SPARE: Symmetrized Point-to-Plane Distance for Robust Non-Rigid 3D Registration

TL;DR

SPARE introduces a symmetrized point-to-plane distance for non-rigid 3D registration, enhancing accuracy and robustness by leveraging geometry-aware metrics and efficient optimization strategies.

Contribution

It proposes a novel symmetrized point-to-plane distance formulation combined with an as-rigid-as-possible regulation and a deformation graph-based initialization, improving registration accuracy and efficiency.

Findings

Significantly improves registration accuracy over existing methods.

Maintains high efficiency in non-rigid registration tasks.

Demonstrates robustness across various experimental scenarios.

Abstract

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 introduce an as-rigid-as-possible regulation term to estimate the deformed normals and 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.