SGMatch: Semantic-Guided Non-Rigid Shape Matching with Flow Regularization

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.

Learning dense correspondences across deformable 3D shapes remains a long-standing challenge due to structural variability, non-isometric deformation, and inconsistent topology. Existing methods typically trade off generalization, geometric fidelity, and efficiency. We address this by proposing SGSoft, a unified intrinsic pipeline that (i) constructs a geodesic correspondence field on a canonical template, (ii) learns multimodal dense descriptors guided by pretrained semantic priors with this geodesic correspondence field supervision, (iii) retrieves dense correspondences in a single feed-forward pass via nearest-neighbor search in descriptor space. This formulation enables stable and topology-invariant supervision under large pose variation, structural differences, and remeshing. SGSoft achieves state-of-the-art inter-category generalization while offering the best accuracy-efficiency trade-off among prior methods. It also achieves near real-time inference without pre-alignment, pairwise optimization, or post-refinement. Learned descriptors can be transferred effectively to downstream tasks such as semantic segmentation and deformation transfer, establishing a scalable and deployment-ready paradigm for dense 3D correspondence.

While data-driven 3D shape correspondence estimation has recently seen substantial progress, robust matching under partial observations and strong non-isometric deformations remains challenging. Existing learning-based approaches often rely on hand-crafted descriptors or template-based representations, whereas recent generative models over functional maps suffer from high inference cost, limited interpretability, and poor generalisation to partial shapes. In response to these limitations, this paper introduces TokenMatch, a new transformer-based unified model for estimating 3D shape correspondences. Our feed-forward approach trained exclusively on BeCoS, a challenging non-isometric partial-to-partial shape-matching dataset, can generalise to matching full shapes without retraining or fine-tuning. TokenMatch uses self- and cross-attention mechanisms to efficiently learn patch-level and point-level relations as well as dense correspondences between shape pairs. Our core insight is that meshes can be adaptively tokenised into patches using shape curvature guidance, enabling effective learning of shape-specific geometric descriptors for correspondence estimation. We evaluate TokenMatch on standard benchmarks for partial and full shape matching, including CP2P, PSMAL, BeCoS, FAUST, SCAPE, and SHREC'19. Our method achieves consistently high performance, in most cases outperforming existing methods for partial and full shape matching in the mean geodesic error and intersection-over-union metrics, while also running faster at sub-second inference speeds.