Efficient Deformable Shape Correspondence via Kernel Matching

TL;DR

This paper introduces a scalable method for matching 3D shapes under complex deformations by formulating it as a descriptor matching problem and solving it with a projected descent optimization, achieving meaningful correspondences.

Contribution

It proposes a novel approach combining descriptor matching with a DC programming-inspired optimization for non-isometric shape correspondence.

Findings

Method converges to meaningful mappings in most experiments.

Scales well to complex shape matching scenarios.

Provides preliminary theoretical insights into the approach.

Abstract

We present a method to match three dimensional shapes under non-isometric deformations, topology changes and partiality. We formulate the problem as matching between a set of pair-wise and point-wise descriptors, imposing a continuity prior on the mapping, and propose a projected descent optimization procedure inspired by difference of convex functions (DC) programming. Surprisingly, in spite of the highly non-convex nature of the resulting quadratic assignment problem, our method converges to a semantically meaningful and continuous mapping in most of our experiments, and scales well. We provide preliminary theoretical analysis and several interpretations of the method.