Unsupervised Scale-Invariant Multispectral Shape Matching

TL;DR

This paper introduces an unsupervised neural network approach for shape matching that leverages scale-invariant spectral geometry, effectively handling non-rigid deformations across different shape domains.

Contribution

It proposes a novel unsupervised architecture based on spectral domain invariance and multiple geometries, improving shape matching beyond local features.

Findings

Outperforms existing spectral methods in cross-domain shape matching

Handles non-rigid, scale-invariant deformations effectively

Demonstrates superior accuracy on benchmark datasets

Abstract

Alignment between non-rigid stretchable structures is one of the most challenging tasks in computer vision, as the invariant properties are hard to define, and there is no labeled data for real datasets. We present unsupervised neural network architecture based upon the spectral domain of scale-invariant geometry. We build on top of the functional maps architecture, but show that learning local features, as done until now, is not enough once the isometry assumption breaks. We demonstrate the use of multiple scale-invariant geometries for solving this problem. Our method is agnostic to local-scale deformations and shows superior performance for matching shapes from different domains when compared to existing spectral state-of-the-art solutions.