DiscoMatch: Fast Discrete Optimisation for Geometrically Consistent 3D Shape Matching

TL;DR

DiscoMatch introduces a fast, scalable combinatorial solver for 3D shape matching that ensures geometric consistency and achieves globally optimal results without requiring initial user input.

Contribution

It presents a novel, initialization-free combinatorial optimization method that is highly parallelizable, provides optimality gaps, and improves matching quality and speed.

Findings

Achieves globally optimal 3D shape matchings in practical runtimes.

Provides a scalable, initialization-free optimization approach.

Delivers improved matching quality with decreased runtime.

Abstract

In this work we propose to combine the advantages of learningbased and combinatorial formalisms for 3D shape matching. While learningbased methods lead to state-of-the-art matching performance, they do not ensure geometric consistency, so that obtained matchings are locally non-smooth. On the contrary, axiomatic, optimisation-based methods allow to take geometric consistency into account by explicitly constraining the space of valid matchings. However, existing axiomatic formalisms do not scale to practically relevant problem sizes, and require user input for the initialisation of non-convex optimisation problems. We work towards closing this gap by proposing a novel combinatorial solver that combines a unique set of favourable properties: our approach (i) is initialisation free, (ii) is massively parallelisable and powered by a quasi-Newton method, (iii) provides optimality gaps, and (iv) delivers improved matching quality with decreased runtime and globally optimal results for many instances.