On Nonrigid Shape Similarity and Correspondence

TL;DR

This paper introduces a spectral domain approach for nonrigid shape correspondence, utilizing spectral distances and a new spectral quasi-conformal distance to improve shape matching accuracy.

Contribution

It proposes a novel spectral quasi-conformal distance and an automatic framework for intrinsic shape correspondence, achieving state-of-the-art results.

Findings

Achieved state-of-the-art accuracy on TOSCA and SCAPE benchmarks.

Demonstrated effectiveness of spectral distances in shape correspondence.

Introduced a fully automatic shape matching framework.

Abstract

An important operation in geometry processing is finding the correspondences between pairs of shapes. The Gromov-Hausdorff distance, a measure of dissimilarity between metric spaces, has been found to be highly useful for nonrigid shape comparison. Here, we explore the applicability of related shape similarity measures to the problem of shape correspondence, adopting spectral type distances. We propose to evaluate the spectral kernel distance, the spectral embedding distance and the novel spectral quasi-conformal distance, comparing the manifolds from different viewpoints. By matching the shapes in the spectral domain, important attributes of surface structure are being aligned. For the purpose of testing our ideas, we introduce a fully automatic framework for finding intrinsic correspondence between two shapes. The proposed method achieves state-of-the-art results on the Princeton isometric shape matching protocol applied, as usual, to the TOSCA and SCAPE benchmarks.