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.

翻译：我们提出了一种新颖的混合整数规划（MIP）公式，用于生成高度非刚体形状的精确稀疏对应关系。为此，我们引入了投影拉普拉斯-贝尔特拉米算子（PLBO），该算子结合内蕴与外蕴几何信息，以衡量预测对应关系所引发的形变质量。我们将PLBO与方向感知正则化项结合，集成到一个新颖的MIP公式中，该公式可在许多实际问题中求解至全局最优。与以往方法相比，我们的方法对刚性变换和全局缩放具有可证明的不变性，无需初始化，具备最优性保证，且可扩展至高分辨率网格（经验观测复杂度为线性时间）。我们在多个具有挑战性的三维数据集上展示了稀疏非刚体匹配的最新成果，包括网格不一致的数据，以及网格到点云匹配的应用。