  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.
