Robust Point Cloud Registration via High-Dimensional Complex Kernel

Abstract

Robust and efficient point cloud registration is fundamental to robotic perception tasks such as SLAM, 3D reconstruction, and autonomous navigation. Traditional methods often rely on fragile point correspondences and iterative optimization, struggling under conditions like poor initialization, partial overlap, and perceptual aliasing. We propose Complex Kernel Registration (CKR), a novel framework that replaces fragile point-level correspondences with a robust alignment of high-level block descriptors. CKR operates by establishing coarse matches between local block descriptors in a high-dimensional complex Hilbert space. CKR extracts compact 8D descriptors capturing both geometric structure and LiDAR reflectance, embeds them via Random Fourier Features, and estimates rigid transformations using Wirtinger gradient descent. This formulation bypasses explicit point matching, yielding fast, accurate, and robust registration, even in cluttered, occluded, and low-texture environments. Extensive experiments on real-world LiDAR datasets demonstrate that CKR outperforms classical and learning-based baselines in accuracy, robustness, and computational efficiency, which is practical for deployment on resource-constrained robotic platforms without specialized hardware.