Fast Discrete Optimisation for Geometrically Consistent 3D Shape Matching

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