Organizations: Zhejiang University, China · Zhejiang Lab, China · Wenzhou University of Technology, China
Abstract
Non-rigid 3D shape matching is a fundamental task in computer vision and graphics. In this paper, we propose a hybrid self-supervised method based on a coarse-to-fine strategy, which ensures consistency between the coarse mapping and the refined correspondence produced by our refinement module. The architecture features a dual-branch design, consisting of two symmetric functional map learning streams: one based on the Laplacian basis and the other utilizing the elastic basis. Extensive experiments show that our approach not only maintains computational efficiency, but also achieves state-of-the-art performance across a variety of challenging scenarios, including non-isometric deformations and topological noise. Finally, we rigorously demonstrate that contrastive energies promote feature discrimination. Furthermore, integrating these energies with existing methods yields consistent improvements, validating the overall efficacy of our approach. Our code is available at https://github.com/LuoFeifan77/Coarse-to-Fine-Hybrid-Self-Supervised-Matching.
Establishing accurate point-to-point correspondences between non-rigid 3D shapes remains a critical challenge, particularly under non-isometric deformations and topological noise. Existing functional map pipelines suffer from ambiguities that geometric descriptors alone cannot resolve, and spatial inconsistencies inherent in the projection of truncated spectral bases to dense pointwise correspondences. In this paper, we introduce SGMatch, a learning-based framework that couples 3D-lifted semantic cues with trajectory-level feature transport regularization. Specifically, we design a Semantic-Guided Local Cross-Attention module that integrates semantic features from vision foundation models into geometric descriptors while preserving local structural continuity. Furthermore, we adapt conditional flow matching as a time-conditioned feature transport regularizer that promotes spatially coherent point-wise recovery. Experimental results on multiple benchmarks demonstrate that SGMatch achieves competitive performance across near-isometric settings and consistent improvements under non-isometric deformations and topological noise.
Functional maps are the cornerstone of recent non-rigid 3D shape matching methods due to their efficiency and performance. However, existing methods struggle with challenging scenarios, such as partiality, topological noise, and raw point clouds. A primary bottleneck is that significant intrinsic distortion prevents truncated spectral bases from being accurately aligned via linear transformations (i.e., functional maps). To address this, we introduce a hyper-network that predicts non-linear neural functional maps (NFM), learned in an unsupervised manner, to better align spectral bases. Specifically, we model the NFM as an MLP with skip-connection to refine standard FM and employ a hyper-network to predict its weights, conditioned on standard FM. Our framework is trained using a novel unsupervised spectral alignment loss. Experiments demonstrate that our approach can be seamlessly integrated into state-of-the-art unsupervised deep functional map pipelines, substantially improving matching accuracy in demanding scenarios.
Finding dense correspondences between 3D shapes is a fundamental yet unresolved challenge, especially in real-world environments. These environments present severe challenges, including the lack of time and sufficient samples for training, the prevalence of uncurated extreme-high resolution data with topological distortions, and the need to handle diverse 3D representations. In this paper, we present ATM, a zero-shot framework that requires no correspondence-specific training and robustly addresses these issues at once through an articulate-then-match paradigm. Rather than relying on intrinsic geometric properties, we leverage powerful pretrained vision foundation models and parametric shape priors to estimate parametric shape models from multi-view renderings, and systematically ground these estimations via multi-view geometric consistency. By mapping diverse inputs into a shared canonical parametric space, we inherently establish robust coarse correspondences that bypass topological noise, which are then refined into precise dense mappings via spectral refinement. Operating purely on test-time optimized parametric reconstructions, ATM requires no correspondence training data, is naturally immune to connectivity artifacts, and seamlessly handles diverse 3D modalities, including meshes, point clouds, and 3D Gaussians. Extensive experiments demonstrate that our method achieves strong results on non-isometric benchmarks (average geodesic errors of 2.4-TOPKIDS, 3.8-SMAL), reducing errors by 73% and 37% respectively compared to the baseline URSSM. Furthermore, it exhibits unprecedented robustness on in-the-wild raw scans of up to 200k vertices per shape while maintaining near-constant computation time and consistent superior accuracy.