A correspondence-less approach to matching of deformable shapes

TL;DR

This paper introduces a novel correspondence-less method for matching deformable shape fragments to entire shapes using diffusion descriptors and Mumford-Shah regularization, avoiding explicit point-wise correspondences.

Contribution

It proposes a new approach that matches shape fragments without establishing point-wise correspondences, utilizing diffusion descriptors and a Mumford-Shah based regularization on integration domains.

Findings

Successfully matches deformable shape fragments without point-wise correspondence

Uses diffusion geometric descriptors for shape comparison

Employs an efficient Ambrosio-Tortorelli discretization for implementation

Abstract

Finding a match between partially available deformable shapes is a challenging problem with numerous applications. The problem is usually approached by computing local descriptors on a pair of shapes and then establishing a point-wise correspondence between the two. In this paper, we introduce an alternative correspondence-less approach to matching fragments to an entire shape undergoing a non-rigid deformation. We use diffusion geometric descriptors and optimize over the integration domains on which the integral descriptors of the two parts match. The problem is regularized using the Mumford-Shah functional. We show an efficient discretization based on the Ambrosio-Tortorelli approximation generalized to triangular meshes. Experiments demonstrating the success of the proposed method are presented.