Existing optimization-based methods for non-rigid registration typically minimize an alignment error metric based on the point-to-point or point-to-plane distance between corresponding point pairs on the source surface and target surface. However, these metrics can result in slow convergence or a loss of detail. In this paper, we propose SPARE, a novel formulation that utilizes a symmetrized point-to-plane distance for robust non-rigid registration. The symmetrized point-to-plane distance relies on both the positions and normals of the corresponding points, resulting in a more accurate approximation of the underlying geometry and can achieve higher accuracy than existing methods. To solve this optimization problem efficiently, we propose an alternating minimization solver using a majorization-minimization strategy. Moreover, for effective initialization of the solver, we incorporate a deformation graph-based coarse alignment that improves registration quality and efficiency. Extensive experiments show that the proposed method greatly improves the accuracy of non-rigid registration problems and maintains relatively high solution efficiency. The code is publicly available at https://github.com/yaoyx689/spare.

翻译：现有的非刚性配准优化方法通常通过最小化源表面与目标表面上对应点对之间的点对点或点对面距离来构建对齐误差度量。然而，这些度量可能导致收敛速度缓慢或细节丢失。本文提出SPARE，一种利用对称点对面距离进行鲁棒非刚性配准的新颖方法。对称点对面距离同时利用对应点的位置与法向量信息，能够更精确地逼近底层几何结构，从而获得比现有方法更高的精度。为高效求解该优化问题，我们提出一种采用优化-最小化策略的交替最小化解法。此外，为有效初始化求解器，我们引入基于变形图的粗对齐步骤，以提升配准质量与效率。大量实验表明，所提方法显著提升了非刚性配准问题的精度，同时保持了较高的求解效率。代码已公开于 https://github.com/yaoyx689/spare。