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
this http URL .

提出了可扩展的组合算法，用于全局优化 3D 形状之间具有几何一致性的映射空间，通过整数线性规划公式和原始启发式方法以及拉格朗日对偶问题相结合，实现了比以前更快、更高效的解决方法，成功地匹配了多个形状。