Coarse-to-Fine: A Hybrid Self-Supervised Method for Non-rigid 3D Shape Matching

Non-rigid 3D shape matching is a fundamental problem in computer vision, yet existing deep learning approaches often face a trade-off between accuracy and computational efficiency. Many state-of-the-art methods rely on time-consuming linear system solvers or iterative fine-tuning to maintain performance, which limits their scalability. This paper addresses this by proposing a hybrid self-supervised framework that avoids these bottlenecks while maintaining high matching precision.

The authors introduce a coarse-to-fine strategy that aligns coarse mappings with refined correspondences. The architecture features a dual-branch design: an intrinsic branch using the orthonormal Laplacian basis and an extrinsic branch using the non-orthogonal elastic basis. Instead of solving complex least-squares problems, the model uses a generalized refinement method that works across both basis types. The framework is supervised by three novel contrastive energy terms—spatial, spectral, and spatial-spectral—which promote feature discrimination and ensure consistency between the coarse and refined maps.

The proposed method achieves state-of-the-art performance across challenging benchmarks, including non-isometric deformations and topological noise, while significantly reducing computational overhead compared to traditional functional map approaches. The authors provide a rigorous proof that their contrastive energies effectively induce feature discrimination. Furthermore, they demonstrate that these energies can be integrated into existing baseline methods to yield consistent performance improvements, validating the robustness of their framework.