 2 show that LEDs  $^{+ + }$  outperforms Imagc on TEdBench despite a greatly reduced runtime (Tab. 1). The difference is even stronger when comparing both methods on the same pre-trained DM, i.e., SD1.5. The high success rate on TEdBench  $^{+ + }$ $(87\\%)$  and the examples shown in Fig. 1 and 6a once again highlight LEDs  $^{+ + }$ 's versatility. Overall, our proposed method can reliably perform a diverse set of editing instructions for real images.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "High-quality edits with LEDs++. While investigating both methods' performance we observed a substantial difference in edit quality. The examples in Fig. 6b particularly highlight the discrepancy in compositional robustness and object coherence. Hence, we also assessed both methods' editing quality on TEdBench++. We focus on samples where both methods performed a successful edit, i.e., were labeled as successful by users. We show the perceptual similarity (LPIPS) to the input image in Tab. 2. One can observe that the LPIPS scores for LEDs++ are much lower than for Imagic, empirically supporting the qualitative examples in Fig. 6b. When manually inspecting the generated images, we often found Imagic to generate a completely new image based on the edit instruction, entirely disregarding the input image (cf. App. Fig. 11a).",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "7. Discussion",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Let us now discuss open research questions and limitations.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Model Dependency. While LEDs++ achieves impressive results on a large variety of image manipulation tasks, there are external factors to consider. Since the",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "page_footnote",
+        "text": "3 https://huggingface.co/datasets/AIML-TUDA/TEdBench_plusplus",
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "page_number",
+        "text": "8867",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/be4dfb3e9df3f04561b13dffc758c1f1e4f3c2a54aa97cbf03fd80af2b3c79db.jpg",
+        "image_caption": [
+            "(a) Novel challenging examples of TEdBench++ and LEDs++ applied, showcasing the versatility of supported edits."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/80bbbd9c3d251bbf51c623aac6607686525a4f1e1fe8d544eeb4757123cb27e6.jpg",
+        "image_caption": [
+            "(b) Qualitative comparison of LEDs++ and Imagic on TEd-Bench, clearly highlighting the performance improvement.",
+            "Figure 6. Benchmark examples for LEDs++ and Imagc on TEdBench  $(++)$  . (Best viewed in color)"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "method is architecture-agnostic, it can be easily used with any DM. At the same time, the general editing quality strongly depends on the overall capabilities of the underlying pre-trained DM. Naturally, more capable models will also enable better edits. But, at times, specific editing instructions may fail because the used DM does not have a decent representation of the targeted concept to begin with. One example is the model failing to edit a giraffe to be sitting since the underlying DM generally fails to generate this pose (cf. App. F). This effect can also clearly be seen in Tab. 2, with the editing success rate of a method varying strongly between DMs. Although the same image editing method is employed (LEDITS++, the more capable SD-XL variant outperforms the weaker SD1.5 model. Nonetheless, this means that the architecture-agnostic LEDs++ will benefit from increasingly powerful DMs.",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Coherence Trade-offs. Next to the benefits of LEDs++'s semantic grounding, there are also downsides to this approach. Overall, implicit masking limits changes to relevant portions of the image and achieves strong coherence with the original image composition. Yet, the object and its identity within the masked area may change based on various factors. Generic prompts, like \"a standing cat\" (cf. App. F), do not contain detailed information about this specific object (\"cat\"). Thus, an edit with this prompt does not guarantee to preserve object identity, particularly for strong hyperparameters. We observed that fine-tuning approaches like Imagic make the opposite trade-off, better preserving the object identity while changing the background and image composition substantially (cf. App. F). A potential remedy for a loss in object coherence with LEDs++, is more descriptive edit prompting, e.g. using textual inversion [12].",
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+    {
+        "type": "text",
+        "text": "Lastly, the automatically-inferred implicit masks allow for easy use of LEDs++ without users tediously providing masks. Nonetheless, user intentions are diverse and cannot always be automatically inferred. Sometimes, in-",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "individual user masks provide better control over the editing process. Such user masks can be easily integrated into LEDs++ (cf. App. F), wherefore we encourage future research in this promising direction.",
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+    {
+        "type": "text",
+        "text": "Societal Impact. LEDs++ is an easy-to-use image editing technique that lowers the barrier for users and puts them in control for fruitful human-machine collaboration. Yet, the underlying text-to-image models offer both promise and peril, as highlighted by prior research [4, 11]. The (societal) biases within these models will also impact image editing applications [11]. Moreover, image manipulation can also be used adversarially to generate inappropriate [39] or fake content. Hence, we advocate for a cautious deployment of generative models together with image editing methods.",
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+    {
+        "type": "text",
+        "text": "8. Conclusion",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We introduced LEDs++, an efficient yet versatile and precise method for textual image manipulation with diffusion models. It facilitates the editing of complex concepts in real images. Our approach requires no finetuning nor optimization, can be computed extremely efficiently, and is architecture agnostic. At the same time, it perfectly reconstructs an input image and uses implicit masking to limit changes to relevant image regions, thus editing precisely. Our large experimental evaluation confirms the efficiency, versatility, and precision of LEDs++ and its components, as well as its benefits over several related methods.",
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+    },
+    {
+        "type": "text",
+        "text": "Acknowledgements We gratefully acknowledge support from the BMBF (Grant No 01IS22091). This work benefited from the ICT-48 Network of AI Research Excellence Center \"TAILOR\" (EU Horizon 2020, GA No 952215), the Hessian research priority program LOEWE within the project WhiteBox, the HMWK cluster projects \"Adaptive Mind\" and \"Third Wave of AI\", and from the NHR4CES.",
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+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
+            78,
+            89,
+            174,
+            106
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
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2024/LEDITS++_ Limitless Image Editing using Text-to-Image Models/f8bff481-3f32-424c-92f1-b66a29a1df02_model.json

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+    [
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+            "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "angle": 0,
+            "content": "LEDS: Limitless Image Editing using Text-to-Image Models"
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+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": "Figure 1. LEDs++ facilitates versatile image-to-image editing. Several complex cases are available now."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "angle": 0,
+            "content": "Abstract"
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+            "bbox": [
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+            "angle": 0,
+            "content": "Text-to-image diffusion models have recently received increasing interest for their astonishing ability to produce high-fidelity images from solely text inputs. Subsequent research efforts aim to exploit and apply their capabilities to real image editing. However, existing image-to-image methods are often inefficient, imprecise, and of limited versatility. They either require time-consuming fine-tuning, deviate unnecessarily strongly from the input image, and/or lack support for multiple, simultaneous edits. To address these issues, we introduce LEDs++, an efficient yet versatile and precise textual image manipulation technique. LEDs++'s novel inversion approach requires no tuning nor optimization and produces high-fidelity results with a few diffusion steps. Second, our methodology supports multiple simultaneous edits and is architecture-agnostic. Third, we use a novel implicit masking technique that limits changes to relevant image regions. We propose the novel TEdBench++ benchmark as part of our exhaustive evaluation. Our results demonstrate the capabilities of LEDs++ and its improvements over previous methods."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "angle": 0,
+            "content": "1. Introduction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.871,
+                0.47,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Text-to-image diffusion models (DM) have garnered recognition for their ability to generate high-quality images from"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.473,
+                0.892,
+                0.684
+            ],
+            "angle": 0,
+            "content": "textual descriptions. A growing body of research has recently been dedicated to utilizing these models for manipulating real images. However, several barriers prevent many real-world applications of diffusion-based image editing. Current methods often entail computationally expensive model tuning or other optimization, presenting practical challenges [6, 18, 28, 30, 44]. Additionally, existing techniques have the proclivity to induce profound changes to the original image [17, 26], often resulting in completely different images. Lastly, all these approaches are inherently constrained when editing multiple (arbitrary) concepts simultaneously. We tackle these problems by introducing LEDs++\\(^{1}\\), a diffusion-based image editing technique addressing these limitations."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": "LEDITS++<sup>2</sup> offers a streamlined approach for textual image editing, eliminating the need for extensive parameter tuning. To this end, we derive image inversion for a more efficient diffusion sampling algorithm to a) drastically reduce computational resources and b) guarantee perfect image reconstruction. Thus, we overcome computational obstacles and avoid changes in the edited image in the first place. Furthermore, we use a novel implicit masking approach to semantically ground each edit instruction to its relevant image region. This further optimizes changes to the image by retaining the overall image composition and object identity."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.52,
+                0.863,
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+            ],
+            "angle": 0,
+            "content": "*Equal contribution †Partially as research intern at Adobe"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.52,
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+                0.852,
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+            ],
+            "angle": 0,
+            "content": "1LEDITS++ stands for Limitless Edits with sde-dpm-solver++."
+        },
+        {
+            "type": "text",
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+            "angle": 0,
+            "content": "2https://huggingface.co/spaces/leditsplusplus/project"
+        },
+        {
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+        },
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+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.08,
+                0.092,
+                0.468,
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+            ],
+            "angle": 0,
+            "content": "Additionally, LEDs++ is the only method to date to facilitate easy and versatile image editing by supporting multiple simultaneous instructions without causing undue interference. Finally, its lightweight architecture-agnostic nature ensures compatibility with both latent and pixel-based diffusion models, providing high accessibility."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.08,
+                0.183,
+                0.468,
+                0.362
+            ],
+            "angle": 0,
+            "content": "In this work, we establish the methodical benefits of LEDs++ and demonstrate that this intuitive, lightweight approach offers sophisticated semantic control for image editing. Specifically, we contribute by (i) devising a formal definition of LEDs++ while (ii) deriving perfect inversion for a more efficient diffusion sampling method, (iii) qualitatively and empirically demonstrating its efficiency, versatility, and precision, (iv) providing an exhaustive empirical comparison to concurrent works with automatic and human user metrics, and thereby (v) introducing Textual Editing Benchmark++ (TEdBench++, a more holistic and coherent testbed for evaluating textual image manipulation."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "angle": 0,
+            "content": "2. Background"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.08,
+                0.403,
+                0.468,
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+            ],
+            "angle": 0,
+            "content": "Recently, large-scale, text-guided DMs have enabled versatile applications in image generation [3, 33, 37]. Especially latent diffusion models [31, 34] have gained attention for their computational efficiency. Below, we discuss related work for efficient, versatile image manipulation with DMs."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.08,
+                0.479,
+                0.468,
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+            ],
+            "angle": 0,
+            "content": "Diffusion Sampling. Generating outputs with DMs requires multiple iterative denoising steps that constitute the main bottleneck at inference. Commonly used sampling methods such as DDPM [15] or DDIM [42] require tens or hundreds of steps to produce high-quality samples. Consequently, numerous works have been dedicated to speeding up the sampling process without loss in quality. Distillation efforts progressively reduce the number of required steps through further training [25, 27]. Other works focus on improving the sampling itself, e.g. using high-order ODE-solvers [22, 23, 46]. Such solvers can be readily combined with pre-trained DMs at inference to lower the number of denoising steps. With LEDs++, we derive perfect image inversion with the DPM-Solver++, allowing image editing in as few as 20 total steps."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.08,
+                0.705,
+                0.468,
+                0.9
+            ],
+            "angle": 0,
+            "content": "Semantic Control during Diffusion. While text-to-image DMs generate new, astonishing images, fine-grained control over the generative process remains challenging. Minor changes to the text prompt lead to entirely different outputs. Wu et al. [45] studied concept disentanglement using linear combinations of text embeddings to gain semantic control. Methods like Prompt-to-Prompt [14] and other works [8, 30] utilize the DM's attention layers to attribute pixels to tokens from the text prompt. Dedicated operations on the attention maps enable more control over the generated images. Other works have focused on the noise estimates of DMs [5, 20] providing semantic control over the generation process. With LEDs++, we now enable"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.504,
+                0.092,
+                0.89,
+                0.121
+            ],
+            "angle": 0,
+            "content": "fine-grained semantic control for manipulating real images, going beyond purely generative applications."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.504,
+                0.122,
+                0.89,
+                0.348
+            ],
+            "angle": 0,
+            "content": "Real Image Editing. Since DMs' rise in popularity for text-to-image generation, they have also been explored for (real) image-to-image editing. As a first, simple approach, SDEdit added noise to the image for an intermediate step in the diffusion process [26]. While lightweight, the resulting image diverges substantially from the input as it is (partially) regenerated. Inpainting allows to keep the change small by having a user provide additional masks to restrict changes to certain image regions [2, 29]. Yet, user masks are costly or often simply unavailable. Other works have thus explored semantically grounded approaches using cross-attention instead to better control image manipulation [7, 28, 30]. In contrast, LEDs++ leverages both attention-and noise-based masking to obtain fine-grained masks, enabling strong semantic control over real images."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.504,
+                0.349,
+                0.89,
+                0.665
+            ],
+            "angle": 0,
+            "content": "Another important aspect of image manipulation methods is the required tuning and overall runtime. Instruct-Pix2Pix continues training a DM at scale to enable image editing capabilities [6]. Finetuning instead on each individual input to constrain the generation on the real image has shown helpful [18, 44] but not computationally efficient. Consequently, recent works have largely relied on inverting the deterministic DDIM sampling process [42] to save computational resources. DDIM inversion identifies an initial noise vector that results in the input image when denoised again. However, faithful reconstructions are only obtained in the limit of small steps, thus requiring large numbers of inversion steps. Moreover, small errors will still incur at each timestep, often accumulating into meaningful deviations from the input, requiring costly error correction through optimization [28, 30]. Recently, Huberman-Spiegelglas et al. proposed an inversion technique [17] for the DDPM sampler [15] to address the limitations of DDIM inversion. LEDs++ provides the same guarantees of perfect inversion with even further reduced runtime alongside an edit-friendly latent space, enabling more versatility."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.504,
+                0.679,
+                0.872,
+                0.696
+            ],
+            "angle": 0,
+            "content": "3. Image Editing with Text-to-Image Models"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.504,
+                0.705,
+                0.89,
+                0.9
+            ],
+            "angle": 0,
+            "content": "Before devising the methodology of LEDs++, let us first motivate the desired features and use cases. Specifically, we aim for efficiency, versatility, and precision. The goal is to provide a method that enables a fast exploratory workflow for image editing in which a user can iteratively interact with the model and explore various edits. Consequently, LEDs++ produces outputs quickly with no tuning or optimization to not disrupt the creative process. Further, arbitrary editing instructions and combinations thereof are supported to facilitate a wide range of image manipulations (e.g., complex multi-editing). Lastly, we provide precise and sophisticated semantic control over the image editing. Each of the (potentially multiple) edit instruc"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.485,
+                0.947,
+                0.514,
+                0.956
+            ],
+            "angle": 0,
+            "content": "8862"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.092,
+                0.47,
+                0.138
+            ],
+            "angle": 0,
+            "content": "tions can be steered individually, and changes are automatically restricted to relevant image regions. Importantly, with LEDs++ we prioritize compositional robustness."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.146,
+                0.308,
+                0.16
+            ],
+            "angle": 0,
+            "content": "3.1. Guided Diffusion Models"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.169,
+                0.469,
+                0.244
+            ],
+            "angle": 0,
+            "content": "Let us first define some general background for diffusion models. DMs iteratively denoise a Gaussian distributed variable to produce samples of a learned data distribution. Let's consider a diffusion process that gradually turns an image \\( x_0 \\) into Gaussian noise."
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.115,
+                0.254,
+                0.469,
+                0.273
+            ],
+            "angle": 0,
+            "content": "\\[\nx _ {t} = \\sqrt {1 - \\beta_ {t}} x _ {t - 1} + \\sqrt {\\beta_ {t}} n _ {t}, \\quad t = 1, \\dots , T \\tag {1}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.282,
+                0.469,
+                0.313
+            ],
+            "angle": 0,
+            "content": "where \\( n_t \\) are iid normal distributed vectors and \\( \\beta_t \\) a variance schedule. The diffusion process is equivalently expressed as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.183,
+                0.321,
+                0.469,
+                0.339
+            ],
+            "angle": 0,
+            "content": "\\[\nx _ {t} = \\sqrt {\\bar {\\alpha} _ {t}} x _ {0} + \\sqrt {1 - \\bar {\\alpha} _ {t}} \\epsilon_ {t} \\tag {2}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.348,
+                0.469,
+                0.438
+            ],
+            "angle": 0,
+            "content": "where \\(\\alpha_{t} = 1 - \\beta_{t}\\), \\(\\bar{\\alpha}_{t} = \\Pi_{s=1}^{t} \\alpha_{s}\\) and \\(\\epsilon_{t} \\sim \\mathcal{N}(0, \\mathbf{I})\\). Importantly, all \\(\\epsilon_{t}\\) are not statistically independent. Instead, consecutive pairs \\(\\epsilon_{t}, \\epsilon_{t-1}\\) are strongly dependent, which will be relevant later. To generate an (new) image \\(\\hat{x}_{0}\\) the reverse diffusion process starts from random noise \\(x_{T} \\sim \\mathcal{N}(0, \\mathbf{I})\\) which can be iteratively denoised as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.14,
+                0.449,
+                0.469,
+                0.465
+            ],
+            "angle": 0,
+            "content": "\\[\nx _ {t - 1} = \\hat {\\mu} _ {t} \\left(x _ {t}\\right) + \\sigma_ {t} z _ {t}, \\quad t = T, \\dots , 1 \\tag {3}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.475,
+                0.469,
+                0.505
+            ],
+            "angle": 0,
+            "content": "Here \\( z_{t} \\) are iid standard normal vectors, and common variance schedulers \\( \\sigma_{t} \\) can be expressed in the general form"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.207,
+                0.513,
+                0.339,
+                0.544
+            ],
+            "angle": 0,
+            "content": "\\[\n\\sigma_ {t} = \\eta \\beta_ {t} \\frac {1 - \\bar {\\alpha} _ {t - 1}}{1 - \\bar {\\alpha} _ {t}}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.552,
+                0.469,
+                0.599
+            ],
+            "angle": 0,
+            "content": "where \\(\\eta \\in [0,1]\\). In this formulation, \\(\\eta = 0\\) corresponds to the deterministic DDIM [42] and \\(\\eta = 1\\) to the DDPM scheme [15]. Lastly, in theses cases, we have \\(\\hat{\\mu}_t(x_t) =\\)"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.09,
+                0.607,
+                0.455,
+                0.641
+            ],
+            "angle": 0,
+            "content": "\\[\n\\sqrt {\\bar {\\alpha} _ {t - 1}} \\frac {x _ {t} - \\sqrt {1 - \\bar {\\alpha} _ {t}} \\hat {\\epsilon} _ {\\theta} (x _ {t})}{\\sqrt {\\bar {\\alpha} _ {t}}} + \\sqrt {1 - \\bar {\\alpha} _ {t - 1} - \\sigma_ {t} ^ {2}} \\hat {\\epsilon} _ {\\theta} (x _ {t})\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.649,
+                0.469,
+                0.77
+            ],
+            "angle": 0,
+            "content": "Here \\(\\hat{\\epsilon}_{\\theta}(x_{t})\\) is an estimate of \\(\\epsilon_{t}\\) produced by our neural network DM with learned parameters \\(\\theta\\), commonly implemented as a U-Net [35]. For text-to-image generation, the model is conditioned on a text prompt \\(p\\) to produce images faithful to that prompt. The DM is trained to produce the noise estimate \\(\\hat{\\epsilon}_{\\theta}(x_{t})\\) needed for iteratively sampling \\(\\hat{x}_0\\) (Eq. 3). For text-conditioned DMs, \\(\\hat{\\epsilon}_{\\theta}\\) is calculated using specific guidance techniques."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.77,
+                0.469,
+                0.876
+            ],
+            "angle": 0,
+            "content": "Most DMs rely on classifier-free guidance [16], a conditioning method using a purely generative diffusion model, eliminating the need for an additional classifier. During training, the text conditioning \\( c_{p} \\) is randomly dropped with a fixed probability, resulting in a joint model for unconditional and conditional objectives. During inference, the score estimates for the \\( \\epsilon \\)-prediction are adjusted so that:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.117,
+                0.885,
+                0.469,
+                0.903
+            ],
+            "angle": 0,
+            "content": "\\[\n\\hat {\\epsilon} _ {\\theta} \\left(x _ {t}, c _ {p}\\right) := \\hat {\\epsilon} _ {\\theta} \\left(x _ {t}\\right) + s _ {g} \\left(\\hat {\\epsilon} _ {\\theta} \\left(x _ {t}, c _ {p}\\right) - \\hat {\\epsilon} _ {\\theta} \\left(x _ {t}\\right)\\right) \\tag {4}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.092,
+                0.892,
+                0.153
+            ],
+            "angle": 0,
+            "content": "with guidance scale \\( s_g \\) and \\( \\hat{\\epsilon}_{\\theta} \\) defining the noise estimate with parameters \\( \\theta \\). Intuitively, the unconditioned \\( \\epsilon \\)-prediction is pushed in the direction of the conditioned one, with \\( s_g \\) determining the extent of the adjustment."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.161,
+                0.613,
+                0.175
+            ],
+            "angle": 0,
+            "content": "3.2.LEDITS++"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.184,
+                0.892,
+                0.244
+            ],
+            "angle": 0,
+            "content": "With the fundamentals established, the methodology of LEDs++ can now be broken down into three components: (1) efficient image inversion, (2) versatile textual editing, and (3) semantic grounding of image changes."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.245,
+                0.892,
+                0.365
+            ],
+            "angle": 0,
+            "content": "Component 1: Perfect Inversion. Utilizing text-to-image models for editing real images requires conditioning the generation on the input image. Recent works have largely relied on inverting the sampling process to identify \\( x_{T} \\) that will be denoised to the input image \\( x_{0} \\) [28, 30]. Inverting the DDPM scheduler is generally preferred over DDIM inversion since the former can be achieved in fewer timesteps and with no reconstruction error [17]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.366,
+                0.892,
+                0.547
+            ],
+            "angle": 0,
+            "content": "However, there exist more efficient schemes than DDPM for sampling DMs that greatly reduce the required number of steps and consequently DM evaluations. We here propose a more efficient inversion method by deriving the desired inversion properties for such a scheme. As demonstrated by Song et al.[43], DDPM can be viewed as a first-order stochastic differential equation (SDE) solver when formulating the reverse diffusion process as an SDE. This SDE can be solved more efficiently—in fewer steps—using a higher-order differential equation solver, here dpmsolver++ [23]. The reverse diffusion process from Eq. 3 for the second-order sde-dpm-solver++ can be written as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.544,
+                0.558,
+                0.891,
+                0.573
+            ],
+            "angle": 0,
+            "content": "\\[\nx _ {t - 1} = \\hat {\\mu} _ {t} \\left(x _ {t}, x _ {t + 1}\\right) + \\sigma_ {t} z _ {t}, \\quad t = T, \\dots , 1 \\tag {5}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.585,
+                0.578,
+                0.597
+            ],
+            "angle": 0,
+            "content": "where now"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.587,
+                0.606,
+                0.805,
+                0.626
+            ],
+            "angle": 0,
+            "content": "\\[\n\\sigma_ {t} = \\sqrt {1 - \\bar {\\alpha} _ {t - 1}} \\sqrt {1 - e ^ {- 2 h _ {t - 1}}}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.636,
+                0.89,
+                0.667
+            ],
+            "angle": 0,
+            "content": "and higher-order \\(\\hat{\\mu}_t\\) depends now on \\(x\\) from two timesteps, \\(x_t\\) and \\(x_{t + 1}\\). Such that \\(\\hat{\\mu}_t(x_t,x_{t + 1}) =\\)"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.518,
+                0.676,
+                0.873,
+                0.743
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} \\frac {\\sqrt {1 - \\bar {\\alpha} _ {t - 1}}}{\\sqrt {1 - \\bar {\\alpha} _ {t}}} e ^ {- h _ {t - 1}} x _ {t} + \\sqrt {\\bar {\\alpha} _ {t - 1}} \\left(1 - e ^ {- 2 h _ {t - 1}}\\right) \\hat {\\epsilon} _ {\\theta} (x _ {t}) \\\\ + 0. 5 \\sqrt {\\bar {\\alpha} _ {t - 1}} \\left(1 - e ^ {- 2 h _ {t - 1}}\\right) \\frac {- h _ {t}}{h _ {t - 1}} \\left(\\hat {\\epsilon} _ {\\theta} \\left(x _ {t + 1}\\right) - \\hat {\\epsilon} _ {\\theta} \\left(x _ {t}\\right)\\right) \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.501,
+                0.751,
+                0.535,
+                0.764
+            ],
+            "angle": 0,
+            "content": "with"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.568,
+                0.762,
+                0.824,
+                0.796
+            ],
+            "angle": 0,
+            "content": "\\[\nh _ {t} = \\frac {\\ln (\\sqrt {\\bar {\\alpha} _ {t}})}{\\ln (\\sqrt {1 - \\bar {\\alpha} _ {t}})} - \\frac {\\ln (\\sqrt {\\bar {\\alpha} _ {t + 1}})}{\\ln (\\sqrt {1 - \\bar {\\alpha} _ {t + 1}})}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.8,
+                0.892,
+                0.875
+            ],
+            "angle": 0,
+            "content": "For the detailed derivation of the solver and proof of faster convergence, we refer the reader to the relevant literature [22, 23]. Based on the above, we now devise our inversion process. Given an input image \\( x_0 \\) we construct an auxiliary reconstruction sequence of noise images \\( x_1, \\ldots, x_T \\) as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.606,
+                0.885,
+                0.891,
+                0.901
+            ],
+            "angle": 0,
+            "content": "\\[\nx _ {t} = \\sqrt {\\bar {\\alpha} _ {t}} x _ {0} + \\sqrt {1 - \\bar {\\alpha} _ {t}} \\tilde {\\varepsilon} _ {t} \\tag {6}\n\\]"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "8863"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.091,
+                0.47,
+                0.152
+            ],
+            "angle": 0,
+            "content": "where \\(\\tilde{\\epsilon}_t\\sim \\mathcal{N}(0,\\mathbf{I})\\). Contrary to Eq. 2, the \\(\\tilde{\\epsilon}_t\\) are now statistically independent, which is a desirable property for image editing [17]. Lastly, the respective \\(z_{t}\\) for the inversion can be derived from Eq. 5 as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.129,
+                0.162,
+                0.469,
+                0.194
+            ],
+            "angle": 0,
+            "content": "\\[\nz _ {t} = \\frac {x _ {t - 1} - \\hat {\\mu} _ {t} \\left(x _ {t} , x _ {t + 1}\\right)}{\\sigma_ {t}}, \\quad t = T,.., 1 \\tag {7}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.203,
+                0.469,
+                0.354
+            ],
+            "angle": 0,
+            "content": "with \\(\\hat{\\mu}\\) and \\(\\sigma_{t}\\) as defined above. We base our implementation on the multistep variant of sde-dpm-solver++, which only requires one evaluation of the DM at each diffusion timestep by reusing the estimates from the previous step. The number of timesteps can be reduced further by stopping the inversion at an intermediate step \\(t < T\\) and starting the generation at that step. Empirically, we observed that \\(t\\in [0.9T,0.8T]\\) usually produces edits of the same fidelity as \\(t = T\\), supporting observations in previous work [17, 26] that earlier timesteps are less relevant to the edit."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.355,
+                0.469,
+                0.476
+            ],
+            "angle": 0,
+            "content": "Component 2: Textual Editing. After creating our reconstruction sequence \\( x_{1}, \\ldots, x_{T} \\) and calculating the respective \\( z_{t} \\), we now edit the image by manipulating the noise estimate \\( \\hat{\\epsilon}_{\\theta} \\) based on a set of edit instructions \\( \\{e_i\\}_{i \\in I} \\). We devise a dedicated guidance term for each concept \\( e_{i} \\) based on conditioned and unconditioned estimates. Let us formally define LEDs++'s guidance by starting with a single editing prompt \\( e \\). We compute"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.166,
+                0.487,
+                0.469,
+                0.503
+            ],
+            "angle": 0,
+            "content": "\\[\n\\hat {\\epsilon} _ {\\theta} \\left(x _ {t}, c _ {e}\\right) := \\hat {\\epsilon} _ {\\theta} \\left(x _ {t}\\right) + \\gamma \\left(x _ {t}, c _ {e}\\right) \\tag {8}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.514,
+                0.469,
+                0.59
+            ],
+            "angle": 0,
+            "content": "with guidance term \\(\\gamma\\). Consequently, setting \\(\\gamma = 0\\) will reconstruct the input image \\(x_0\\). We construct \\(\\gamma\\) to push the unconditioned score estimate \\(\\hat{\\epsilon}_{\\theta}(x_t)\\) —i.e. the input image reconstruction—away from/towards the edit concept estimate \\(\\hat{\\epsilon}_{\\theta}(x_t, c_e)\\), depending on the guidance direction:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.164,
+                0.602,
+                0.469,
+                0.618
+            ],
+            "angle": 0,
+            "content": "\\[\n\\gamma \\left(x _ {t}, c _ {e}\\right) = \\phi (\\psi ; s _ {e}, \\lambda) \\psi \\left(x _ {t}, c _ {e}\\right) \\tag {9}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.629,
+                0.469,
+                0.66
+            ],
+            "angle": 0,
+            "content": "where \\(\\phi\\) applies an edit guidance scale \\(s_e\\) element-wise, and \\(\\psi\\) depends on the edit direction: \\(\\psi(x_t, c_e) =\\)"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.106,
+                0.671,
+                0.469,
+                0.71
+            ],
+            "angle": 0,
+            "content": "\\[\n\\left\\{ \\begin{array}{l} \\hat {\\epsilon} _ {\\theta} \\left(x _ {t}, c _ {e}\\right) - \\hat {\\epsilon} _ {\\theta} \\left(x _ {t}\\right) \\quad \\text {i f p o s . g u i d a n c e} \\\\ - \\left(\\hat {\\epsilon} _ {\\theta} \\left(x _ {t}, c _ {e}\\right) - \\hat {\\epsilon} _ {\\theta} \\left(x _ {t}\\right)\\right) \\quad \\text {i f n e g . g u i d a n c e} \\end{array} \\right. \\tag {10}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.72,
+                0.469,
+                0.87
+            ],
+            "angle": 0,
+            "content": "Thus, changing the guidance direction is reflected by the direction between \\(\\hat{\\epsilon}_{\\theta}(x_t,c_e)\\) and \\(\\hat{\\epsilon}_{\\theta}(x_t)\\). The term \\(\\phi\\) identifies those dimensions of the image and respective \\(\\hat{\\epsilon}_{\\theta}\\) that are relevant to a prompt \\(e\\). Consequently, \\(\\phi\\) returns 0 for all irrelevant dimensions and a scaling factor \\(s_e\\) for the others. We describe the construction of \\(\\phi\\) in detail below. Larger \\(s_e\\) will increase the effect of the edit, and \\(\\lambda \\in (0,1)\\) reflects the percentage of the pixels selected as relevant by \\(\\phi\\). Notably, for a single concept \\(e\\) and uniform \\(\\phi = s_e\\), Eq. 8 generalizes to the classifier-free guidance term in Eq. 4."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.871,
+                0.469,
+                0.902
+            ],
+            "angle": 0,
+            "content": "For multiple \\( e_i \\), we calculate \\( \\gamma_t^i \\) as described above, with each defining their own hyperparameter values \\( \\lambda^i \\), \\( s_e^i \\). The"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.091,
+                0.654,
+                0.107
+            ],
+            "angle": 0,
+            "content": "sum of all \\(\\gamma_t^i\\) results in"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.59,
+                0.116,
+                0.892,
+                0.141
+            ],
+            "angle": 0,
+            "content": "\\[\n\\hat {\\gamma} _ {t} \\left(x _ {t}, c _ {e _ {i}}\\right) = \\sum_ {i \\in I} \\gamma_ {t} ^ {i} \\left(x _ {t}, c _ {e _ {i}}\\right) \\tag {11}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.147,
+                0.892,
+                0.193
+            ],
+            "angle": 0,
+            "content": "Component 3: Semantic Grounding. The masking term \\(\\phi\\) (Eq. 9) is the intersection (pointwise product) of binary masks \\(M^1\\) and \\(M^2\\) combined with scaling factor \\(s_e\\):"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.609,
+                0.201,
+                0.892,
+                0.218
+            ],
+            "angle": 0,
+            "content": "\\[\n\\phi (\\psi ; s _ {e _ {i}}, \\lambda) = s _ {e _ {i}} M _ {i} ^ {1} M _ {i} ^ {2} \\tag {12}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.227,
+                0.892,
+                0.422
+            ],
+            "angle": 0,
+            "content": "where \\( M_{i}^{1} \\) is a binary mask generated from the U-Net's cross-attention layers and \\( M_{i}^{2} \\) is a binary mask derived from the noise estimate. Intuitively, each mask is an importance map, where \\( M_{i}^{1} \\) is more strongly grounded than \\( M_{i}^{2} \\), but of significantly coarser granularity. Therefore, the intersection of the two yields a mask both focused on relevant image regions and of fine granularity. With LEDs++, we empirically demonstrate that these maps can also capture regions of an image relevant to an editing concept that is not already present. Specifically for multiple edits, calculating a dedicated mask for each edit prompt ensures that the corresponding guidance terms remain largely isolated, limiting interference between them."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.424,
+                0.892,
+                0.606
+            ],
+            "angle": 0,
+            "content": "Formally, at each time step \\( t \\), a U-Net forward pass with editing prompt \\( e_i \\) is performed to generate cross-attention maps for each token of the editing prompt. All cross-attention maps of the smallest resolution (e.g., \\( 16 \\times 16 \\) for SD) are averaged over all heads and layers, and the resulting maps are summed over all editing tokens, resulting in a single map \\( A_t^{e_i} \\in R^{16 \\times 16} \\). Importantly, we utilize the same U-Net evaluation \\( \\hat{\\epsilon}_{\\theta}(x_t, c_e) \\) already performed in Eq. 10 to produce \\( M^1 \\) with minimal overhead. Each map \\( A_t^{e_i} \\) is up-sampled to match the size of \\( x_t \\). Cross-attention mask \\( M^1 \\) is derived by calculating the \\( \\lambda \\)-th percentile of up-sampled \\( A_t^{e_i} \\) and"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.576,
+                0.614,
+                0.891,
+                0.655
+            ],
+            "angle": 0,
+            "content": "\\[\nM _ {i} ^ {1} = \\left\\{ \\begin{array}{l l} 1 & \\text {i f} \\left| A _ {t} ^ {e _ {i}} \\right| \\geq \\eta_ {\\lambda} \\left(\\left| A _ {t} ^ {e _ {i}} \\right|\\right) \\\\ 0 & \\text {e l s e} \\end{array} \\right. \\tag {13}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.663,
+                0.891,
+                0.708
+            ],
+            "angle": 0,
+            "content": "where \\(\\eta_{\\lambda}(|\\cdot|)\\) is the \\(\\lambda\\)-th percentile. By definition, \\(M^1\\) only selects image regions that correlate strongly with the editing prompt, and \\(\\lambda\\) determines the size of this selected region."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.709,
+                0.891,
+                0.8
+            ],
+            "angle": 0,
+            "content": "The fine-grained mask \\( M^2 \\) is calculated based on the guidance vector \\( \\psi \\) of noise estimates derived in Eq. 10. The difference between unconditioned and conditioned \\( \\hat{\\epsilon}_{\\theta} \\), generally captures outlines and object edges of \\( x_{t} \\). Consequently, the largest absolute values of \\( \\psi \\) provide meaningful segmentation information of fine granularity for \\( M^2 \\)"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.59,
+                0.808,
+                0.892,
+                0.848
+            ],
+            "angle": 0,
+            "content": "\\[\nM ^ {2} = \\left\\{ \\begin{array}{l l} 1 & \\text {i f} | \\psi | \\geq \\eta_ {\\lambda} (| \\psi |) \\\\ 0 & \\text {e l s e} \\end{array} \\right. \\tag {14}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.856,
+                0.892,
+                0.902
+            ],
+            "angle": 0,
+            "content": "In general, threshold \\(\\lambda\\) should correspond to the performed edit. Changes affecting the entire image, such as style transfer, should choose smaller \\(\\lambda (\\rightarrow 0)\\), whereas edits targeting"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.956
+            ],
+            "angle": 0,
+            "content": "8864"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.162,
+                0.089,
+                0.812,
+                0.266
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.272,
+                0.895,
+                0.302
+            ],
+            "angle": 0,
+            "content": "Figure 2. Comparison of image editing methods. (top) LEDs++ is the only method to restrict edits to the tree leaves and position of the car. (bottom) Ours is the only approach faithfully executing all three edits and keeping changes minimal. (Best viewed in color)"
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.162,
+                0.313,
+                0.812,
+                0.442
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Method</td><td>Reconstruction \nError (RMSE) ↓</td><td>Execution \nTime (s) ↓</td><td>Variation/ \nSampling</td><td>Semantic \nGrounding</td><td>Multi- \nEditing</td></tr><tr><td>SDEdit [26]</td><td>0.81 ±0.07</td><td>2.10 ±0.02</td><td>✓</td><td>X</td><td>X</td></tr><tr><td>Imagic [18]</td><td>0.58 ±0.12</td><td>349.98 ±0.45</td><td>✓</td><td>X</td><td>X</td></tr><tr><td>Vanilla DDIM Inversion</td><td>0.22 ±0.10</td><td>37.23 ±0.04</td><td>X</td><td>X</td><td>X</td></tr><tr><td>Pix2Pix-Zero [30]</td><td>0.20 ±0.09</td><td>56.78 ±0.14</td><td>(✓)</td><td>✓</td><td>X</td></tr><tr><td>DiffEdit [9]</td><td>0.13±0.03</td><td>27.65 ±0.03</td><td>✓</td><td>✓</td><td>X</td></tr><tr><td>Edit-friendly DDPM [17]</td><td>0.00</td><td>10.36 ±0.05</td><td>✓</td><td>X</td><td>X</td></tr><tr><td>LEDSITS++ (Ours)</td><td>0.00</td><td>1.78 ±0.03</td><td>✓</td><td>✓</td><td>✓</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.447,
+                0.893,
+                0.489
+            ],
+            "angle": 0,
+            "content": "Table 1. Comparing key properties for diffusion-based image editing techniques, with LEDs++ offering clear methodological benefits. Due to LEDs++'s efficient perfect inversion, it is the fastest and error-free method. At the same time, its methodology is the only enabling versatility in terms of variation, semantic grounding, and multi-editing. Subscript numbers indicate standard deviation."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.51,
+                0.47,
+                0.541
+            ],
+            "angle": 0,
+            "content": "specific objects or regions should use \\(\\lambda\\) proportional to the region's prominence in the image."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.557,
+                0.308,
+                0.574
+            ],
+            "angle": 0,
+            "content": "4. Properties of LEDs++"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.582,
+                0.47,
+                0.613
+            ],
+            "angle": 0,
+            "content": "With the fundamentals of LEDs++ established, we next showcase its unique properties and capabilities."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.614,
+                0.471,
+                0.854
+            ],
+            "angle": 0,
+            "content": "Efficiency. First off, LEDs++ offers substantial performance improvements over other image editing methods. In Tab. 1, we provide a qualitative runtime comparison, with all methods being implemented for Stable Diffusion (SD) 1.5 [34]. As a parameter-free approach, LEDs++ does not require any computationally expensive fine-tuning or optimization. Consequently, LEDs++ is orders of magnitude faster than methods like Imagic [18] or Pix2Pix-Zero [30]. Further, we only need to invert the same number of diffusion steps used at inference, which results in significant runtime improvements over the standard DDIM inversion (21x). In addition to efficient inversion, we use a recent, fast scheduler that generally requires fewer total steps, further boosting performance. This way, LEDs++ is six times faster than recent DDPM inversion [17] and on par with fast but poor-quality SDEdit [26]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.856,
+                0.47,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Versatility. In addition to its efficiency, LEDs++ remains versatile, enabling sheer limitless editing possibilities. In Fig. 1, we showcase a broad range of edit types."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.51,
+                0.892,
+                0.722
+            ],
+            "angle": 0,
+            "content": "LEDITS++ facilitates fine-grained edits (adding/removing glasses) and holistic changes such as style transfer (painting/sketch). Furthermore, object removal and replacement facilitate even more image editing tasks. Importantly, the overall image composition is preserved in all cases. To our knowledge, LEDs++ is the only diffusion-based image editing method inherently supporting multiple edits in isolation, which allows for more complex image manipulation. Fig. 2 highlights LEDs++ benefits over previous methods. Our method produces the highest edit fidelity and is the only approach capable of faithfully executing multiple, simultaneous instructions. Moreover, LEDs++ also makes the least changes to unrelated objects and the overall background and composition of the image."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.728,
+                0.892,
+                0.835
+            ],
+            "angle": 0,
+            "content": "Lastly, the editing versatility benefits from the stochastic nature of the perfect but non-deterministic inversion. LEDs++ provides meaningful image variations by resampling \\(\\tilde{c}_t\\). Additionally, the visual expression of each concept in the edited image scales monotonically with \\(s_e\\), and the direction and magnitude of each concept can be varied freely. We present examples of both features in App. B."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.84,
+                0.893,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Precision. Furthermore, LEDs++'s methodology keeps edits concise and avoids unnecessary deviations from the input image (Fig. 2). First, the perfect inversion will reconstruct the exact input image if no edit is applied (cf."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.956
+            ],
+            "angle": 0,
+            "content": "8865"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.119,
+                0.089,
+                0.43,
+                0.19
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.196,
+                0.471,
+                0.239
+            ],
+            "angle": 0,
+            "content": "Figure 3. Exemplary edit performed with LEDs++ in only 25 diffusion steps with SD1.5. We apply a complex, compounded edit and ground each to a semantically reasonable image region."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.253,
+                0.47,
+                0.451
+            ],
+            "angle": 0,
+            "content": "Sec. 3.2). Consequently, we already improve on faithfulness to the input image even before applying any edits. This benefit over other methods is highlighted by the reconstruction error in Tab. 1. Second, implicit masking will semantically ground each edit to relevant image regions. This is specifically important for editing multiple concepts at the same time. While other methods only utilize one prompt for all instructions, LEDs++ isolates edits from each other (Eq. 11). Thus, we get dedicated masks for each concept as shown in Fig. 3. This design ensures that each instruction (e.g., red mask for 'cherry blossom') will be only applied where necessary. Subsequently, we provide further evidence for the efficacy of LEDs++'s masking approach."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.466,
+                0.424,
+                0.484
+            ],
+            "angle": 0,
+            "content": "5. Semantically Grounded Image Editing"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.492,
+                0.47,
+                0.765
+            ],
+            "angle": 0,
+            "content": "Cross-attention maps of DMs have been used extensively to ground regions of interest during image generation semantically [7, 8, 14, 30]. Nonetheless, these have not been combined with noise-based masks so far and thus lack fine granularity. Hence, we empirically evaluate the quality of implicit masks, i.e., attention maps \\( M^1 \\) and noise maps \\( M^2 \\) (Eq. 13 and 14) in the LEDs++ setup. We use a broad segmentation task for common objects as a proxy to measure the performance of implicit masks in identifying relevant image areas from edit instructions. Specifically, we utilize segmentation masks from the COCO panoptic segmentation challenge [19]. For each unique object in an image, we retrieve the masks \\( M^1 \\), \\( M^2 \\), and their intersection per diffusion step. We use the (semantic) class label (e.g. 'person' or 'TV') as editing concept \\( e \\). We consider masks at each of 50 total diffusion steps without actually editing the input image. Furthermore, we approximate mask threshold \\( \\lambda \\) based on the relative size of an object's bounding box."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.765,
+                0.47,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Concise masks with LEDs++. Fig. 4 shows implicit masking as a reliable means to identify relevant image regions. Importantly, the intersection of both cross-attention masks \\( M^1 \\) and noise maps \\( M^2 \\) clearly outperforms each separate mask. The overall performance is even similar to a dedicated CLIPSeg model [24], despite LEDs++. masks being implicitly calculated at inference with only minimal overhead. At the same time, LEDs++.'s masking is superior to DiffEdit's [3]. Consequently, our method's inter"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.525,
+                0.093,
+                0.868,
+                0.23
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.237,
+                0.892,
+                0.293
+            ],
+            "angle": 0,
+            "content": "Figure 4. Semantic segmentation quality of LEDs++. We show the intersection over union (higher is better) for COCO panoptic segmentation. The intersection masks outperform each by a clear margin, close to the CLIPSeg reference. (Best viewed in color)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.308,
+                0.892,
+                0.355
+            ],
+            "angle": 0,
+            "content": "section of cross-attention masks and noise maps provides strong semantic grounding while being efficient during image manipulation to ensure precise editing."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.37,
+                0.742,
+                0.387
+            ],
+            "angle": 0,
+            "content": "6. Image Editing Evaluation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.396,
+                0.891,
+                0.427
+            ],
+            "angle": 0,
+            "content": "Let us now compare LEDs++ to current SOTA methods for image manipulation on two benchmarks."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.438,
+                0.74,
+                0.456
+            ],
+            "angle": 0,
+            "content": "6.1. Editing Multiple Concepts"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.462,
+                0.892,
+                0.734
+            ],
+            "angle": 0,
+            "content": "First, we investigate the complex task of performing multiple edits simultaneously. We rely on a well-established setup for semantic image manipulation [5] to evaluate multi-conditioned attribute manipulation in facial images. In our experiment, we consider 100 images from the CelebA dataset [21]. For each image, we simultaneously edit three attributes out of a set of five, leading to ten total combinations of edit concepts. Further, we perform each edit across ten different seeds, resulting in 10,000 evaluated images for each method and hyperparameter setting, over 1M images in total. As measures for comparison, we employ CLIP and LPIPS scores. CLIP measures the text-to-image similarity of the edit instruction to the edited image, and LPIPS measures the image-to-image similarity of the real to the edited image. This way, we assess the tradeoff between the versatility of edits (CLIP) and the precision of those manipulations (LPIPS). We implement all methods based on SD1.5 and provide more details in App. C."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.735,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "LEDS++ outperforms competing methods. Fig. 5 shows the resulting CLIP vs. LPIPS plots for all methods. The top left corner represents the ideal editing method with maximum edit alignment without deviating from the initial image. Generally, one can observe a natural trade-off between versatility and precision for all methods, i.e., higher image-to-text alignment comes at the expense of lower similarity to the original image. LEDS++ is closest to the ideal region and thus clearly outperforms the other methods. In particular, the outputs remain close to the original image (low LPIPS scores), thanks to the precise implicit masking."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.956
+            ],
+            "angle": 0,
+            "content": "8866"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.102,
+                0.092,
+                0.445,
+                0.271
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.275,
+                0.47,
+                0.358
+            ],
+            "angle": 0,
+            "content": "Figure 5. Comparison of instruction-alignment vs. image similarity trade-off for different editing methods. Results were reported for simultaneous manipulation of three facial attributes on CelebA. We plot CLIP scores (higher is better) of the target attributes against LPIPS similarity (lower is better). LEDs++ clearly outperforms all competing methods. (Best viewed in color)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.373,
+                0.473,
+                0.601
+            ],
+            "angle": 0,
+            "content": "At the same time, it faithfully performs the edits (high CLIP scores) due to the dedicated, isolated editing for each concept. The depicted scores reflect our qualitative inspections for Pix2Pix-Zero and Imagic on such complex manipulations (cf. Fig. 2). We observed that these methods often break—either failing to perform all three edits and/or drastically altering the input image. Only edit-friendly DDPM [17] and LEDs++ reliably achieve the maximum average CLIP score of over 0.25. This value seems to represent an upper bound according to our manual investigations, as each attribute is edited correctly for all input images, and higher scores are not observed. Despite being computationally very efficient, LEDs++ faithfully executes each edit instruction while keeping the changes to the input low, highlighting the method's versatility and precision."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.61,
+                0.228,
+                0.626
+            ],
+            "angle": 0,
+            "content": "6.2. TEDBench \\((++)\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.634,
+                0.47,
+                0.846
+            ],
+            "angle": 0,
+            "content": "Next, we investigate the versatility of LEDs++'s editing capabilities by running the Textual Editing Benchmark (TEDBench [18]), a collection of 100 input images paired with textual edit instructions. However, we observed a variety of inconsistencies in TEDBench and a lack of relevant editing tasks. Therefore, we propose TEDBench++ (Fig. 6a and App. D), a more challenging revised benchmark now containing 120 entries in total.<sup>3</sup> We addressed misspellings and rephrased ambiguous and inconclusive instructions. In addition to resolving these issues, we added instructions targeting challenging types of image manipulations previously not included in TEDBench: multi-conditioning, object/concept removal, style transfer, and complex replacements (Fig. 6a). We provide more details in App. D."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.847,
+                0.469,
+                0.876
+            ],
+            "angle": 0,
+            "content": "We compare LEDs++ on TEdBench \\((++)\\) to one of the strongest editing methods, Imagic [18] with Imagen [37]."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.514,
+                0.089,
+                0.878,
+                0.175
+            ],
+            "angle": 0,
+            "content": "<table><tr><td></td><td colspan=\"2\">TEDBench</td><td colspan=\"2\">TEDBench++</td></tr><tr><td></td><td>SR ↑</td><td>LPIPS ↓</td><td>SR ↑</td><td>LPIPS ↓</td></tr><tr><td>Imagic w/ SD1.5</td><td>0.55</td><td>0.56</td><td>0.58</td><td>0.57</td></tr><tr><td>LEDITS++ w/ SD1.5</td><td>0.75</td><td>0.28</td><td>0.79</td><td>0.30</td></tr><tr><td>Imagic w/Imagen [18]</td><td>0.83</td><td>0.59</td><td>—</td><td>—</td></tr><tr><td>LEDITS++ w/ SD-XL</td><td>0.84</td><td>0.33</td><td>0.87</td><td>0.34</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.499,
+                0.181,
+                0.892,
+                0.236
+            ],
+            "angle": 0,
+            "content": "Table 2. Success rate (SR) and LPIPS scores on the original TedBench [18] and our revised version (TEDBench++) We compare Imagic to LEDs++ based on different DMs and find the latter to outperform on both metrics and benchmarks."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.248,
+                0.892,
+                0.4
+            ],
+            "angle": 0,
+            "content": "Since both are not publicly available, we can only compare to this specific combination of DM and editing method using Kawar et al.'s [18] curated outputs for TEdBench. Additionally, we, therefore, cannot combine LEDs++ with Imagen[37] and instead use a similarly advanced diffusion model, SD-XL [32]. However, to not only compete for the best fidelity outputs but focus the evaluation on methodological differences—not the pre-trained DM—we also compare both methods implemented with SD1.5. We provide further details in App. C."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.401,
+                0.893,
+                0.568
+            ],
+            "angle": 0,
+            "content": "LEDS \\(^{+ + }\\) edits images reliably. We first asked users to assess the overall success of edits, i.e., if an edit instruction was faithfully realized for a given input image. The results in Tab. 2 show that LEDs \\(^{+ + }\\) outperforms Imagc on TEdBench despite a greatly reduced runtime (Tab. 1). The difference is even stronger when comparing both methods on the same pre-trained DM, i.e., SD1.5. The high success rate on TEdBench \\(^{+ + }\\) \\((87\\%)\\) and the examples shown in Fig. 1 and 6a once again highlight LEDs \\(^{+ + }\\)'s versatility. Overall, our proposed method can reliably perform a diverse set of editing instructions for real images."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.569,
+                0.892,
+                0.796
+            ],
+            "angle": 0,
+            "content": "High-quality edits with LEDs++. While investigating both methods' performance we observed a substantial difference in edit quality. The examples in Fig. 6b particularly highlight the discrepancy in compositional robustness and object coherence. Hence, we also assessed both methods' editing quality on TEdBench++. We focus on samples where both methods performed a successful edit, i.e., were labeled as successful by users. We show the perceptual similarity (LPIPS) to the input image in Tab. 2. One can observe that the LPIPS scores for LEDs++ are much lower than for Imagic, empirically supporting the qualitative examples in Fig. 6b. When manually inspecting the generated images, we often found Imagic to generate a completely new image based on the edit instruction, entirely disregarding the input image (cf. App. Fig. 11a)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.813,
+                0.614,
+                0.829
+            ],
+            "angle": 0,
+            "content": "7. Discussion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.84,
+                0.89,
+                0.854
+            ],
+            "angle": 0,
+            "content": "Let us now discuss open research questions and limitations."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.856,
+                0.892,
+                0.9
+            ],
+            "angle": 0,
+            "content": "Model Dependency. While LEDs++ achieves impressive results on a large variety of image manipulation tasks, there are external factors to consider. Since the"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.096,
+                0.887,
+                0.395,
+                0.9
+            ],
+            "angle": 0,
+            "content": "3 https://huggingface.co/datasets/AIML-TUDA/TEdBench_plusplus"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": "8867"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.084,
+                0.089,
+                0.526,
+                0.292
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.078,
+                0.294,
+                0.529,
+                0.32
+            ],
+            "angle": 0,
+            "content": "(a) Novel challenging examples of TEdBench++ and LEDs++ applied, showcasing the versatility of supported edits."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.568,
+                0.089,
+                0.891,
+                0.292
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.563,
+                0.294,
+                0.892,
+                0.32
+            ],
+            "angle": 0,
+            "content": "(b) Qualitative comparison of LEDs++ and Imagic on TEd-Bench, clearly highlighting the performance improvement."
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.184,
+                0.325,
+                0.785,
+                0.34
+            ],
+            "angle": 0,
+            "content": "Figure 6. Benchmark examples for LEDs++ and Imagc on TEdBench \\((++)\\) . (Best viewed in color)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.353,
+                0.473,
+                0.595
+            ],
+            "angle": 0,
+            "content": "method is architecture-agnostic, it can be easily used with any DM. At the same time, the general editing quality strongly depends on the overall capabilities of the underlying pre-trained DM. Naturally, more capable models will also enable better edits. But, at times, specific editing instructions may fail because the used DM does not have a decent representation of the targeted concept to begin with. One example is the model failing to edit a giraffe to be sitting since the underlying DM generally fails to generate this pose (cf. App. F). This effect can also clearly be seen in Tab. 2, with the editing success rate of a method varying strongly between DMs. Although the same image editing method is employed (LEDITS++, the more capable SD-XL variant outperforms the weaker SD1.5 model. Nonetheless, this means that the architecture-agnostic LEDs++ will benefit from increasingly powerful DMs."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.597,
+                0.47,
+                0.839
+            ],
+            "angle": 0,
+            "content": "Coherence Trade-offs. Next to the benefits of LEDs++'s semantic grounding, there are also downsides to this approach. Overall, implicit masking limits changes to relevant portions of the image and achieves strong coherence with the original image composition. Yet, the object and its identity within the masked area may change based on various factors. Generic prompts, like \"a standing cat\" (cf. App. F), do not contain detailed information about this specific object (\"cat\"). Thus, an edit with this prompt does not guarantee to preserve object identity, particularly for strong hyperparameters. We observed that fine-tuning approaches like Imagic make the opposite trade-off, better preserving the object identity while changing the background and image composition substantially (cf. App. F). A potential remedy for a loss in object coherence with LEDs++, is more descriptive edit prompting, e.g. using textual inversion [12]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.84,
+                0.471,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Lastly, the automatically-inferred implicit masks allow for easy use of LEDs++ without users tediously providing masks. Nonetheless, user intentions are diverse and cannot always be automatically inferred. Sometimes, in-"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.353,
+                0.892,
+                0.414
+            ],
+            "angle": 0,
+            "content": "individual user masks provide better control over the editing process. Such user masks can be easily integrated into LEDs++ (cf. App. F), wherefore we encourage future research in this promising direction."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.415,
+                0.893,
+                0.567
+            ],
+            "angle": 0,
+            "content": "Societal Impact. LEDs++ is an easy-to-use image editing technique that lowers the barrier for users and puts them in control for fruitful human-machine collaboration. Yet, the underlying text-to-image models offer both promise and peril, as highlighted by prior research [4, 11]. The (societal) biases within these models will also impact image editing applications [11]. Moreover, image manipulation can also be used adversarially to generate inappropriate [39] or fake content. Hence, we advocate for a cautious deployment of generative models together with image editing methods."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.584,
+                0.619,
+                0.6
+            ],
+            "angle": 0,
+            "content": "8. Conclusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.61,
+                0.892,
+                0.776
+            ],
+            "angle": 0,
+            "content": "We introduced LEDs++, an efficient yet versatile and precise method for textual image manipulation with diffusion models. It facilitates the editing of complex concepts in real images. Our approach requires no finetuning nor optimization, can be computed extremely efficiently, and is architecture agnostic. At the same time, it perfectly reconstructs an input image and uses implicit masking to limit changes to relevant image regions, thus editing precisely. Our large experimental evaluation confirms the efficiency, versatility, and precision of LEDs++ and its components, as well as its benefits over several related methods."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.796,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Acknowledgements We gratefully acknowledge support from the BMBF (Grant No 01IS22091). This work benefited from the ICT-48 Network of AI Research Excellence Center \"TAILOR\" (EU Horizon 2020, GA No 952215), the Hessian research priority program LOEWE within the project WhiteBox, the HMWK cluster projects \"Adaptive Mind\" and \"Third Wave of AI\", and from the NHR4CES."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
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+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "8868"
+        }
+    ],
+    [
+        {
+            "type": "title",
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2024/LEDITS++_ Limitless Image Editing using Text-to-Image Models/f8bff481-3f32-424c-92f1-b66a29a1df02_origin.pdf

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2024/LEDITS++_ Limitless Image Editing using Text-to-Image Models/full.md

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+# LEDS: Limitless Image Editing using Text-to-Image Models
+
+![](images/d8f7be564b6332796a8cb8adaad3a2d7a5f0c215956e770c5c1a33382a955dd0.jpg)
+
+![](images/fd68bca424e2d5b2224b8fd297e5ce3f861d71132db180895b57fbeebd7121b1.jpg)  
+Figure 1. LEDs++ facilitates versatile image-to-image editing. Several complex cases are available now.
+
+# Abstract
+
+Text-to-image diffusion models have recently received increasing interest for their astonishing ability to produce high-fidelity images from solely text inputs. Subsequent research efforts aim to exploit and apply their capabilities to real image editing. However, existing image-to-image methods are often inefficient, imprecise, and of limited versatility. They either require time-consuming fine-tuning, deviate unnecessarily strongly from the input image, and/or lack support for multiple, simultaneous edits. To address these issues, we introduce LEDs++, an efficient yet versatile and precise textual image manipulation technique. LEDs++'s novel inversion approach requires no tuning nor optimization and produces high-fidelity results with a few diffusion steps. Second, our methodology supports multiple simultaneous edits and is architecture-agnostic. Third, we use a novel implicit masking technique that limits changes to relevant image regions. We propose the novel TEdBench++ benchmark as part of our exhaustive evaluation. Our results demonstrate the capabilities of LEDs++ and its improvements over previous methods.
+
+# 1. Introduction
+
+Text-to-image diffusion models (DM) have garnered recognition for their ability to generate high-quality images from
+
+textual descriptions. A growing body of research has recently been dedicated to utilizing these models for manipulating real images. However, several barriers prevent many real-world applications of diffusion-based image editing. Current methods often entail computationally expensive model tuning or other optimization, presenting practical challenges [6, 18, 28, 30, 44]. Additionally, existing techniques have the proclivity to induce profound changes to the original image [17, 26], often resulting in completely different images. Lastly, all these approaches are inherently constrained when editing multiple (arbitrary) concepts simultaneously. We tackle these problems by introducing LEDs++ $^{1}$ , a diffusion-based image editing technique addressing these limitations.
+
+LEDITS++<sup>2</sup> offers a streamlined approach for textual image editing, eliminating the need for extensive parameter tuning. To this end, we derive image inversion for a more efficient diffusion sampling algorithm to a) drastically reduce computational resources and b) guarantee perfect image reconstruction. Thus, we overcome computational obstacles and avoid changes in the edited image in the first place. Furthermore, we use a novel implicit masking approach to semantically ground each edit instruction to its relevant image region. This further optimizes changes to the image by retaining the overall image composition and object identity.
+
+*Equal contribution †Partially as research intern at Adobe  
+1LEDITS++ stands for Limitless Edits with sde-dpm-solver++.  
+2https://huggingface.co/spaces/leditsplusplus/project
+
+Additionally, LEDs++ is the only method to date to facilitate easy and versatile image editing by supporting multiple simultaneous instructions without causing undue interference. Finally, its lightweight architecture-agnostic nature ensures compatibility with both latent and pixel-based diffusion models, providing high accessibility.
+
+In this work, we establish the methodical benefits of LEDs++ and demonstrate that this intuitive, lightweight approach offers sophisticated semantic control for image editing. Specifically, we contribute by (i) devising a formal definition of LEDs++ while (ii) deriving perfect inversion for a more efficient diffusion sampling method, (iii) qualitatively and empirically demonstrating its efficiency, versatility, and precision, (iv) providing an exhaustive empirical comparison to concurrent works with automatic and human user metrics, and thereby (v) introducing Textual Editing Benchmark++ (TEdBench++, a more holistic and coherent testbed for evaluating textual image manipulation.
+
+# 2. Background
+
+Recently, large-scale, text-guided DMs have enabled versatile applications in image generation [3, 33, 37]. Especially latent diffusion models [31, 34] have gained attention for their computational efficiency. Below, we discuss related work for efficient, versatile image manipulation with DMs.
+
+Diffusion Sampling. Generating outputs with DMs requires multiple iterative denoising steps that constitute the main bottleneck at inference. Commonly used sampling methods such as DDPM [15] or DDIM [42] require tens or hundreds of steps to produce high-quality samples. Consequently, numerous works have been dedicated to speeding up the sampling process without loss in quality. Distillation efforts progressively reduce the number of required steps through further training [25, 27]. Other works focus on improving the sampling itself, e.g. using high-order ODE-solvers [22, 23, 46]. Such solvers can be readily combined with pre-trained DMs at inference to lower the number of denoising steps. With LEDs++, we derive perfect image inversion with the DPM-Solver++, allowing image editing in as few as 20 total steps.
+
+Semantic Control during Diffusion. While text-to-image DMs generate new, astonishing images, fine-grained control over the generative process remains challenging. Minor changes to the text prompt lead to entirely different outputs. Wu et al. [45] studied concept disentanglement using linear combinations of text embeddings to gain semantic control. Methods like Prompt-to-Prompt [14] and other works [8, 30] utilize the DM's attention layers to attribute pixels to tokens from the text prompt. Dedicated operations on the attention maps enable more control over the generated images. Other works have focused on the noise estimates of DMs [5, 20] providing semantic control over the generation process. With LEDs++, we now enable
+
+fine-grained semantic control for manipulating real images, going beyond purely generative applications.
+
+Real Image Editing. Since DMs' rise in popularity for text-to-image generation, they have also been explored for (real) image-to-image editing. As a first, simple approach, SDEdit added noise to the image for an intermediate step in the diffusion process [26]. While lightweight, the resulting image diverges substantially from the input as it is (partially) regenerated. Inpainting allows to keep the change small by having a user provide additional masks to restrict changes to certain image regions [2, 29]. Yet, user masks are costly or often simply unavailable. Other works have thus explored semantically grounded approaches using cross-attention instead to better control image manipulation [7, 28, 30]. In contrast, LEDs++ leverages both attention-and noise-based masking to obtain fine-grained masks, enabling strong semantic control over real images.
+
+Another important aspect of image manipulation methods is the required tuning and overall runtime. Instruct-Pix2Pix continues training a DM at scale to enable image editing capabilities [6]. Finetuning instead on each individual input to constrain the generation on the real image has shown helpful [18, 44] but not computationally efficient. Consequently, recent works have largely relied on inverting the deterministic DDIM sampling process [42] to save computational resources. DDIM inversion identifies an initial noise vector that results in the input image when denoised again. However, faithful reconstructions are only obtained in the limit of small steps, thus requiring large numbers of inversion steps. Moreover, small errors will still incur at each timestep, often accumulating into meaningful deviations from the input, requiring costly error correction through optimization [28, 30]. Recently, Huberman-Spiegelglas et al. proposed an inversion technique [17] for the DDPM sampler [15] to address the limitations of DDIM inversion. LEDs++ provides the same guarantees of perfect inversion with even further reduced runtime alongside an edit-friendly latent space, enabling more versatility.
+
+# 3. Image Editing with Text-to-Image Models
+
+Before devising the methodology of LEDs++, let us first motivate the desired features and use cases. Specifically, we aim for efficiency, versatility, and precision. The goal is to provide a method that enables a fast exploratory workflow for image editing in which a user can iteratively interact with the model and explore various edits. Consequently, LEDs++ produces outputs quickly with no tuning or optimization to not disrupt the creative process. Further, arbitrary editing instructions and combinations thereof are supported to facilitate a wide range of image manipulations (e.g., complex multi-editing). Lastly, we provide precise and sophisticated semantic control over the image editing. Each of the (potentially multiple) edit instruc
+
+tions can be steered individually, and changes are automatically restricted to relevant image regions. Importantly, with LEDs++ we prioritize compositional robustness.
+
+# 3.1. Guided Diffusion Models
+
+Let us first define some general background for diffusion models. DMs iteratively denoise a Gaussian distributed variable to produce samples of a learned data distribution. Let's consider a diffusion process that gradually turns an image  $x_0$  into Gaussian noise.
+
+$$
+x _ {t} = \sqrt {1 - \beta_ {t}} x _ {t - 1} + \sqrt {\beta_ {t}} n _ {t}, \quad t = 1, \dots , T \tag {1}
+$$
+
+where  $n_t$  are iid normal distributed vectors and  $\beta_t$  a variance schedule. The diffusion process is equivalently expressed as
+
+$$
+x _ {t} = \sqrt {\bar {\alpha} _ {t}} x _ {0} + \sqrt {1 - \bar {\alpha} _ {t}} \epsilon_ {t} \tag {2}
+$$
+
+where  $\alpha_{t} = 1 - \beta_{t}$ ,  $\bar{\alpha}_{t} = \Pi_{s=1}^{t} \alpha_{s}$  and  $\epsilon_{t} \sim \mathcal{N}(0, \mathbf{I})$ . Importantly, all  $\epsilon_{t}$  are not statistically independent. Instead, consecutive pairs  $\epsilon_{t}, \epsilon_{t-1}$  are strongly dependent, which will be relevant later. To generate an (new) image  $\hat{x}_{0}$  the reverse diffusion process starts from random noise  $x_{T} \sim \mathcal{N}(0, \mathbf{I})$  which can be iteratively denoised as
+
+$$
+x _ {t - 1} = \hat {\mu} _ {t} \left(x _ {t}\right) + \sigma_ {t} z _ {t}, \quad t = T, \dots , 1 \tag {3}
+$$
+
+Here  $z_{t}$  are iid standard normal vectors, and common variance schedulers  $\sigma_{t}$  can be expressed in the general form
+
+$$
+\sigma_ {t} = \eta \beta_ {t} \frac {1 - \bar {\alpha} _ {t - 1}}{1 - \bar {\alpha} _ {t}}
+$$
+
+where  $\eta \in [0,1]$ . In this formulation,  $\eta = 0$  corresponds to the deterministic DDIM [42] and  $\eta = 1$  to the DDPM scheme [15]. Lastly, in theses cases, we have  $\hat{\mu}_t(x_t) =$
+
+$$
+\sqrt {\bar {\alpha} _ {t - 1}} \frac {x _ {t} - \sqrt {1 - \bar {\alpha} _ {t}} \hat {\epsilon} _ {\theta} (x _ {t})}{\sqrt {\bar {\alpha} _ {t}}} + \sqrt {1 - \bar {\alpha} _ {t - 1} - \sigma_ {t} ^ {2}} \hat {\epsilon} _ {\theta} (x _ {t})
+$$
+
+Here  $\hat{\epsilon}_{\theta}(x_{t})$  is an estimate of  $\epsilon_{t}$  produced by our neural network DM with learned parameters  $\theta$ , commonly implemented as a U-Net [35]. For text-to-image generation, the model is conditioned on a text prompt  $p$  to produce images faithful to that prompt. The DM is trained to produce the noise estimate  $\hat{\epsilon}_{\theta}(x_{t})$  needed for iteratively sampling  $\hat{x}_0$  (Eq. 3). For text-conditioned DMs,  $\hat{\epsilon}_{\theta}$  is calculated using specific guidance techniques.
+
+Most DMs rely on classifier-free guidance [16], a conditioning method using a purely generative diffusion model, eliminating the need for an additional classifier. During training, the text conditioning  $c_{p}$  is randomly dropped with a fixed probability, resulting in a joint model for unconditional and conditional objectives. During inference, the score estimates for the  $\epsilon$ -prediction are adjusted so that:
+
+$$
+\hat {\epsilon} _ {\theta} \left(x _ {t}, c _ {p}\right) := \hat {\epsilon} _ {\theta} \left(x _ {t}\right) + s _ {g} \left(\hat {\epsilon} _ {\theta} \left(x _ {t}, c _ {p}\right) - \hat {\epsilon} _ {\theta} \left(x _ {t}\right)\right) \tag {4}
+$$
+
+with guidance scale  $s_g$  and  $\hat{\epsilon}_{\theta}$  defining the noise estimate with parameters  $\theta$ . Intuitively, the unconditioned  $\epsilon$ -prediction is pushed in the direction of the conditioned one, with  $s_g$  determining the extent of the adjustment.
+
+# 3.2.LEDITS++
+
+With the fundamentals established, the methodology of LEDs++ can now be broken down into three components: (1) efficient image inversion, (2) versatile textual editing, and (3) semantic grounding of image changes.
+
+Component 1: Perfect Inversion. Utilizing text-to-image models for editing real images requires conditioning the generation on the input image. Recent works have largely relied on inverting the sampling process to identify  $x_{T}$  that will be denoised to the input image  $x_{0}$  [28, 30]. Inverting the DDPM scheduler is generally preferred over DDIM inversion since the former can be achieved in fewer timesteps and with no reconstruction error [17].
+
+However, there exist more efficient schemes than DDPM for sampling DMs that greatly reduce the required number of steps and consequently DM evaluations. We here propose a more efficient inversion method by deriving the desired inversion properties for such a scheme. As demonstrated by Song et al.[43], DDPM can be viewed as a first-order stochastic differential equation (SDE) solver when formulating the reverse diffusion process as an SDE. This SDE can be solved more efficiently—in fewer steps—using a higher-order differential equation solver, here dpmsolver++ [23]. The reverse diffusion process from Eq. 3 for the second-order sde-dpm-solver++ can be written as
+
+$$
+x _ {t - 1} = \hat {\mu} _ {t} \left(x _ {t}, x _ {t + 1}\right) + \sigma_ {t} z _ {t}, \quad t = T, \dots , 1 \tag {5}
+$$
+
+where now
+
+$$
+\sigma_ {t} = \sqrt {1 - \bar {\alpha} _ {t - 1}} \sqrt {1 - e ^ {- 2 h _ {t - 1}}}
+$$
+
+and higher-order  $\hat{\mu}_t$  depends now on  $x$  from two timesteps,  $x_t$  and  $x_{t + 1}$ . Such that  $\hat{\mu}_t(x_t,x_{t + 1}) =$
+
+$$
+\begin{array}{l} \frac {\sqrt {1 - \bar {\alpha} _ {t - 1}}}{\sqrt {1 - \bar {\alpha} _ {t}}} e ^ {- h _ {t - 1}} x _ {t} + \sqrt {\bar {\alpha} _ {t - 1}} \left(1 - e ^ {- 2 h _ {t - 1}}\right) \hat {\epsilon} _ {\theta} (x _ {t}) \\ + 0. 5 \sqrt {\bar {\alpha} _ {t - 1}} \left(1 - e ^ {- 2 h _ {t - 1}}\right) \frac {- h _ {t}}{h _ {t - 1}} \left(\hat {\epsilon} _ {\theta} \left(x _ {t + 1}\right) - \hat {\epsilon} _ {\theta} \left(x _ {t}\right)\right) \\ \end{array}
+$$
+
+with
+
+$$
+h _ {t} = \frac {\ln (\sqrt {\bar {\alpha} _ {t}})}{\ln (\sqrt {1 - \bar {\alpha} _ {t}})} - \frac {\ln (\sqrt {\bar {\alpha} _ {t + 1}})}{\ln (\sqrt {1 - \bar {\alpha} _ {t + 1}})}
+$$
+
+For the detailed derivation of the solver and proof of faster convergence, we refer the reader to the relevant literature [22, 23]. Based on the above, we now devise our inversion process. Given an input image  $x_0$  we construct an auxiliary reconstruction sequence of noise images  $x_1, \ldots, x_T$  as
+
+$$
+x _ {t} = \sqrt {\bar {\alpha} _ {t}} x _ {0} + \sqrt {1 - \bar {\alpha} _ {t}} \tilde {\varepsilon} _ {t} \tag {6}
+$$
+
+where  $\tilde{\epsilon}_t\sim \mathcal{N}(0,\mathbf{I})$ . Contrary to Eq. 2, the  $\tilde{\epsilon}_t$  are now statistically independent, which is a desirable property for image editing [17]. Lastly, the respective  $z_{t}$  for the inversion can be derived from Eq. 5 as
+
+$$
+z _ {t} = \frac {x _ {t - 1} - \hat {\mu} _ {t} \left(x _ {t} , x _ {t + 1}\right)}{\sigma_ {t}}, \quad t = T,.., 1 \tag {7}
+$$
+
+with  $\hat{\mu}$  and  $\sigma_{t}$  as defined above. We base our implementation on the multistep variant of sde-dpm-solver++, which only requires one evaluation of the DM at each diffusion timestep by reusing the estimates from the previous step. The number of timesteps can be reduced further by stopping the inversion at an intermediate step  $t < T$  and starting the generation at that step. Empirically, we observed that  $t\in [0.9T,0.8T]$  usually produces edits of the same fidelity as  $t = T$ , supporting observations in previous work [17, 26] that earlier timesteps are less relevant to the edit.
+
+Component 2: Textual Editing. After creating our reconstruction sequence  $x_{1}, \ldots, x_{T}$  and calculating the respective  $z_{t}$ , we now edit the image by manipulating the noise estimate  $\hat{\epsilon}_{\theta}$  based on a set of edit instructions  $\{e_i\}_{i \in I}$ . We devise a dedicated guidance term for each concept  $e_{i}$  based on conditioned and unconditioned estimates. Let us formally define LEDs++'s guidance by starting with a single editing prompt  $e$ . We compute
+
+$$
+\hat {\epsilon} _ {\theta} \left(x _ {t}, c _ {e}\right) := \hat {\epsilon} _ {\theta} \left(x _ {t}\right) + \gamma \left(x _ {t}, c _ {e}\right) \tag {8}
+$$
+
+with guidance term  $\gamma$ . Consequently, setting  $\gamma = 0$  will reconstruct the input image  $x_0$ . We construct  $\gamma$  to push the unconditioned score estimate  $\hat{\epsilon}_{\theta}(x_t)$  —i.e. the input image reconstruction—away from/towards the edit concept estimate  $\hat{\epsilon}_{\theta}(x_t, c_e)$ , depending on the guidance direction:
+
+$$
+\gamma \left(x _ {t}, c _ {e}\right) = \phi (\psi ; s _ {e}, \lambda) \psi \left(x _ {t}, c _ {e}\right) \tag {9}
+$$
+
+where  $\phi$  applies an edit guidance scale  $s_e$  element-wise, and  $\psi$  depends on the edit direction:  $\psi(x_t, c_e) =$
+
+$$
+\left\{ \begin{array}{l} \hat {\epsilon} _ {\theta} \left(x _ {t}, c _ {e}\right) - \hat {\epsilon} _ {\theta} \left(x _ {t}\right) \quad \text {i f p o s . g u i d a n c e} \\ - \left(\hat {\epsilon} _ {\theta} \left(x _ {t}, c _ {e}\right) - \hat {\epsilon} _ {\theta} \left(x _ {t}\right)\right) \quad \text {i f n e g . g u i d a n c e} \end{array} \right. \tag {10}
+$$
+
+Thus, changing the guidance direction is reflected by the direction between  $\hat{\epsilon}_{\theta}(x_t,c_e)$  and  $\hat{\epsilon}_{\theta}(x_t)$ . The term  $\phi$  identifies those dimensions of the image and respective  $\hat{\epsilon}_{\theta}$  that are relevant to a prompt  $e$ . Consequently,  $\phi$  returns 0 for all irrelevant dimensions and a scaling factor  $s_e$  for the others. We describe the construction of  $\phi$  in detail below. Larger  $s_e$  will increase the effect of the edit, and  $\lambda \in (0,1)$  reflects the percentage of the pixels selected as relevant by  $\phi$ . Notably, for a single concept  $e$  and uniform  $\phi = s_e$ , Eq. 8 generalizes to the classifier-free guidance term in Eq. 4.
+
+For multiple  $e_i$ , we calculate  $\gamma_t^i$  as described above, with each defining their own hyperparameter values  $\lambda^i$ ,  $s_e^i$ . The
+
+sum of all  $\gamma_t^i$  results in
+
+$$
+\hat {\gamma} _ {t} \left(x _ {t}, c _ {e _ {i}}\right) = \sum_ {i \in I} \gamma_ {t} ^ {i} \left(x _ {t}, c _ {e _ {i}}\right) \tag {11}
+$$
+
+Component 3: Semantic Grounding. The masking term  $\phi$  (Eq. 9) is the intersection (pointwise product) of binary masks  $M^1$  and  $M^2$  combined with scaling factor  $s_e$ :
+
+$$
+\phi (\psi ; s _ {e _ {i}}, \lambda) = s _ {e _ {i}} M _ {i} ^ {1} M _ {i} ^ {2} \tag {12}
+$$
+
+where  $M_{i}^{1}$  is a binary mask generated from the U-Net's cross-attention layers and  $M_{i}^{2}$  is a binary mask derived from the noise estimate. Intuitively, each mask is an importance map, where  $M_{i}^{1}$  is more strongly grounded than  $M_{i}^{2}$ , but of significantly coarser granularity. Therefore, the intersection of the two yields a mask both focused on relevant image regions and of fine granularity. With LEDs++, we empirically demonstrate that these maps can also capture regions of an image relevant to an editing concept that is not already present. Specifically for multiple edits, calculating a dedicated mask for each edit prompt ensures that the corresponding guidance terms remain largely isolated, limiting interference between them.
+
+Formally, at each time step  $t$ , a U-Net forward pass with editing prompt  $e_i$  is performed to generate cross-attention maps for each token of the editing prompt. All cross-attention maps of the smallest resolution (e.g.,  $16 \times 16$  for SD) are averaged over all heads and layers, and the resulting maps are summed over all editing tokens, resulting in a single map  $A_t^{e_i} \in R^{16 \times 16}$ . Importantly, we utilize the same U-Net evaluation  $\hat{\epsilon}_{\theta}(x_t, c_e)$  already performed in Eq. 10 to produce  $M^1$  with minimal overhead. Each map  $A_t^{e_i}$  is up-sampled to match the size of  $x_t$ . Cross-attention mask  $M^1$  is derived by calculating the  $\lambda$ -th percentile of up-sampled  $A_t^{e_i}$  and
+
+$$
+M _ {i} ^ {1} = \left\{ \begin{array}{l l} 1 & \text {i f} \left| A _ {t} ^ {e _ {i}} \right| \geq \eta_ {\lambda} \left(\left| A _ {t} ^ {e _ {i}} \right|\right) \\ 0 & \text {e l s e} \end{array} \right. \tag {13}
+$$
+
+where  $\eta_{\lambda}(|\cdot|)$  is the  $\lambda$ -th percentile. By definition,  $M^1$  only selects image regions that correlate strongly with the editing prompt, and  $\lambda$  determines the size of this selected region.
+
+The fine-grained mask  $M^2$  is calculated based on the guidance vector  $\psi$  of noise estimates derived in Eq. 10. The difference between unconditioned and conditioned  $\hat{\epsilon}_{\theta}$ , generally captures outlines and object edges of  $x_{t}$ . Consequently, the largest absolute values of  $\psi$  provide meaningful segmentation information of fine granularity for  $M^2$
+
+$$
+M ^ {2} = \left\{ \begin{array}{l l} 1 & \text {i f} | \psi | \geq \eta_ {\lambda} (| \psi |) \\ 0 & \text {e l s e} \end{array} \right. \tag {14}
+$$
+
+In general, threshold  $\lambda$  should correspond to the performed edit. Changes affecting the entire image, such as style transfer, should choose smaller  $\lambda (\rightarrow 0)$ , whereas edits targeting
+
+![](images/aa8709af9cdd4c546356fdd95823f9d774fb44ad62023ae5dae09689d981550b.jpg)  
+Figure 2. Comparison of image editing methods. (top) LEDs++ is the only method to restrict edits to the tree leaves and position of the car. (bottom) Ours is the only approach faithfully executing all three edits and keeping changes minimal. (Best viewed in color)
+
+<table><tr><td>Method</td><td>Reconstruction 
+Error (RMSE) ↓</td><td>Execution 
+Time (s) ↓</td><td>Variation/ 
+Sampling</td><td>Semantic 
+Grounding</td><td>Multi- 
+Editing</td></tr><tr><td>SDEdit [26]</td><td>0.81 ±0.07</td><td>2.10 ±0.02</td><td>✓</td><td>X</td><td>X</td></tr><tr><td>Imagic [18]</td><td>0.58 ±0.12</td><td>349.98 ±0.45</td><td>✓</td><td>X</td><td>X</td></tr><tr><td>Vanilla DDIM Inversion</td><td>0.22 ±0.10</td><td>37.23 ±0.04</td><td>X</td><td>X</td><td>X</td></tr><tr><td>Pix2Pix-Zero [30]</td><td>0.20 ±0.09</td><td>56.78 ±0.14</td><td>(✓)</td><td>✓</td><td>X</td></tr><tr><td>DiffEdit [9]</td><td>0.13±0.03</td><td>27.65 ±0.03</td><td>✓</td><td>✓</td><td>X</td></tr><tr><td>Edit-friendly DDPM [17]</td><td>0.00</td><td>10.36 ±0.05</td><td>✓</td><td>X</td><td>X</td></tr><tr><td>LEDSITS++ (Ours)</td><td>0.00</td><td>1.78 ±0.03</td><td>✓</td><td>✓</td><td>✓</td></tr></table>
+
+Table 1. Comparing key properties for diffusion-based image editing techniques, with LEDs++ offering clear methodological benefits. Due to LEDs++'s efficient perfect inversion, it is the fastest and error-free method. At the same time, its methodology is the only enabling versatility in terms of variation, semantic grounding, and multi-editing. Subscript numbers indicate standard deviation.
+
+specific objects or regions should use  $\lambda$  proportional to the region's prominence in the image.
+
+# 4. Properties of LEDs++
+
+With the fundamentals of LEDs++ established, we next showcase its unique properties and capabilities.
+
+Efficiency. First off, LEDs++ offers substantial performance improvements over other image editing methods. In Tab. 1, we provide a qualitative runtime comparison, with all methods being implemented for Stable Diffusion (SD) 1.5 [34]. As a parameter-free approach, LEDs++ does not require any computationally expensive fine-tuning or optimization. Consequently, LEDs++ is orders of magnitude faster than methods like Imagic [18] or Pix2Pix-Zero [30]. Further, we only need to invert the same number of diffusion steps used at inference, which results in significant runtime improvements over the standard DDIM inversion (21x). In addition to efficient inversion, we use a recent, fast scheduler that generally requires fewer total steps, further boosting performance. This way, LEDs++ is six times faster than recent DDPM inversion [17] and on par with fast but poor-quality SDEdit [26].
+
+Versatility. In addition to its efficiency, LEDs++ remains versatile, enabling sheer limitless editing possibilities. In Fig. 1, we showcase a broad range of edit types.
+
+LEDITS++ facilitates fine-grained edits (adding/removing glasses) and holistic changes such as style transfer (painting/sketch). Furthermore, object removal and replacement facilitate even more image editing tasks. Importantly, the overall image composition is preserved in all cases. To our knowledge, LEDs++ is the only diffusion-based image editing method inherently supporting multiple edits in isolation, which allows for more complex image manipulation. Fig. 2 highlights LEDs++ benefits over previous methods. Our method produces the highest edit fidelity and is the only approach capable of faithfully executing multiple, simultaneous instructions. Moreover, LEDs++ also makes the least changes to unrelated objects and the overall background and composition of the image.
+
+Lastly, the editing versatility benefits from the stochastic nature of the perfect but non-deterministic inversion. LEDs++ provides meaningful image variations by resampling  $\tilde{c}_t$ . Additionally, the visual expression of each concept in the edited image scales monotonically with  $s_e$ , and the direction and magnitude of each concept can be varied freely. We present examples of both features in App. B.
+
+Precision. Furthermore, LEDs++'s methodology keeps edits concise and avoids unnecessary deviations from the input image (Fig. 2). First, the perfect inversion will reconstruct the exact input image if no edit is applied (cf.
+
+![](images/65145febf9dc8f5f3ea361c981b25ba7f5ed9a8b34e59e22ec6b15377923bcfe.jpg)  
+Figure 3. Exemplary edit performed with LEDs++ in only 25 diffusion steps with SD1.5. We apply a complex, compounded edit and ground each to a semantically reasonable image region.
+
+Sec. 3.2). Consequently, we already improve on faithfulness to the input image even before applying any edits. This benefit over other methods is highlighted by the reconstruction error in Tab. 1. Second, implicit masking will semantically ground each edit to relevant image regions. This is specifically important for editing multiple concepts at the same time. While other methods only utilize one prompt for all instructions, LEDs++ isolates edits from each other (Eq. 11). Thus, we get dedicated masks for each concept as shown in Fig. 3. This design ensures that each instruction (e.g., red mask for 'cherry blossom') will be only applied where necessary. Subsequently, we provide further evidence for the efficacy of LEDs++'s masking approach.
+
+# 5. Semantically Grounded Image Editing
+
+Cross-attention maps of DMs have been used extensively to ground regions of interest during image generation semantically [7, 8, 14, 30]. Nonetheless, these have not been combined with noise-based masks so far and thus lack fine granularity. Hence, we empirically evaluate the quality of implicit masks, i.e., attention maps  $M^1$  and noise maps  $M^2$  (Eq. 13 and 14) in the LEDs++ setup. We use a broad segmentation task for common objects as a proxy to measure the performance of implicit masks in identifying relevant image areas from edit instructions. Specifically, we utilize segmentation masks from the COCO panoptic segmentation challenge [19]. For each unique object in an image, we retrieve the masks  $M^1$ ,  $M^2$ , and their intersection per diffusion step. We use the (semantic) class label (e.g. 'person' or 'TV') as editing concept  $e$ . We consider masks at each of 50 total diffusion steps without actually editing the input image. Furthermore, we approximate mask threshold  $\lambda$  based on the relative size of an object's bounding box.
+
+Concise masks with LEDs++. Fig. 4 shows implicit masking as a reliable means to identify relevant image regions. Importantly, the intersection of both cross-attention masks  $M^1$  and noise maps  $M^2$  clearly outperforms each separate mask. The overall performance is even similar to a dedicated CLIPSeg model [24], despite LEDs++. masks being implicitly calculated at inference with only minimal overhead. At the same time, LEDs++.'s masking is superior to DiffEdit's [3]. Consequently, our method's inter
+
+![](images/318c6382a39c079543b3cc4819e80b0f71060178d28b71ea7d436599a39f18cc.jpg)  
+Figure 4. Semantic segmentation quality of LEDs++. We show the intersection over union (higher is better) for COCO panoptic segmentation. The intersection masks outperform each by a clear margin, close to the CLIPSeg reference. (Best viewed in color)
+
+section of cross-attention masks and noise maps provides strong semantic grounding while being efficient during image manipulation to ensure precise editing.
+
+# 6. Image Editing Evaluation
+
+Let us now compare LEDs++ to current SOTA methods for image manipulation on two benchmarks.
+
+# 6.1. Editing Multiple Concepts
+
+First, we investigate the complex task of performing multiple edits simultaneously. We rely on a well-established setup for semantic image manipulation [5] to evaluate multi-conditioned attribute manipulation in facial images. In our experiment, we consider 100 images from the CelebA dataset [21]. For each image, we simultaneously edit three attributes out of a set of five, leading to ten total combinations of edit concepts. Further, we perform each edit across ten different seeds, resulting in 10,000 evaluated images for each method and hyperparameter setting, over 1M images in total. As measures for comparison, we employ CLIP and LPIPS scores. CLIP measures the text-to-image similarity of the edit instruction to the edited image, and LPIPS measures the image-to-image similarity of the real to the edited image. This way, we assess the tradeoff between the versatility of edits (CLIP) and the precision of those manipulations (LPIPS). We implement all methods based on SD1.5 and provide more details in App. C.
+
+LEDS++ outperforms competing methods. Fig. 5 shows the resulting CLIP vs. LPIPS plots for all methods. The top left corner represents the ideal editing method with maximum edit alignment without deviating from the initial image. Generally, one can observe a natural trade-off between versatility and precision for all methods, i.e., higher image-to-text alignment comes at the expense of lower similarity to the original image. LEDS++ is closest to the ideal region and thus clearly outperforms the other methods. In particular, the outputs remain close to the original image (low LPIPS scores), thanks to the precise implicit masking.
+
+![](images/110ffe195968c3d76f23e8c672ce8b00d27b845da1c2f8bcb04eed0058e662e0.jpg)  
+Figure 5. Comparison of instruction-alignment vs. image similarity trade-off for different editing methods. Results were reported for simultaneous manipulation of three facial attributes on CelebA. We plot CLIP scores (higher is better) of the target attributes against LPIPS similarity (lower is better). LEDs++ clearly outperforms all competing methods. (Best viewed in color)
+
+At the same time, it faithfully performs the edits (high CLIP scores) due to the dedicated, isolated editing for each concept. The depicted scores reflect our qualitative inspections for Pix2Pix-Zero and Imagic on such complex manipulations (cf. Fig. 2). We observed that these methods often break—either failing to perform all three edits and/or drastically altering the input image. Only edit-friendly DDPM [17] and LEDs++ reliably achieve the maximum average CLIP score of over 0.25. This value seems to represent an upper bound according to our manual investigations, as each attribute is edited correctly for all input images, and higher scores are not observed. Despite being computationally very efficient, LEDs++ faithfully executes each edit instruction while keeping the changes to the input low, highlighting the method's versatility and precision.
+
+# 6.2. TEDBench  $(++)$
+
+Next, we investigate the versatility of LEDs++'s editing capabilities by running the Textual Editing Benchmark (TEDBench [18]), a collection of 100 input images paired with textual edit instructions. However, we observed a variety of inconsistencies in TEDBench and a lack of relevant editing tasks. Therefore, we propose TEDBench++ (Fig. 6a and App. D), a more challenging revised benchmark now containing 120 entries in total.<sup>3</sup> We addressed misspellings and rephrased ambiguous and inconclusive instructions. In addition to resolving these issues, we added instructions targeting challenging types of image manipulations previously not included in TEDBench: multi-conditioning, object/concept removal, style transfer, and complex replacements (Fig. 6a). We provide more details in App. D.
+
+We compare LEDs++ on TEdBench  $(++)$  to one of the strongest editing methods, Imagic [18] with Imagen [37].
+
+<table><tr><td></td><td colspan="2">TEDBench</td><td colspan="2">TEDBench++</td></tr><tr><td></td><td>SR ↑</td><td>LPIPS ↓</td><td>SR ↑</td><td>LPIPS ↓</td></tr><tr><td>Imagic w/ SD1.5</td><td>0.55</td><td>0.56</td><td>0.58</td><td>0.57</td></tr><tr><td>LEDITS++ w/ SD1.5</td><td>0.75</td><td>0.28</td><td>0.79</td><td>0.30</td></tr><tr><td>Imagic w/Imagen [18]</td><td>0.83</td><td>0.59</td><td>—</td><td>—</td></tr><tr><td>LEDITS++ w/ SD-XL</td><td>0.84</td><td>0.33</td><td>0.87</td><td>0.34</td></tr></table>
+
+Table 2. Success rate (SR) and LPIPS scores on the original TedBench [18] and our revised version (TEDBench++) We compare Imagic to LEDs++ based on different DMs and find the latter to outperform on both metrics and benchmarks.
+
+Since both are not publicly available, we can only compare to this specific combination of DM and editing method using Kawar et al.'s [18] curated outputs for TEdBench. Additionally, we, therefore, cannot combine LEDs++ with Imagen[37] and instead use a similarly advanced diffusion model, SD-XL [32]. However, to not only compete for the best fidelity outputs but focus the evaluation on methodological differences—not the pre-trained DM—we also compare both methods implemented with SD1.5. We provide further details in App. C.
+
+LEDS  $^{+ + }$  edits images reliably. We first asked users to assess the overall success of edits, i.e., if an edit instruction was faithfully realized for a given input image. The results in Tab. 2 show that LEDs  $^{+ + }$  outperforms Imagc on TEdBench despite a greatly reduced runtime (Tab. 1). The difference is even stronger when comparing both methods on the same pre-trained DM, i.e., SD1.5. The high success rate on TEdBench  $^{+ + }$ $(87\%)$  and the examples shown in Fig. 1 and 6a once again highlight LEDs  $^{+ + }$ 's versatility. Overall, our proposed method can reliably perform a diverse set of editing instructions for real images.
+
+High-quality edits with LEDs++. While investigating both methods' performance we observed a substantial difference in edit quality. The examples in Fig. 6b particularly highlight the discrepancy in compositional robustness and object coherence. Hence, we also assessed both methods' editing quality on TEdBench++. We focus on samples where both methods performed a successful edit, i.e., were labeled as successful by users. We show the perceptual similarity (LPIPS) to the input image in Tab. 2. One can observe that the LPIPS scores for LEDs++ are much lower than for Imagic, empirically supporting the qualitative examples in Fig. 6b. When manually inspecting the generated images, we often found Imagic to generate a completely new image based on the edit instruction, entirely disregarding the input image (cf. App. Fig. 11a).
+
+# 7. Discussion
+
+Let us now discuss open research questions and limitations.
+
+Model Dependency. While LEDs++ achieves impressive results on a large variety of image manipulation tasks, there are external factors to consider. Since the
+
+![](images/be4dfb3e9df3f04561b13dffc758c1f1e4f3c2a54aa97cbf03fd80af2b3c79db.jpg)  
+(a) Novel challenging examples of TEdBench++ and LEDs++ applied, showcasing the versatility of supported edits.
+
+![](images/80bbbd9c3d251bbf51c623aac6607686525a4f1e1fe8d544eeb4757123cb27e6.jpg)  
+(b) Qualitative comparison of LEDs++ and Imagic on TEd-Bench, clearly highlighting the performance improvement.  
+Figure 6. Benchmark examples for LEDs++ and Imagc on TEdBench  $(++)$  . (Best viewed in color)
+
+method is architecture-agnostic, it can be easily used with any DM. At the same time, the general editing quality strongly depends on the overall capabilities of the underlying pre-trained DM. Naturally, more capable models will also enable better edits. But, at times, specific editing instructions may fail because the used DM does not have a decent representation of the targeted concept to begin with. One example is the model failing to edit a giraffe to be sitting since the underlying DM generally fails to generate this pose (cf. App. F). This effect can also clearly be seen in Tab. 2, with the editing success rate of a method varying strongly between DMs. Although the same image editing method is employed (LEDITS++, the more capable SD-XL variant outperforms the weaker SD1.5 model. Nonetheless, this means that the architecture-agnostic LEDs++ will benefit from increasingly powerful DMs.
+
+Coherence Trade-offs. Next to the benefits of LEDs++'s semantic grounding, there are also downsides to this approach. Overall, implicit masking limits changes to relevant portions of the image and achieves strong coherence with the original image composition. Yet, the object and its identity within the masked area may change based on various factors. Generic prompts, like "a standing cat" (cf. App. F), do not contain detailed information about this specific object ("cat"). Thus, an edit with this prompt does not guarantee to preserve object identity, particularly for strong hyperparameters. We observed that fine-tuning approaches like Imagic make the opposite trade-off, better preserving the object identity while changing the background and image composition substantially (cf. App. F). A potential remedy for a loss in object coherence with LEDs++, is more descriptive edit prompting, e.g. using textual inversion [12].
+
+Lastly, the automatically-inferred implicit masks allow for easy use of LEDs++ without users tediously providing masks. Nonetheless, user intentions are diverse and cannot always be automatically inferred. Sometimes, in-
+
+individual user masks provide better control over the editing process. Such user masks can be easily integrated into LEDs++ (cf. App. F), wherefore we encourage future research in this promising direction.
+
+Societal Impact. LEDs++ is an easy-to-use image editing technique that lowers the barrier for users and puts them in control for fruitful human-machine collaboration. Yet, the underlying text-to-image models offer both promise and peril, as highlighted by prior research [4, 11]. The (societal) biases within these models will also impact image editing applications [11]. Moreover, image manipulation can also be used adversarially to generate inappropriate [39] or fake content. Hence, we advocate for a cautious deployment of generative models together with image editing methods.
+
+# 8. Conclusion
+
+We introduced LEDs++, an efficient yet versatile and precise method for textual image manipulation with diffusion models. It facilitates the editing of complex concepts in real images. Our approach requires no finetuning nor optimization, can be computed extremely efficiently, and is architecture agnostic. At the same time, it perfectly reconstructs an input image and uses implicit masking to limit changes to relevant image regions, thus editing precisely. Our large experimental evaluation confirms the efficiency, versatility, and precision of LEDs++ and its components, as well as its benefits over several related methods.
+
+Acknowledgements We gratefully acknowledge support from the BMBF (Grant No 01IS22091). This work benefited from the ICT-48 Network of AI Research Excellence Center "TAILOR" (EU Horizon 2020, GA No 952215), the Hessian research priority program LOEWE within the project WhiteBox, the HMWK cluster projects "Adaptive Mind" and "Third Wave of AI", and from the NHR4CES.
+
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2024/LED_ A Large-scale Real-world Paired Dataset for Event Camera Denoising/c132a07a-cde4-41ed-ba0e-fbc21a44ee59_content_list.json

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+        "text": "LED: A Large-scale Real-world Paired Dataset for Event Camera Denoising",
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+        "text": "Yuxing Duan",
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+        "text": "$^{1}$ National Key Lab of Multispectral Information Intelligent Processing Technology  \n $^{1}$ Huazhong University of Science and Technology",
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+        "image_caption": [
+            "Figure 1. Illustration of the paired raw/denoised event datasets. The proposed real-world event denoising datasets contribute to addressing the inevitable Background Activity (BA) noise encountered by event cameras application under varying camera settings and illumination."
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+        "text": "Abstract",
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+        "text": "Event camera has significant advantages in capturing dynamic scene information while being prone to noise interference, particularly in challenging conditions like low threshold and low illumination. However, most existing research focuses on gentle situations, hindering event camera applications in realistic complex scenarios. To tackle this limitation and advance the field, we construct a new paired real-world event denoising dataset (LED), including 3K sequences with 18K seconds of high-resolution (1200*680) event streams and showing three notable distinctions compared to others: diverse noise levels and scenes, larger-scale with high-resolution, and high-quality GT. Specifically, it contains stepped parameters and varying illumination with diverse scenarios. Moreover, based on the property of noise events inconsistency and signal events consistency, we propose a novel effective denoising framework(DED) using homogeneous dual events to generate the GT with better separating noise from the raw. Furthermore, we design a bio-inspired baseline leveraging Leaky-Integrate-and-Fire (LIF) neurons with dynamic thresholds to realize accurate denoising. The experimental results demonstrate that the remarkable performance of the proposed approach on different datasets. The dataset and code are at https://github.com/Yee-Sing/led.",
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+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Event cameras possess unique imaging advantages and are demonstrating tremendous potential for various applications [4, 11, 33, 37]. Unlike traditional frame cameras using integration sampling [46], event camera is differential sampling [29], evading the restriction of exposure period. However, due to this sampling mechanism, random fluctuations in analog signals can easily form noise events. In contrast to the dominance of signal components in images, the noise and signal in event cameras are encoded with same magnitude, easily disturbing inherent structural features, such as lane lines shown in Fig. 1. BA noise detrimentally impact on subsequent tasks like reconstruction [36, 39], motion estimation [40, 41] and event-based object detection [5]. Therefore, event denoising becomes a fundamental issue, notably in the booming event-based vision community.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Paired data is a key issue for event denoising in the deep-learning era, thus an intuitive idea is to construct paired data through simulators [17, 22, 38]. However, the image-based simulation cannot be equivalent to reality because of the domain gap. To obtain the 'clean part' from the real-world event, multi-modal data was incorporated to help paired event generation. APS images gradient combined with IMU are used to indicate the event probability within frame period [2]. By jointly estimating the motion parameters with",
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+        "text": "CVF",
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+    {
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+        "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
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+        "img_path": "images/899b3a59222e279a3ed0201e4dbf8f48bed4516c4a15c5b67eb6cc0877473210.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Datasets</td><td>Sequences</td><td>Capture/s</td><td>Source</td><td>Noise level</td><td>Illumination</td><td>Resolution</td><td>Paired</td></tr><tr><td>RGB-DAVIS [45]</td><td>20</td><td>122</td><td>Camera</td><td>X</td><td>Daytime</td><td>180*190</td><td>X</td></tr><tr><td>EventNFS [10]</td><td>100</td><td>4238</td><td>Screen Recording</td><td>X</td><td>Daytime</td><td>224*124</td><td>X</td></tr><tr><td>E-MLB [8]</td><td>1200</td><td>7300</td><td>Camera</td><td>4</td><td>Daytime to Nighttime</td><td>346*260</td><td>X</td></tr><tr><td>DVSNOISE20 [2]</td><td>48</td><td>807</td><td>Camera</td><td>X</td><td>Daytime</td><td>346*260</td><td>✓</td></tr><tr><td>ED-KoGTL [1]</td><td>4</td><td>15</td><td>Camera</td><td>X</td><td>Daytime to Nighttime</td><td>346*260</td><td>✓</td></tr><tr><td>DVSCLEAN [12]</td><td>144</td><td>55</td><td>Synthesis</td><td>2</td><td>Daytime</td><td>1280*720</td><td>✓</td></tr><tr><td>LED</td><td>3000</td><td>18000</td><td>Camera</td><td>4</td><td>Daytime to Nighttime</td><td>1200*680</td><td>✓</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Table 1. Summary of existing event denoising datasets.",
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+        "text": "APS images and event streams [9, 45], the temporal mismatch can be alleviated. Constructing a fixed-track setup [1], the events under various illuminations can be referred to APS images in good lighting. Essentially, these methods align with events via transformed multi-mode features. Unfortunately, this heterogeneous aided information cannot fully match with the event, and their effectiveness is unavailable in situations such as low light and motion blur. Hence, few datasets have considered practical scenes where BA noise is easily deteriorated by camera setting and illumination, appearing as complex and nonuniform distributions.",
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+        "type": "text",
+        "text": "To address this issue, we construct a large-scale, high-quality paired dataset LED for event denoising. LED has three distinct advantages. Firstly, it contains diverse noise levels, covering complex situations under various camera settings and illumination. Secondly, LED includes such as outdoor and indoor scenarios, with abundant objects. Last but not least, LED is collected with the current largest-scale and high-resolution. Moreover, inspired by the multisampling images denoising methods [21, 28, 31, 34], we are the first to explore event multi-sampling for denoising. Based on the homogeneous data, we proposed a dual-events denoising framework that can generate higher-quality GT by more accurately separating BA noise from the raw.",
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+        "type": "text",
+        "text": "The contributions of this paper can be summarized as:",
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+    {
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+        "list_items": [
+            "(1) We provide a large-scale real-world paired dataset for event denoising. So far, LED is the largest paired realworld event denoising dataset (3000 sequences) and high-resolution  $(1200^{*}680)$  with diverse noise levels and scenes.",
+            "(2) We propose a novel dual events denoising framework DED based on noise inconsistency. We provide detailed analysis to show that DED can better separate mixed signals and noisy event streams across various camera threshold parameters, light conditions and motion patterns.",
+            "(3) We introduce a novel baseline DTSNN for event denoising based on the spiking neural network, which utilizes the learnable dynamical spike threshold of the LIF neuron to accurately denoising. Extensive experiments on different real datasets verify the superiority of the proposed method."
+        ],
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+        "text": "2. Related work",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Event Denoising Datasets. Currently, the datasets exclusively designed for event denoising with less attention com",
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "pared to the task-specific ones in the event-based community. In Table 1, we provide an all-sided summary of existing datasets, highlighting the scarcity of real paired datasets.",
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "To address the lack of explicit labels, some paired datasets can be conveniently generated via simulators such as DVSCLEAN [12] and DND21 [20]. However, due to the gap between simulation and real, these simulators fail to fully reflect the actual situation. Other works focus on real paired event denoising data. DVSO noise20 [2] captures data in 16 pure background scenes. RGB-DAVIS [45] provides 20 indoor/outdoor sequences under good lighting conditions. ED-KoGTL [1] constructs indoor data with four illumination levels under constant trajectory. These paired datasets have achieved favorable results, primarily attributable to the gradient cues extracted from APS images. However, the heterogeneity between images and events limits the availability of diverse lighting conditions, motion patterns, and scenarios for constructing paired data.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Event-based Denoising. Research on event denoising can be categorized into two approaches: filtering-based methods and deep learning methods. The former relies on manual priors to design discriminative models for noise removal, such as utilizing density distinction [15, 20, 30, 50] or motion continuity distinction [3, 44, 47] and motion compensation [6, 45] with CM framework [16] in the spatiotemporal domain. However, the validity of this prior knowledge is sensitive to different signal/noise event distributions, limiting their denoising accuracy. For learning-based methods, such as the CNN-based EDNCNN [2], the PointNet-based AEDNet [12] and [1] GNN-transformer were proposed successively. Additionally, the event denoising and super-resolution tasks are combined in [10].",
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+    {
+        "type": "text",
+        "text": "Multi-Sampling Image Denoising. The multi-sampling principle for image denoising has been extensively studied. Techniques like long exposure time or burst captures benefit the direct acquisition of clear data with increased SNR in static scenes. Further, the multi-sampling was explored to the paradigm of indirectly recovering noise-free data. Not only using paired noisy observations to learn the mapping from different noisy samples to clear counterpart [27, 32], but also employing spatial sub-sampling on a single noisy image to learn the mapping from adjacent noisy samples to GT [23, 25]. Evidently, these denoising approaches imply",
+        "bbox": [
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+        "page_idx": 1
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+    {
+        "type": "page_number",
+        "text": "25638",
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+        "img_path": "images/ecd600611afddee70686da699d5581c10880777dd1ae9346566ed6cbc92e300b.jpg",
+        "image_caption": [
+            "(a) Distribution of LED"
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+        "image_caption": [
+            "(b) Scale of LED"
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+        "image_caption": [
+            "(c) Diversity of LED"
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+        "img_path": "images/9746f753be59fadcb8d34d9534ac8b832e2d16c0639bd2bfda08dcfa4a15eeb1.jpg",
+        "image_caption": [
+            "Figure 2. Illustration of the proposed dataset LED. (a) Distribution of noise level and scene of the proposed dataset. (b) Our proposed LED outperforms others in terms of sequences, capture, and resolution (Circles with numbers to indicate). (c) LED collects diverse event streams across various conditions of illumination, depth of field, and target scale.",
+            "(a) Noise in frame camera"
+        ],
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+        "image_caption": [
+            "(b) Noise in event camera",
+            "Figure 3. The substantial noise distinctions between frame/event camera. (a) For a stationary grayscale chart, the frame camera sequentially acquires noisy samples, fluctuating around a latent value within a specific distribution. (b) In a horizontal moving case, the event camera outputs binary signal serially, comprising signal events from motion gradient edges and spurious BA noise."
+        ],
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+    {
+        "type": "text",
+        "text": "that signal resampling could facilitate suppressing random circuit noise and approximating the expectation value.",
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+    {
+        "type": "text",
+        "text": "3. The High-quality Paired LED Dataset",
+        "text_level": 1,
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+        "text": "3.1. Dataset Statistics and Features",
+        "text_level": 1,
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+        "type": "text",
+        "text": "The primary factors affecting BA noise in event cameras can be categorized into intrinsic camera settings and extrinsic lighting conditions. By setting different camera thresholds, we can selectively record events with varying noise levels. Generally, a lower threshold means higher sensitivity but also increases the likelihood of BA noise. In contrast to fixed parameters in other datasets, we use four level thresholds to collect events, starting from the default value of  $0\\%$  and gradually decreasing to  $-10\\%$ ,  $-20\\%$ , and  $-30\\%$ ,",
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+    {
+        "type": "text",
+        "text": "as shown in Fig. 2 (a). To cope with the challenges posed by complex lighting conditions, data collection is from daytime to nighttime, encompassing a transition from high to low illumination and a mixture of natural light with artificial light sources. Thus, the impact of external conditions on the event stream distribution can also be controlled.",
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+    {
+        "type": "text",
+        "text": "Due to the difficulty of constructing real paired datasets, the development of existing datasets remains limited, as shown in Table 1. In this work, we used a vehicle-mounted or pan-tilt equipped with event cameras featuring a  $16\\mathrm{mm}$  lens. Totally, we collected approximately 5 hours of event stream, including 3K sequences. The composition of noise levels and scenes is depicted in Fig. 2 (a), with roughly equal amounts collected during daytime and nighttime. Nearly 20 typical scenes were captured, including urban buildings, traffic roads, natural scenery, indoor exhibits, etc.",
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+        "type": "text",
+        "text": "Our dataset goes beyond just the number of sequences and data volume, primarily aiming to consider the intricate influences of relevant factors on noise. Thus, we endow LED with diversity to reflect the impact of objects and environments on the event, which helps cover the cases of densely and non-uniformly distributed noisy situations in reality both spatially and temporally. In Fig. 2 (c), we exhibit that LED diversity is not only embodied in the richness of noise and illumination levels but also features such as depth of field and scene semantics. Meanwhile, high-resolution imaging aids the event cameras in capturing spatial information more precisely. Unfortunately, most existing ones with low resolution may hinder advanced visual tasks. Therefore, we collected data with  $1200*680$  resolution(after cropping), achieving high spatiotemporal resolution. Additionally, LED includes abundant objects of various scales, including aerial targets, pedestrians, and vehicles, making it well-suited for downstream tasks.",
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+        "img_path": "images/c3167d56f6087147b4ed8f56828d07fe4dc2a9ad090fe27bde62986a45def9c8.jpg",
+        "image_caption": [
+            "(b) Circuit dual-sampled simulation"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "img_path": "images/689fbe4668c25bda81b832c67afd44a047f370e79ed4a62f037fbe6857be358f.jpg",
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+        "img_path": "images/2a87918737ebcc936b450c3c644bdbb624bb35b553664dffef76af5a5af0fd85.jpg",
+        "image_caption": [
+            "(c) Realistic dual-Sampled events"
+        ],
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+    {
+        "type": "image",
+        "img_path": "images/b90971034e6fbf5e8cc54a67a41115fe1a8e6f2e85e9ced63455b31b625b88d9.jpg",
+        "image_caption": [
+            "(d) Statistic of dual-sampled events"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "image",
+        "img_path": "images/4a57266de4d34d4a8077f3e2c06ee67c38a66a4dc12a67ee5cba87f8244cebbe.jpg",
+        "image_caption": [
+            "Figure 4. Illustration of event camera dual-sampling analysis: (a) Given an ideal intensity input, which includes varying and steady stages, generates a series of signal events. (b) The twice samplings of the same input in the circuit model, both generate additional BA noise in previously steady stages, resulting in consistency discrepancies between noise events and signal events. (c) The visualization results of the actual dual-sampled events cumulative frame demonstrate the misalignment of inconsistent dual-sampled noise events and the alignment of coexisting signal events (two color groups indicating the respective polarities of the dual events). (d) The statistical results of the two tests also prove a low overlap rate between dual-sampled event pixels and a much higher one where signal events are present.",
+            "Figure 5. Overview of the dual events denoising framework. (a) Our collection device consists of two identical EVK4s forming a co-axial system with a 1:1 beamsplitter. (b) We first perform spatial similarity processing to retain the consistent parts, followed by sequentially spatiotemporal correlation constraints to remove the residual small amount of noise event from the previous step."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "3.2. Dual Events Denoising Framework",
+        "text_level": 1,
+        "bbox": [
+            76,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Given a noisy event stream, the key lies in properly obtaining paired GT. In this section, we explore utilizing multi-sampling to achieve event stream denoising.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Background. Multi-sampling denoising methods are commonly used in image denoising. For frame images, averaging the results of temporal multi-samples can approximate the true value for each pixel owing to multi-samples smoothing effect on random noise components, as shown in Fig. 3 (a). For event stream, due to their dynamic sampling and the binary values, temporal multi-samples may contain both signal events and BA noise, as illustrated in Fig. 3 (b), directly taking the average of multi-samples cannot yield true signal value. Although the noise forms differ between the two modalities, they ultimately originate from the inherent noise in the circuitry analog signal, while resampling fundamentally helps suppress the random noise source.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Analysis. This concept inspired us to utilize multi-sampling",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "for event denoising, particularly when considering the binary state of events (presence or absence) where just two samplings are required to potentially identify noise. Thus, we initially investigated the noise inconsistency at the pixel level. Based on the DVS working principle [29], we build a circuit model in the Cadence [42] platform to simulate the dual-sampling with twice identical intensity input. The noisy analog signal converted from input generates BA noise at the originally steady stage compared to the ideal case in Fig. 4 (a). Clearly, the two sets of noise exhibit inconsistency, while the signals demonstrate high consistency, causing distinct alignment differences between the two cases as shown in the close-up of Fig. 4 (b).",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "To further explore the inter-class differences between noise and signal events in real-world dual-sampled events stream, we established a collection device as shown in Fig. 5 (a), to construct genuinely spatiotemporal dual-sampling. Two experimental conditions to validate the aforesaid circuit simulation phenomenon are a stationary camera and a moving one respectively. In the former, pure BA noise events was obtained, while the latter captured mixed events containing both noise and signal. In static tests, although at the highest noise level  $(-30\\%)$  threshold), both two sets of events exhibit significant spatiotemporal disparity. As observed in the right zoomed-in patches at the upper row in Fig. 4 (c), the global spatial misalignment of dual BA noises events was evident. The overlap rate of the pixels triggering event is also to be less than  $1\\%$ , as shown in the upperrow histogram of Fig. 4 (d). Not unexpectedly, in dynamic tests, regions with BA noise events remain inconsistency, while the coexistent signal events showing spatiotemporal alignment as depicted in lower-row counterpart, leading to a dramatic increase in overlap rate compared to the pure BA noise cases, as shown in the bottom histogram of Fig. 4 (d).",
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+    {
+        "type": "page_number",
+        "text": "25640",
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+    },
+    {
+        "type": "image",
+        "img_path": "images/635af38e31bb62e5022ecac3e503890e3dd5ff13d4d6d545aa107af50c22528f.jpg",
+        "image_caption": [
+            "Figure 6. Analysis of different event denoising results on our dataset. From left to right, the first column is the raw events, and the remaining five columns represent different methods, namely DWF, STDF, TimeSurface, EvFlow, and the proposed DED. From top to bottom, the first row shows the denoised results, the second row is the residual noise, the third row denotes the statistical distribution of the denoised results and the last row represents the intensity image reconstruction corresponding to the zoomed region denoised events."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "**Formulation.** These results support the insight that the consistency discrepancies between dual-sampled events could naturally help distinguish noise. Therefore, we develop a denoising framework with the dual events stream, called DED. In DED framework, given the spatiotemporal synchronized dual event streams  $Y_{1}$  and  $Y_{2}$ , they are composed of common latent signal  $X$  and respective noise streams  $N_{1}$  and  $N_{2}$ . The noise model can be defined as follows:",
+        "bbox": [
+            75,
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nY _ {1} = X + N _ {1}, Y _ {2} = X + N _ {2}. \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Because of the consistency of signal events and the inconsistency of noise events in  $Y_{1}$  and  $Y_{2}$ , after binary grid operation of event stream according to certain temporal window  $\\Delta t$ , we can perform spatial similarity to process them:",
+        "bbox": [
+            76,
+            530,
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+            590
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nX ^ {*} = \\left\\| \\left\\| X + N _ {1} \\right\\| \\circ \\left\\| X + N _ {2} \\right\\| \\right\\| _ {1}, \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            153,
+            592,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\circ$  denotes the Hadamard product used to obtain the similar part  $X^{*}$  of two groups of raw event binary frames. Due to the probability of a few noises occurring simultaneously in dual-sampling,  $X^{*}$  may still contain some much-isolated noise compared to the raw. As shown in Fig. 5 (b), for finer denoising, we further utilize the spatiotemporal correlation of the signal event stream to remove the residual noise from the previous step. Specifically, we accumulate the events from the relevant spatiotemporal range in corresponding  $X^{*}$  within several consecutive  $\\Delta t$  to form a spatiotemporal relationship set. The presence of these few isolated noise events, which are randomly triggered in the spatiotemporal domain, disrupts the inherent spatiotemporal correlation of signal reflecting a certain motion model. Therefore, to leverage this spatiotemporal continuity, we transform it into the following minimization problem:",
+        "bbox": [
+            75,
+            611,
+            472,
+            852
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\min  \\frac {1}{N - 1} \\sum_ {i = 1} ^ {N} \\left| e _ {\\boldsymbol {x}} ^ {t _ {i} + 1} - e _ {\\boldsymbol {x}} ^ {t _ {i}} \\right|, _ {\\boldsymbol {x} \\in \\Omega , \\Omega \\in X ^ {*}}, \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            127,
+            854,
+            468,
+            895
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $e_{\\pmb{x}}^{t_i}$  denotes the  $i_{th}$  occurring event according to the sorted timestamp,  $\\pmb{x}$  means the event spatial coordinates,  $n$  is the number of selected consecutive time windows,  $\\Omega$  represents the candidate spatial neighborhood, and  $N$  is total events number in  $\\Omega$ . Additionally, the aforesaid processing is all performed on the two channels of event polarity.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.3. Evaluation and Discussion",
+        "text_level": 1,
+        "bbox": [
+            500,
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The quality of GT is critical for a real paired event dataset. However, it is challenging to objectively evaluate the denoising results since directly obtaining clean data is unpractical. To fairly assess the denoising effects of different methods, we conducted a comprehensive evaluation.",
+        "bbox": [
+            496,
+            520,
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Fig. 6 presents comparative results of representative event denoising methods could be used for GT generation: spatiotemporal density filter-based (DWF[20], STDF[15]), smoothness optimization-based (TimeSurface[26]), and motion estimation-based (EvFlow[44]). The first and second rows display the denoised and residual noise visualization, respectively. It can be observed that DED effectively eliminates almost all the scattered BA noise with good preservation of the inherent structured feature, while the others exhibit residual noise and varying degrees of signal event damage. Statistical analysis on the global distribution of the denoised event is shown in the third row. Compared to others, DED demonstrates a higher number of blank patches while maintaining a high event preservation rate, which better reflects the overall sparsity and local concentration of the ideal event stream. Moreover, better denoising often leads to higher-quality reconstruction. In the last row, the intensity images reconstructed by E2VID [39] indicate that DED accurately restores nighttime scene information, such as leaves, building contours, and road signs",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "25641",
+        "bbox": [
+            478,
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+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/7cad2b81f803c427243459a40ec7582b05003a9a556a9c984cc57f638cdf0989.jpg",
+        "image_caption": [
+            "(a) Spike responses with different thresholds"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            76,
+            87,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/dfdc55ad0cd37f28cf8a01602ab2a68dfd9ac575d8acba6a9860dad7514cc7a9.jpg",
+        "image_caption": [
+            "(b) Framework of the DTSNN",
+            "Figure 7. An overview of the DTSNN model. (a) The dynamic threshold mechanism of LIF neuron. (b) The model with two branches consisting of DTB and EDB. Please refer to our supplementary material for more details about network architecture."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "with lower NIQE [35], which further indirectly validates the accuracy of denoised results and also confirms the superior effect of the processed data on reconstruction.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4. DTSNN for Event Denoising",
+        "text_level": 1,
+        "bbox": [
+            76,
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Compared to artificial neural networks(ANN), spiking neural network (SNN) have lower precision but are inherently suited for processing event-driven data due to their and information transfer mode temporal dynamics, gradually gaining prominence in event-based tasks [48, 49, 51, 52].",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Dynamic Threshold Mechanism. Adjustable spiking neuron offers enhanced biological plausibility [7, 13, 43]. Indeed, the neuron firing threshold, similar to the event camera threshold parameter, functions as controlling the output. Intuitively, the dynamic threshold (DT) mechanism can adapt to more complicated situations since a high threshold could suppress noisy input when noise dominates, while a low one helps to sensitively preserve the expected signals. Inspired by this, we transformed the fixed threshold into dynamic ones based on the LIF neuron model [19] to mimic this anisotropic biomechanism. The tendency of decreasing spike quantity of the postsynaptic neurons responses with an increasing threshold as illustrated in Fig. 7(a).",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "DTSNN Model. Therefore, we propose a fully SNN (all synaptic operations are SNN-based) incorporating learnable DT for event denoising, namely DTSNN. As illustrated in Fig. 7 (b), DTSNN consists of a dynamic threshold branch (DTB) and event denoising branch (EDB). The former dynamically generates a threshold map based on the successive event input, indicating the approximate spatial regions of signal or noise. This map is then passed to the latter, controlling the spiking process of LIF neurons in the last layer,",
+        "bbox": [
+            75,
+            763,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "which is depicted in Fig. 7 (b) and can be formulated as:",
+        "bbox": [
+            500,
+            90,
+            872,
+            106
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\left\\{ \\begin{array}{l} H ^ {n, t} = V ^ {n, t - 1} + U ^ {n, t} \\\\ S ^ {n, t} = H e a \\left(H ^ {n, t} - \\mathcal {F} \\left(V _ {\\text {t h}} ^ {t}\\right)\\right) \\\\ V ^ {n, t} = V _ {\\text {r e s e t}} S ^ {n, t} + \\frac {1}{\\tau} H ^ {n, t} \\odot (1 - S ^ {n, t}) \\end{array} \\right. \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            550,
+            111,
+            890,
+            181
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where  $n$  and  $t$  denote the layer number and time step respectively.  $H^{n,t}$  is the membrane potential which is produced by coupling the spatial feature  $U^{n,t}$  and the temporal input  $V^{n,t-1}$ . The DT map  $\\mathcal{F}(V_{\\mathrm{th}}^t)$  determines whether the output spiking matrix  $S^{n,t}$  should be fired or stay as zero, formulating the final denoised event matrix  $\\pmb{X}$ .  $Hea(x) = 1$  represents the Heaviside step function when  $x \\geq 0$ , otherwise  $Hea(x) = 0$ , and  $\\odot$  means a element-wise multiplication.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Notably, both two branches receive the same consecutive data as input, which is a binary event frame within a certain time window of  $\\Delta t$ . The denoising branch is supervised by the GT of signal events within  $\\Delta t$ , while the threshold map label of the dynamic threshold branch comes from the signal events over a longer temporal period.",
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+    },
+    {
+        "type": "text",
+        "text": "5. Experiments",
+        "text_level": 1,
+        "bbox": [
+            500,
+            415,
+            632,
+            431
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5.1. Experiments Setup",
+        "text_level": 1,
+        "bbox": [
+            500,
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+    },
+    {
+        "type": "text",
+        "text": "Implementation Details. We use a combined loss consisting of the L1-norm and BCE to train the proposed network. Our models are implemented with the open-source framework SpikingJelly [14], using NVIDIA A100 GPU. The Adam optimizer is employed with a batch size of 8 and a learning rate of 0.002. A fixed threshold of 0.5 is chosen for the rest of the neurons except at the last membrane potential layer. Besides, the reset value  $V_{\\mathrm{reset}}$  and the membrane time constant  $\\tau$  of all LIF neurons are set to 0 and 2, respectively. Datasets. We conduct quantitative experiments on existing paired datasets. Due to the enormous scale of billions of events in LED, training them all would be extremely time-consuming and resource-intensive. Therefore, 600 sequences were randomly selected for training with each consisting of consecutive 10 segments, and 60 sequences were randomly chosen for testing. To further evaluate the performance of the discrepancy of different datasets, we qualitatively test on typical public datasets DSEC [18] and E-MLB [8]. For event-based denoising methods, besides the methods in Sec.3.3 we select the representative supervised denoising methods including EDnCNN [2] and AEDNet[12].",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Evaluation Methods. We use an index of event denoising accuracy  $DA = \\frac{1}{2}\\left(\\frac{TP}{GP} +\\frac{TN}{GN}\\right)$  to measure the denoising performance on LED, where TP, TN, GP and GN are the number of true signal, true noise, total signal, and total noise respectively, forming two parts: signal retain (SR) and noise removal (NR). The metrics on other paired datasets are adopted from their proposed ones. Moreover, visualization results was qualitatively evaluated on other datasets.",
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+    {
+        "type": "page_number",
+        "text": "25642",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/74efc3c1ddc5247ce45110fb35169883c356218366efd09583afe6382e0e1cf4.jpg",
+        "image_caption": [
+            "Figure 8. Visual comparisons on LED. Comparing with state-of-the-arts, DTSNN achieves excellent denoising results and it is capable of removing noise events scattered around in sky, ground, and structural contours, simultaneously better preserve scene details."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            80,
+            89,
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+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/3919f0adfb27e5dfae5a0370515998b332852c159eda044bcfe760902307a6f7.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Datasets</td><td colspan=\"3\">LED</td><td>DVS CLEAN</td><td>DVS NOISE20</td><td>Average</td></tr><tr><td>Metrics</td><td>SR↑</td><td>NR↑</td><td>DA↑</td><td>SNR↑</td><td>RPMD↓</td><td>Runtime↓</td></tr><tr><td>Knoise[24]</td><td>16.4</td><td>98.9</td><td>57.6</td><td>25.21</td><td>17.64</td><td>1.33 ms</td></tr><tr><td>DWF[20]</td><td>42.6</td><td>83.9</td><td>63.3</td><td>26.96</td><td>31.39</td><td>3.67 ms</td></tr><tr><td>STDF[15]</td><td>37.4</td><td>99.1</td><td>68.3</td><td>19.30</td><td>30.23</td><td>2.04 ms</td></tr><tr><td>TS[26]</td><td>30.6</td><td>98.3</td><td>64.5</td><td>13.98</td><td>15.25</td><td>5.76 ms</td></tr><tr><td>EvFlow[44]</td><td>52.3</td><td>96.4</td><td>74.4</td><td>23.74</td><td>22.50</td><td>150.5 ms</td></tr><tr><td>EDnCNN[2]</td><td>80.0</td><td>82.0</td><td>81.0</td><td>20.29</td><td>22.25</td><td>251.4 ms</td></tr><tr><td>AEDNet[12]</td><td>81.2</td><td>83.6</td><td>82.4</td><td>25.58</td><td>18.51</td><td>708.1 ms</td></tr><tr><td>DTSNN</td><td>86.0</td><td>86.5</td><td>86.2</td><td>29.26</td><td>16.13</td><td>8.20 ms</td></tr></table>",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Table 2. Quantitative results comparison on different datasets. We mark the best and second best.",
+        "bbox": [
+            76,
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+        "type": "text",
+        "text": "5.2. Quantitative Evaluation",
+        "text_level": 1,
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+        "type": "text",
+        "text": "The main quantitative results are presented in Table 2. In summary, the proposed method achieves the best overall results on three datasets, followed by AEDNet. Particularly, DTSNN balances signal retention and noise removal effectively, demonstrating the highest denoising accuracy. Meanwhile, our model also achieved faster inference speed on average among them. Notably, the runtime from  $120 * 120$  events indicates that the efficiency of grid-based event representation and processing is significantly higher than the manner based on a single-event level, although the latter better preserves the asynchronous property of the event.",
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+        "type": "text",
+        "text": "5.3. Qualitative Evaluation",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Evaluation on LED Dataset. To further evaluate the denoising performance, we compare with the qualitative results of typical methods on LED. As shown in Fig. 8, DTSNN outperforms other methods by achieving visually pleasing results, which not only effectively removes noise events in areas such as the sky, ground and building con",
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+        "type": "image",
+        "img_path": "images/6523c29e1f781551da43c365219b16e27a0c4233fefb2e60845b2f37554ce107.jpg",
+        "image_caption": [
+            "Figure 9. Illustration of the LED diversity. We train DTSNN on different datasets: DVSCLEAN, DVSNOISE20 and LED, and test on real unpaired datasets (from left to right: DSEC  $\\rightarrow$  E-MLB). The model trained on LED has achieved better denoising results."
+        ],
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+    {
+        "type": "text",
+        "text": "tours, but also preserve the structural features of the scene and objects well. For example, the zoomed region of first row in Fig. 8 highlights that our method is the only one successfully preserving the information of small airborne target after denoising. Similarly, our method also stands out in retain lane marking located in the bottom-left of second row.",
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+    {
+        "type": "text",
+        "text": "Evaluation on Public Datasets. To evaluate the generalization across different datasets, we also train DTSNN on synthetic event denoising dataset DVSCLEAN [12] and real one DVSNoise20 [2] respectively, testing on DSEC [18] and E-MLB [8], the former is resolution of  $640^{*}480$  and the latter is resolution of  $346^{*}260$ . As shown in Fig. 9, the model trained on DVSCLEAN performs poorly due to the huge domain gap between. DVSNoise20 excels at removing noise effectively but inevitably loses some details. The",
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+    {
+        "type": "image",
+        "img_path": "images/b95fafc3640319eeedd7ac5e26b22757d12ea4f390cb3f3f50f3111cf878e018.jpg",
+        "image_caption": [
+            "Figure 10. Ablation study of the dual events denoising framework. The first column represents the noisy raw and the remaining three columns represent the flow without spatial similarity, without spatiotemporal correlation constraint and complete DED"
+        ],
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+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Architecture</td><td>Denoising Accuracy</td><td>Energy Ratio</td></tr><tr><td>ANN</td><td>84.5</td><td>18×</td></tr><tr><td>SNN</td><td>86.0</td><td>1×</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "model trained on LED achieves satisfactory results across various scenes in these datasets which simultaneously removes noise without apparent signal loss, strongly supporting the great generalization of the proposed LED dataset.",
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+    {
+        "type": "text",
+        "text": "5.4. Ablation Study and Discussion",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Effectiveness of DED Framework. The DED framework aims to fully exploit the property of noise inconsistency /signal consistency in dual events and the self-correlation in a single event stream. As shown in Fig. 10, the small target signal is overwhelmed by noise events, utilizing solely spatiotemporal correlation constraints can only remove partial noise events because some of them also satisfy this relationship. Relying on the spatial similarity of dual event streams effectively disassembles the mutual relationship in the dense noise event group. Therefore, combining both procedures can achieve a more refined denoising result.",
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+    {
+        "type": "text",
+        "text": "Effectiveness of Spiking Neuron. Intuitively, the inherent spatiotemporal sparsity of event streams seamlessly aligns with SNN because of the temporal information ability of spiking neurons. To compare the performance differences between SNN and ANN architectures in the event denoising tasks, the evaluation was conducted on the same structure. As shown in Table 3, the SNN based on LIF neuron achieves better denoising accuracy while maintaining  $18 \\times$  lower power consumption advantage compared to its ANN version (the spiking neurons replaced with ReLU).",
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+    {
+        "type": "text",
+        "text": "Effectiveness of DT Module. To evaluate the effects of the proposed learnable threshold mechanism of DTSNN, we train the network with various fixed threshold neurons and dynamic threshold neurons, respectively. As can be observed from Table 4 and Fig. 11 (a), the denoising accuracy improves after introducing the DT module due to the network has the tendency to increasing spiking probability for signal pixels according to threshold prediction, and the Fig. 11 (b) illustrates DT module could assist in locating the approximate signal or noise region to retain more signal events from structural area compared to the FT model.",
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+    {
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+        "img_path": "images/9c01e4afe428d8a84921e8c4b8360c27458ac2ad6065abbaca991f12d07ed2d8.jpg",
+        "image_caption": [
+            "(a) Inference process",
+            "(b) Denoised results"
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+        "image_footnote": [],
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+    {
+        "type": "image",
+        "img_path": "images/4e76dfc37e764591ebd63fb682e8268a4e361fa4ffa58923df0002092348c432.jpg",
+        "image_caption": [
+            "Figure 11. Illustration of the DT model Effectiveness. (a) Inference accuracy of SNN with various fixed thresholds and with DT. (b) Denoised results without DT and with DT, respectively."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "table",
+        "img_path": "images/82915b09feacbad9eac7988ef42c25e246c322dbb7a0b5449666790f529ee07e.jpg",
+        "table_caption": [
+            "Table 3. Comparison between ANN and SNN."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Type</td><td>FTSNN (0.3 th)</td><td>FTSNN (0.5 th)</td><td>FTSNN (0.8 th)</td><td>DTSNN</td></tr><tr><td>Accuracy</td><td>85.5</td><td>86.0</td><td>85.7</td><td>86.2</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Table 4. Inference accuracy with proposed methods implemented.",
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+    },
+    {
+        "type": "text",
+        "text": "Discussion. Essentially, true events comes from intensity changes. When artificial light source variations exist, the light source itself, its coverage area and reflection from ground texture would result in relevant events. These signal events exhibit noise-like features with discontinuous structure, while the proposed DED framework considers them as signal event that should be preserved. Thus, with the supervision of such signal labels, the proposed model also tend to retain such events arise from lamp as shown in left two columns of Fig. 9 despite their visually unappealing effect.",
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+    {
+        "type": "text",
+        "text": "Limitation. The DED framework may fail in extreme cases where similar part are dominated by noise events. However, such globally anomalous high-frequency noise is rare in practice. Moreover, the proposed model struggles to capture those insignificant signals attaching to structural periphery, limiting signal retain performance in metrics.",
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+    {
+        "type": "text",
+        "text": "6. Conclusion",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we construct a new large-scale high-quality paired real event denoising dataset LED, which provides diverse noise levels and scenes which aims to cover various internal and external conditions. Based on the consistency difference of noise and signal events, the proposed DED framework could effectively generate high-quality GT and detailed analysis confirms our better results than others. In addition, we propose a novel baseline DTSNN for event denoising featuring with dynamic threshold mechanism of LIF neuron. The experimental results demonstrate the superiority of the proposed dataset and denoising method.",
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+    {
+        "type": "text",
+        "text": "Acknowledgments. The computation is completed in the HPC Platform of Huazhong University of Science and Technology. This work was supported by the National Natural Science Foundation of China under Grant 62371203.",
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+    {
+        "type": "text",
+        "text": "References",
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