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Articles

Vol. 1 No. 4 (2026)

Deformation-Consistent Functional Correspondence for Unsupervised Nonrigid Shape Matching Tasks

Submitted
September 13, 2026
Published
September 27, 2026

Abstract

The problem of computing accurate and dense correspondences between nonrigid 3D shapes is a foundational challenge in computer vision, computer graphics, and geometric data processing. While recent advancements in geometric deep learning have significantly improved the performance of shape matching algorithms, the reliance on large-scale datasets with ground-truth correspondence annotations severely limits the applicability of supervised methods. Consequently, unsupervised learning paradigms based on the functional map framework have gained traction. However, existing unsupervised approaches frequently struggle with highly non-isometric deformations and complex topological variations, as they rely heavily on standard isometric regularizers that fail to capture the underlying physics of large-scale distortions. This paper introduces a novel deformation-consistent functional correspondence approach tailored for unsupervised nonrigid shape matching. By modeling the expected geometric distortion through a self-supervised deformation field, the proposed method aligns the spectral functional map with local geometric consistency. We present a comprehensive theoretical framework that translates spatial deformation cues into the spectral domain, enforcing consistency between the predicted functional correspondence and the implicit local non-isometric transformations. Extensive evaluations across multiple standard benchmark datasets demonstrate that the proposed deformation-consistent methodology substantially outperforms existing unsupervised techniques and achieves performance on par with fully supervised models. The insights provided in this study offer a robust pathway toward more generalized and physically plausible shape analysis without the need for manual annotations.

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