CVPR 2026 Papers

Conference on Computer Vision and Pattern Recognition

Decision breakdown

4,042papers

Counted from the official paper list; may differ slightly from the number the conference announced.

  • Oral
    1383.4%
  • Poster
    3,90496.6%

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VGGT-Segmentor: Geometry-Enhanced Cross-View Segmentation

Yulu Gao, Bohao Zhang, Zongheng Tang, Jitong Liao, Wenjun Wu, Si Liu

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Instance-level object segmentation across disparate egocentric and exocentric views is a fundamental challenge in visual understanding, critical for applications in embodied AI and remote collaboration. This task is exceptionally difficult due to severe changes in scale, perspective, and occlusion, which destabilize direct pixel-level matching. While recent geometry-aware models like VGGT provide a strong foundation for feature alignment, we find they often fail at dense prediction tasks due to significant pixel-level projection drift, even when their internal object-level attention remains consistent. To bridge this gap, we introduce VGGT-Segmentor (VGGT-S), a framework that unifies robust geometric modeling with pixel-accurate semantic segmentation. VGGT-S leverages VGGT's powerful cross-view feature representation and introduces a novel Union Segmentation Head. This head operates in three stages: mask prompt fusion, point-guided prediction, and iterative mask refinement, effectively translating high-level feature alignment into a precise segmentation mask. Furthermore, we propose a single-image self-supervised training strategy that eliminates the need for paired annotations and enables strong generalization. On the Ego-Exo4D benchmark, VGGT-S sets a new state-of-the-art, achieving 67.7% and 68.0% average IoU for Ego-Exo and Exo-Ego tasks, respectively, significantly outperforming prior methods. Notably, our correspondence-free pretrained model surpasses most fully-supervised baselines, demonstrating the effectiveness and scalability of our approach.

Oral
SPARK: Sim-ready Part-level Articulated Reconstruction with VLM Knowledge

Yumeng He, Ying Jiang, Jiayin Lu, Yin Yang, Chenfanfu Jiang

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Articulated 3D objects are critical for embodied AI, robotics, and scene understanding, yet creating simulation-ready assets remains labor-intensive and requires expert modeling of part hierarchies and motion structures. We introduce SPARK, a framework for reconstructing physically consistent, kinematic part-level articulated objects from a single RGB image. Given the image, we first leverage VLMs to extract coarse URDF parameters and generate part-level reference images. We then integrate the part-image guidance and the inferred structure graph into a diffusion transformer to synthesize consistent part and complete shapes of articulated objects. To further refine the URDF parameters, we explore a VLM-based reprediction strategy for discrete attribute refinement and a differentiable forward kinematics module for continuous parameter optimization under VLM-generated open-state supervision. Extensive experiments show that SPARK produces high-quality, simulation-ready articulated assets across diverse categories, enabling downstream applications such as robotic manipulation and interaction modeling.

Oral
Hearing the Room Through the Shape of the Drum: Modal-Guided Sound Recovery from Multi-Point Surface Vibrations

Shai Bagon, Matan Kichler, Mark Sheinin

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Optical vibration sensing enables recovering the scene sound directly from the surface vibration of nearby objects, turning everyday objects into "visual microphones". However, most prior methods had focused on capturing the vibrations of specific objects with highly favorable vibration responses. These include objects where the surface vibrations are generated by the object itself (e.g., speaker membrane or guitar body) or objects consisting of a thin membrane which is highly reactive to sound (e.g., a chip bag or the leaf of a plant).In this paper, we tackle sound recovery for a more challenging class of solid objects whose vibration responses are poor or highly resonant. We simultaneously capture vibrations for multiple surface points on the object using a speckle-based vibrometry imaging system. Then, we derive a novel physics-guided vibration formation model that relates the scene sound source to the captured multi-point multi-axis vibrations via the object's vibrational modes. The model is then used to reverse the resonant transfer function of the vibrating object, fusing the plurality of vibration signals to estimate the original sound source of the scene. We evaluate our approach by recovering sound from a variety of everyday objects, demonstrating that it significantly outperforms traditional single-point speckle vibrometry in challenging scenarios where it performs poorly.

Oral
Proxy-GS: Unified Occlusion Priors for Training and Inference in Structured 3D Gaussian Splatting

Yuanyuan Gao, Yuning Gong, Yifei Liu, Jingfeng Li, Dan Xu, Yanci Zhang, Dingwen Zhang, Xiao Sun, Zhihang Zhong

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3D Gaussian Splatting (3DGS) has emerged as an efficient approach for photorealistic rendering. Recent MLP-based variants further improve visual fidelity but introduce substantial decoding overhead during rendering. To reduce the computational cost, several pruning strategies and level-of-detail (LOD) techniques have been introduced to reduce the number of Gaussian primitives in large-scale scenes. However, our analysis reveals that significant redundancy still remains due to the lack of occlusion awareness. In this work, we propose Proxy-GS, a novel pipeline that uses a proxy representation to introduce occlusion awareness for Gaussians from arbitrary views. At the core of our approach is a fast proxy system capable of producing precise occlusion depth maps at a resolution of 1000 x 1000 in under 1 ms. This proxy serves two roles. First, it guides the culling of anchors and Gaussians to accelerate rendering. Second, it guides densification toward scene surfaces during training, reducing inconsistencies in occluded regions and thereby improving rendering quality. In heavily occluded scenarios such as the MatrixCity Streets dataset, Proxy-GS achieves more than a 2.5x speedup over Octree-GS while also improving rendering quality.

Oral
Memory-Augmented Scene Understanding and Exploration for Open-World Aerial Object-Goal Navigation

Jiacong Zhou, Jiaxu Miao, Yourun Lin, Xianyun Wang, Jun Xiao, Jun Yu

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Aerial object-goal navigation (Aerial ObjectNav) requires an Unmanned Aerial Vehicle (UAV) to navigate to target objects in large-scale outdoor environments using only visual observations and high-level object descriptions, without detailed step-by-step instructions. Existing approaches rely on local observations or short-term history, lacking comprehensive scene understanding and efficient spatial exploration strategies, which constrains their navigation capability in complex aerial scenarios. To address these challenges, we propose OctMem-Agent, an octree memory-augmented framework for aerial object-goal navigation. Specifically, we introduce an Adaptive Octree Memory that incrementally aggregates RGB-D observations into a hierarchical 3D representation, capturing both explored regions and unexplored frontiers across large-scale aerial environments. We further propose a Instruction-Guided Memory Query module that extracts task-relevant scene and exploration tokens through instruction-modulated queries. By integrating these tokens with visual observations and language instructions, OctoMem-Agent achieves comprehensive scene understanding and effective spatial exploration for target localization. Extensive experiments on the Aerial ObjectNav benchmark UAV-ON demonstrate that our method achieves a significant 7.5% improvement in success rate over existing methods, validating the effectiveness of our design.

Oral
Linear Fundamental Matrix Estimation from 7 or 5 Points

Taci Ata Kucukpinar, Juan Mogollon, Joshua Fraser, Timothy Duff, Kannappan Palaniappan

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We revisit the problem of estimating the fundamental matrix of a pair of perspective cameras, a cornerstone of geometric computer vision. As is well-known, linear solvers require at least 8 point correspondences, whereas nonlinear minimal solvers require just 7 in the uncalibrated case or 5 in the calibrated case. In this paper, we consider a special case of the 7-point problem where 5 of the points are configured to lie on two lines, which has previously been shown to have a unique solution. As a theoretical contribution, we offer a completely elementary analysis of how this uniqueness manifests in the standard 7-point algorithm. On a practical level, we provide the first linear solver for the minimal problem associated to this special configuration. Additionally, we evaluate a heuristic 5-point fundamental matrix solver based on the construction of virtual midpoints. When combined with early non-minimal fitting, the runtime and accuracy of our solver is competitive with the state-of-the-art (SOTA) on multiple benchmarks. Code is available at https://github.com/CIVA-Lab/v-umlaut.

Oral
ARGUS: Defending Against Multimodal Indirect Prompt Injection via Steering Instruction-Following Behavior

Weikai Lu, Ziqian Zeng, Kehua Zhang, Haoran Li, Huiping Zhuang, Ruidong Wang, Cen Chen, Hao Peng

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Multimodal Large Language Models (MLLMs) are increasingly vulnerable to multimodal Indirect Prompt Injection (IPI) attacks, which embed malicious instructions in images, videos, or audio to hijack model behavior. Existing defenses, designed primarily for text-only LLMs, are unsuitable for countering these multimodal threats, as they are easily bypassed, modality-dependent, or generalize poorly. Inspired by activation steering research, we hypothesize that a robust, general defense independent of modality can be achieved by steering the model's behavior in the representation space. Through extensive experiments, we discover that the instruction-following behavior of MLLMs is encoded in a subspace. Steering along directions within this subspace can enforce adherence to user instructions, forming the basis of a defense. However, we also found that a naive defense direction could be coupled with a utility-degrading direction, and excessive intervention strength harms model performance. To address this, we propose ARGUS, which searches for an optimal defense direction within the safety subspace that decouples from the utility degradation direction, further combining adaptive strength steering to achieve a better safety-utility trade-off. ARGUS also introduces a lightweight injection detection stage to activate the defense on-demand, and a post-filtering stage to verify defense success. Experimental results show that ARGUS can achieve robust defense against multimodal IPI while maximally preserving the MLLM's utility. Our code will be available at https://github.com/ZeroNLP/ARGUS.

Oral
Molmo2: Open Weights and Data for Vision-Language Models with Video Understanding and Grounding

Christopher Clark, Jieyu Zhang, Zixian Ma, Jae Sung Park, Rohun Tripathi, Sangho Lee, Mohammadreza Salehi, Jason Ren, Chris Dongjoo Kim, Yinuo Yang, Vincent Shao, Yue Yang, Weikai Huang, Ziqi Gao, Taira Anderson, Jianrui Zhang, Jitesh Jain, George Stoica, Ali Farhadi, Ranjay Krishna

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Today's strongest video-language models (VLMs) remain proprietary, and the strongest open-weight models often rely on synthetic data from proprietary VLMs and do not disclose their training data or recipe. As a result, the open-source community lacks the foundations needed to improve on the state-of-the-art video (and image) language models. Crucially, many downstream applications require grounding--either by pointing or by tracking in pixels. Even proprietary models lack this capability. We present Molmo2, a new family of VLMs that are state-of-the-art among open-source models and demonstrate exceptional new capabilities in point-driven grounding in single image, multi-image, and video tasks. Our key contribution is a collection of 7 new video datasets and 2 multi-image datasets, including a dataset of highly detailed video captions for pre-training, a free-form video Q&A dataset for fine-tuning, a new object tracking dataset with complex queries, and an innovative new video pointing dataset, all collected without the use of closed VLMs. We also present a training recipe for this data utilizing an efficient packing and message-tree encoding scheme, and show bi-directional attention on vision tokens and a novel token-weight strategy improves performance. Our best-in-class 8B model outperforms others in the class of open weight and data models on short videos, counting, and captioning, and is competitive on long-videos. On video-grounding Molmo2 significantly outperforms existing open-weight models like Qwen3-VL (35.5 vs 29.6 accuracy on video counting) and surpasses proprietary models like Gemini 3 Pro on some tasks (38.4 vs 20.0 F1 on video pointing and 56.2 vs 41.1 J&F on video tracking). Our model weights, new datasets, and source code are available at https://allenai.org/blog/molmo2.

Oral
Spectrum from Defocus: Fast Spectral Imaging with Chromatic Focal Stack

M. Kerem Aydin, Yi-Chun Hung, Jaclyn Pytlarz, Qi Guo, Emma Alexander

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Hyperspectral cameras rely on spectral filters, dispersive optics, or coded apertures, which reduce light throughput and increase hardware complexity. These systems face harsh trade-offs between spatial, spectral, and temporal resolution in inherently low-photon conditions. Computational imaging systems break through these trade-offs with compressive sensing, but have typically required complex optics and/or extensive computation. We present Spectrum from Defocus (SfD), a chromatic focal sweep method that achieves state-of-the-art hyperspectral imaging using only two off-the-shelf lenses, a grayscale sensor, and less than one second of reconstruction time. By capturing a chromatically-aberrated focal stack that preserves nearly all incident light, and reconstructing it with a fast physics-based iterative algorithm, SfD delivers sharp, accurate hyperspectral images. The combination of photon efficiency, optical simplicity, and physical interpretability makes SfD a promising solution for fast, compact, and interpretable hyperspectral imaging.

Oral
Dual-level Adapter Boosting Prompt-free Curvilinear Structure Segmentation

Kai Zhu, Li Chen, Jun Cheng

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Curvilinear structure segmentation is essential in domains such as medical imaging, remote sensing, and materials science. Existing methods often require extensive domain-specific training and lack generalization to novel domains. To overcome these limitations, we propose the Segment Anything Curve Model (SACM) -- a universal, curvilinear segmentation framework built upon the pretrained Segment Anything Model (SAM). SACM introduces a dual-level adapter architecture that enables both fine-grained and domain-adaptive enhancement: block-level internal adapters refine local structural representations, while external adapters facilitate cross-domain feature alignment. Specifically, the internal adapters are embedded within each Transformer block to locally adapt and refine features for thin and intricate curvilinear patterns, while the external adapters operate across blocks to capture global, multi-layer contextual information and facilitate domain adaptation. Furthermore, SACM introduces a feature fusion mechanism that aggregates multi-layer features from all external adapters and fuses them via a Feed-Forward Network (FFN) module, and a dual-stage refinement process in the mask decoder to enhance topology and connectivity. This design enables prompt-free, data-efficient fine-tuning and achieves robust cross-domain generalization when trained with only 18 annotated images. Extensive experiments across twelve diverse curvilinear datasets validate that SACM achieves state-of-the-art performance.

Oral
SEATrack: Simple, Efficient, and Adaptive Multimodal Tracker

Junbin Su, Ziteng Xue, Shihui Zhang, Kun Chen, Weiming Hu, Zhipeng Zhang

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Parameter-efficient fine-tuning (PEFT) in multimodal tracking reveals a concerning trend where recent performance gains are often achieved at the cost of inflated parameter budgets, which fundamentally erodes PEFT's efficiency promise. In this work, we introduce SEATrack, a Simple, Efficient, and Adaptive two-stream multimodal tracker that tackles this performance-efficiency dilemma from two complementary perspectives. We first prioritize cross-modal alignment of matching responses, an underexplored yet pivotal factor that we argue is essential for breaking the trade-off. Specifically, we observe that modality-specific biases in existing two-stream methods generate conflicting matching attention maps, thereby hindering effective joint representation learning. To mitigate this, we propose AMG-LoRA, which seamlessly integrates Low-Rank Adaptation (LoRA) for domain adaptation with Adaptive Mutual Guidance (AMG) to dynamically refine and align attention maps across modalities. We then depart from conventional local fusion approaches by introducing a Hierarchical Mixture of Experts (HMoE) that enables efficient global relation modeling, effectively balancing expressiveness and computational efficiency in cross-modal fusion. Equipped with these innovations, SEATrack advances notable progress over state-of-the-art methods in balancing performance with efficiency across RGB-T, RGB-D, and RGB-E tracking tasks. Code is available.

Oral
FedAdamom: Adaptive Momentum for Improved Generalization in Federated Optimization

Wenjie Hou, Tianxiang Chen, Feng Wang, Tiantong Wu, Zhiming Zheng, Shaoting Tang, Wei Yang Bryan Lim

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Federated learning (FL) has emerged as a widely adopted training paradigm for privacy-preserving machine learning. Despite the past success of SGD-based methods, they still suffer from severe data heterogeneity and the lack of adaptivity in practical applications. While several adaptive federated optimization methods (such as FedAdam) have been proposed and demonstrated to achieve faster convergence, they fail to show significant improvements in generalization performance under highly heterogeneous data distributions, and their optimization and generalization mechanisms remain insufficiently understood. To fill this gap, we introduce diffusion theory into the adaptive federated optimization framework and analyze the distinct effects of adaptive learning rate and global momentum from the perspectives of saddle-point escaping and flat-minima selection. Theoretical results show that although FedAdam outperforms FedAvg/FedAvgM in escaping saddle points, the latter escapes sharp minima more efficiently. The root cause lies in that adaptive learning rates, while enhancing saddle-point escape, weaken the preference for flat minima. Motivated by these insights, we propose FedAdamom, a new adaptive federated optimization algorithm that adapts the momentum hyperparameter rather than the learning rate. FedAdamom maintains strong saddle-point escaping capability while enhancing flat-minima selection. We further establish its convergence guarantees under non-convex objectives. Extensive experiments demonstrate that FedAdamom significantly outperforms existing adaptive federated optimization methods in terms of convergence speed, generalization performance, and preference for flat minima.

Oral
Energy-GS: Image Energy-guided Pose Alignment Gaussian Splatting with redesigned pose gradient flow

Yu Gao, Lutong Su, Ruixiang Huang, Tianji Jiang, Jiadong Tang, Yufeng Yue, Yi Yang

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High-quality 3D scene representation in radiance fields relies on accurate camera poses which are often difficult to acquire in real-world scenarios. An effective solution is to use RGB images for the joint optimization of radiance fields and camera poses, an approach that has been well explored in NeRF series methods. However, unlike NeRF, joint optimization in 3D Gaussian Splatting (3DGS) often requires additional regularization or prior spatial knowledge to reach comparable performance. To eliminate these dependencies, we introduce Energy-GS, a pose-aware Gaussian splatting framework that jointly optimizes scene representation and camera poses using only RGB images. We observe that pose gradients in joint optimization are unstable due to the point-based rendering mechanism. Furthermore, unlike NeRF's spatial sampling framework that enables coarse-to-fine pose alignment, rasterization-based 3DGS lacks controllable sampling and thus cannot support progressive pose refinement. To address these challenges, we redesign the optimization strategy of Gaussian primitives and introduce an image-energy-guided constraint that encourages progressive alignment of camera poses. Experiments on both synthetic and real-world datasets show that Energy-GS can effectively optimize the scene reconstruction and resolve camera pose misalignment at the same time. Benefiting from reliance on only RGB images, we believe this work provides promising insights for visual localization and dense mapping applications such as SLAM. The Code is available at \href https://github.com/SkylerGao/ENGS https://github.com/SkylerGao/ENGS

Oral
Differentiable Laplacian Matrix Guided Superpixel Segmentation

Jeremy Juybari, Josh Hamilton, Shuvra Das, Chaofan Chen, Andre Khalil, Yifeng Zhu

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Superpixels partition an image into perceptually coherent regions, reducing the cost of downstream vision tasks. Modern deep learning methods excel at superpixel generation but often yield irregular boundaries and isolated pixels, necessitating non-differentiable post-processing to enforce connectivity. This undermines the end-to-end learning capabilities. We propose a simple, fully differentiable graph-Laplacian loss that encourages spatial regularity and connectivity during training. The loss is model-agnostic and can be seamlessly integrated into the training of existing architectures to improve the quality of superpixels. In addition, we introduce two novel metrics, the average stray pixel count and excess component count, to measure the quality of superpixels. We demonstrate both qualitative and quantitative improvements over state-of-the-art methods with and without enforced connectivity. Our approach represents a significant step toward eliminating non-differentiable post-processing. Project code: https://github.com/jeremyJJB/Differentiable-Laplacian-Matrix-Guided-Superpixel-Segmentation.

Oral
CineBrain: A Large-Scale Multi-Modal Audiovisual Brain Dataset for Brain-Conditioned Video Generation

Jianxiong Gao, Yichang Liu, Baofeng Yang, Jianfeng Feng, Yanwei Fu

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Most research decoding brain signals into images, often using them as priors for generative models, has focused only on visual content. This overlooks the brain's natural ability to integrate auditory and visual information, for instance, sound strongly influences how we perceive visual scenes. To investigate this, we propose a new task of reconstructing continuous video stimuli from multimodal brain signals recorded during audiovisual stimulation. To enable this, we introduce CineBrain, the first large-scale dataset that synchronizes fMRI and EEG during audiovisual viewing, featuring six hours of The Big Bang Theory episodes for cross-modal alignment. We also conduct the first systematic exploration of combining fMRI and EEG for video reconstruction and present CineSync, a framework for reconstructing dynamic video using a Multi-Modal Fusion Encoder and a Neural Latent Decoder. CineSync achieves state-of-the-art performance in dynamic reconstruction, leveraging the complementary strengths of fMRI and EEG to improve visual fidelity. Our analysis shows that auditory cortical activations enhance decoding accuracy, highlighting the role of auditory input in visual perception. Project Page: https://jianxgao.github.io/CineBrain.

Oral
Breaking Semantic Boundaries: Distribution-Guided Semantic Exploration for Creative Generation

Fu Feng, Yucheng Xie, Ruixiao Shi, Xu Yang, Jing Wang, Xin Geng

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Text-to-image (T2I) diffusion models effectively produce semantically aligned images, but their reliance on training distributions constrains their capacity for synthesizing truly novel, out-of-distribution concepts. Existing methods attempt to enhance creativity through semantic exploration, such as fusing known concept pairs, but the resulting images remain linguistically describable and confined to familiar semantic spaces. Inspired by the soft probabilistic outputs of classifiers on novel or out-of-distribution inputs, we propose Distribution-Conditional Generation, a paradigm that models novel concepts as image synthesis conditioned on class distributions, enabling controllable yet semantically unconstrained creative generation. Building on this, we propose DisTok, an encoder-decoder framework that unifies conditional and unconditional creative generation by decoding latent representations--either randomly sampled or mapped from conditions (e.g., class distributions)--into tokens representing novel concepts. DisTok is trained by iteratively sampling and fusing concept pairs from a dynamic pool to model progressively complex distributions, while enforcing semantic consistency through a vision-language model that aligns the class distributions of generated images with the input distributions. Extensive experiments demonstrate that DisTok enables efficient and flexible semantic exploration for token-level creative synthesis, achieving state-of-the-art text-image alignment and human preference.

Oral
SmokeSVD: Smoke Reconstruction from A Single View via Progressive Novel View Synthesis and Refinement with Diffusion Models

Chen Li, Shanshan Dong, Sheng Qiu, Jianmin Han, Yibo Zhao, Zan Gao, Taku Komura, Kemeng Huang

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Reconstructing dynamic fluids from sparse views is a long-standing and challenging problem, due to the severe lack of 3D information from insufficient view coverage. While several pioneering approaches have attempted to address this issue using differentiable rendering or novel view synthesis, they are often limited by time-consuming optimization under ill-posed conditions. We propose SmokeSVD, an efficient and effective framework to progressively reconstruct dynamic smoke from a single video by integrating the generative capabilities of diffusion models with physically guided consistency optimization. Specifically, we first propose a physically guided side-view synthesizer based on diffusion models, which explicitly incorporates velocity field constraints to generate spatio-temporally consistent side-view images frame by frame, significantly alleviating the ill-posedness of single-view reconstruction. Subsequently, we iteratively refine novel-view images and reconstruct 3D density fields through a progressive multi-stage process that renders and enhances images from increasing viewing angles, generating high-quality multi-view sequences. Finally, we estimate fine-grained density and velocity fields via differentiable advection by leveraging the Navier-Stokes equations. Our approach supports re-simulation and downstream applications while achieving superior reconstruction quality and computational efficiency compared to state-of-the-art methods.

Oral
CoSMo3D: Open-World Promptable 3D Semantic Segmentation through LLM-Guided Canonical Spatial Modeling

Li Jin, Weikai Chen, Yujie Wang, Yingda Yin, Zeyu HU, Runze Zhang, keyang luo, Shengju Qian, Xin Wang, Xueying Qin

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Open-world promptable 3D semantic segmentation remains brittle as semantics are inferred in the input sensor coordinates. Yet, humans, in contrast, interpret parts via functional roles in a canonical space -- wings extend laterally, handles protrude to the side, and legs support from below. Psychophysical evidence shows that we mentally rotate objects into canonical frames to reveal these roles. To fill this gap, we propose CoSMo3D, which attains canonical space perception by inducing a latent canonical reference frame learned directly from data. By construction, we create a unified canonical dataset through LLM-guided intra- and cross-category alignment, exposing canonical spatial regularities across 200 categories. By induction, we realize canonicality inside the model through a dual-branch architecture with canonical map anchoring and canonical box calibration, collapsing pose variation and symmetry into a stable canonical embedding. This shift from input pose space to canonical representation yields far more stable and transferable part semantics. Experimental results show that CoSMo3D establishes new state of the art in open-world promptable 3D segmentation.

Oral
Learning Convex Decomposition via Feature Fields

Yuezhi Yang, Qixing Huang, Mikaela Angelina Uy, Nicholas Sharp

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This work proposes a new formulation to the long-standing problem of convex decomposition through learning feature fields, enabling the first feed-forward model for open-world learning of convex decomposition. Our method produces high-quality decompositions of 3D shapes into a union of convex bodies, which are essential to accelerate collision detection in physical simulation, amongst many other applications.The key insight is to adopt a feature learning approach and learn a continuous feature field that can later be clustered to yield a good convex decomposition via our self-supervised, purely-geometric objective derived from the classical definition of convexity.Our formulation can be used for single shape optimization, but more importantly, feature prediction unlocks scalable, self-supervised learning on large datasets resulting in the first learned open-world for convex decomposition.Experiments show that our decompositions are higher-quality than alternatives and generalize across open-world objects as well as across representations to meshes, CAD models, and even Gaussian splats.

Oral
Learning Eigenstructures of Unstructured Data Manifolds

Roy Velich, Arkadi Piven, David Bensaid, Daniel Cremers, Thomas Dagès, Ron Kimmel

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We introduce a novel framework that directly learns a spectral basis for shape and manifold analysis from unstructured data, eliminating the need for traditional operator selection, discretization, and eigensolvers. Grounded in optimal-approximation theory, we train a network to decompose an implicit approximation operator by minimizing the reconstruction error in the learned basis over a chosen distribution of probe functions. For suitable distributions, they can be seen as an approximation of the Laplacian operator and its eigendecomposition, which are fundamental in geometry processing. Furthermore, our method recovers in a unified manner not only the spectral basis, but also the implicit metric's sampling density and the eigenvalues of the underlying operator. Notably, our unsupervised method makes no assumption on the data manifold, such as meshing or manifold dimensionality, allowing it to scale to arbitrary datasets of any dimension. On point clouds lying on surfaces in 3D and high-dimensional image manifolds, our approach yields meaningful spectral bases, that can resemble those of the Laplacian, without explicit construction of an operator. By replacing the traditional operator selection, construction, and eigendecomposition with a learning-based approach, our framework offers a principled, data-driven alternative to conventional pipelines. This opens new possibilities in geometry processing for unstructured data, particularly in high-dimensional spaces.

Oral