  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 .
