Sparse Modeling of Intrinsic Correspondences

TL;DR

This paper introduces a novel sparse modeling approach for non-rigid shape matching that uses only repeatable regions without descriptors, achieving accurate correspondences through permuted sparse coding.

Contribution

It is the first to apply sparse models to shape correspondence, formulating permuted sparse coding to handle unknown region correspondences and permutations.

Findings

Accurate shape correspondences achieved with minimal region information

Efficient solution via alternating linear assignment and sparse coding

Validated on synthetic and scanned object benchmarks

Abstract

We present a novel sparse modeling approach to non-rigid shape matching using only the ability to detect repeatable regions. As the input to our algorithm, we are given only two sets of regions in two shapes; no descriptors are provided so the correspondence between the regions is not know, nor we know how many regions correspond in the two shapes. We show that even with such scarce information, it is possible to establish very accurate correspondence between the shapes by using methods from the field of sparse modeling, being this, the first non-trivial use of sparse models in shape correspondence. We formulate the problem of permuted sparse coding, in which we solve simultaneously for an unknown permutation ordering the regions on two shapes and for an unknown correspondence in functional representation. We also propose a robust variant capable of handling incomplete matches. Numerically, the problem is solved efficiently by alternating the solution of a linear assignment and a sparse coding problem. The proposed methods are evaluated qualitatively and quantitatively on standard benchmarks containing both synthetic and scanned objects.