A Scalable Combinatorial Solver for Elastic Geometrically Consistent 3D Shape Matching

TL;DR

This paper introduces a fast, scalable combinatorial algorithm for globally optimizing geometrically consistent mappings between 3D shapes, enabling matching of larger and partial shapes efficiently.

Contribution

A novel primal heuristic with a Lagrange dual approach significantly improves scalability and speed over previous 3D shape matching solvers.

Findings

Handles shapes with more triangles than previous methods

Effective in matching partial shapes without complete data

Achieves faster optimization times by orders of magnitude

Abstract

We present a scalable combinatorial algorithm for globally optimizing over the space of geometrically consistent mappings between 3D shapes. We use the mathematically elegant formalism proposed by Windheuser et al. (ICCV 2011) where 3D shape matching was formulated as an integer linear program over the space of orientation-preserving diffeomorphisms. Until now, the resulting formulation had limited practical applicability due to its complicated constraint structure and its large size. We propose a novel primal heuristic coupled with a Lagrange dual problem that is several orders of magnitudes faster compared to previous solvers. This allows us to handle shapes with substantially more triangles than previously solvable. We demonstrate compelling results on diverse datasets, and, even showcase that we can address the challenging setting of matching two partial shapes without availability of complete shapes. Our code is publicly available at http://github.com/paul0noah/sm-comb .