Unsupervised Contrastive Learning for Efficient and Robust Spectral Shape Matching

2026-03-19

AI Summary

This work proposes the first unsupervised contrastive learning framework for estimating correspondences between non-rigidly deformable 3D shapes, addressing limitations in feature representation quality and computational efficiency. By constructing positive and negative sample pairs to enhance both consistency and discriminability in the embedding space, the method integrates a streamlined functional map architecture within an end-to-end dual-branch pipeline. It eliminates traditional time-consuming solvers and auxiliary losses, significantly improving efficiency without sacrificing accuracy. Extensive evaluations on challenging benchmarks—including near-isometric, non-isometric, and topologically inconsistent scenarios—demonstrate that the proposed approach achieves state-of-the-art performance in both accuracy and speed, even outperforming supervised methods.

Technology Category

• Computer Vision: 3D Computer Vision
• Machine Learning: Learning with Manifolds
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Estimating correspondences between pairs of non-rigid deformable 3D shapes remains a significant challenge in computer vision and graphics. While deep functional map methods have become the go-to solution for addressing this problem, they primarily focus on optimizing pointwise and functional maps either individually or jointly, rather than directly enhancing feature representations in the embedding space, which often results in inadequate feature quality and suboptimal matching performance. Furthermore, these approaches heavily rely on traditional functional map techniques, such as time-consuming functional map solvers, which incur substantial computational costs. In this work, we introduce, for the first time, a novel unsupervised contrastive learning-based approach for efficient and robust 3D shape matching. We begin by presenting an unsupervised contrastive learning framework that promotes feature learning by maximizing consistency within positive similarity pairs and minimizing it within negative similarity pairs, thereby improving both the consistency and discriminability of the learned features.We then design a significantly simplified functional map learning architecture that eliminates the need for computationally expensive functional map solvers and multiple auxiliary functional map losses, greatly enhancing computational efficiency. By integrating these two components into a unified two-branch pipeline, our method achieves state-of-the-art performance in both accuracy and efficiency. Extensive experiments demonstrate that our approach is not only computationally efficient but also outperforms current state-of-the-art methods across various challenging benchmarks, including near-isometric, non-isometric, and topologically inconsistent scenarios, even surpassing supervised techniques.

Problem

• 3D shape matching
• non-rigid deformation
• functional maps
• feature representation
• correspondence estimation

Innovation

• unsupervised contrastive learning
• spectral shape matching
• functional map
• feature representation
• computational efficiency