We propose a novel mixed-integer programming (MIP) formulation for generating
precise sparse correspondences for highly non-rigid shapes. To this end, we
introduce a projected Laplace-Beltrami operator (PLBO) which combines intrinsic
and extrinsic geometric information to measure the deformation quality induced
by predicted correspondences. We integrate the PLBO, together with an
orientation-aware regulariser, into a novel MIP formulation that can be solved
to global optimality for many practical problems. In contrast to previous
methods, our approach is provably invariant to rigid transformations and global
scaling, initialisation-free, has optimality guarantees, and scales to high
resolution meshes with (empirically observed) linear time. We show
state-of-the-art results for sparse non-rigid matching on several challenging
3D datasets, including data with inconsistent meshing, as well as applications
in mesh-to-point-cloud matching.

基于混合整数规划的稀疏对应关系生成方法，结合投影拉普拉斯 - 贝尔特拉米算子、旋转感知正则化器，实现全局最优解，适用于非刚性形状匹配，并具有高效性能。