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，用于生成高度非刚性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），该算子结合内在与外在几何信息来度量由预测对应关系引起的变形质量。我们将PLBO与方向感知正则化项相结合，融入一种新颖的MIP公式中，该公式在许多实际问题中可求解至全局最优。与先前方法相比，我们的方法可证明对刚性变换和全局尺度缩放具有不变性，无需初始化，具有最优性保证，且能（经验观测下）以线性时间扩展到高分辨率网格。我们在多个具有挑战性的3D数据集（包括网格不一致的数据）上展示了稀疏非刚性匹配的最优结果，并将其应用于网格到点云匹配。