  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.
