DiscoMatch: Fast Discrete Optimisation for Geometrically Consistent 3D Shape Matching
This addresses the challenge of geometrically consistent 3D shape matching for computer vision and graphics applications, offering a novel combinatorial solver that bridges gaps in existing methods.
The paper tackles the problem of 3D shape matching by combining learning-based and combinatorial methods to ensure geometric consistency, resulting in a solver that is initialisation-free, parallelisable, and delivers improved matching quality with decreased runtime and globally optimal results for many instances.
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.