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

2024-05-30

arXiv.org

AI Summary

Traditional point-to-point or point-to-plane distance metrics in non-rigid point cloud registration suffer from slow convergence and geometric detail loss. To address this, we propose a symmetric point-to-plane distance metric that jointly enforces positional and normal-based geometric constraints, significantly improving geometric fidelity. Methodologically, we introduce the first symmetric distance formulation for non-rigid registration and integrate it with a deformation-graph-based coarse alignment followed by an alternating optimization scheme within the Majorization-Minimization (MM) framework—balancing robustness, accuracy, and efficiency. Extensive experiments on multiple benchmark datasets demonstrate that our approach achieves state-of-the-art registration accuracy while maintaining high computational efficiency. The source code is publicly available.

Technology Category

• Computer Vision: Motion & Tracking
• Search and Optimization: Non-convex Optimization
• Machine Learning: Learning with Manifolds

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

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 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.

Problem

• Improves non-rigid registration accuracy with symmetrized point-to-plane distance
• Addresses slow convergence and detail loss in surface alignment
• Enhances geometry approximation using positions and normals of points

Innovation

• Symmetrized point-to-plane distance for registration
• As-rigid-as-possible regulation with alternating minimization
• Deformation graph-based coarse alignment initialization