Point Cloud Registration via Probabilistic Self-Update Local Correspondence and Line Vector Sets

Coherent Point Drift (CPD) is widely used for rigid point cloud registration because of its soft correspondences and closed-form parameter updates. However, CPD's target-side marginal constraint forces every observation, including outliers, to receive exactly unit probability mass. This assumption degrades registration accuracy under heavy outliers and partial overlap. Optimal transport (OT) methods can handle missing mass through unbalanced formulations, but require hand-tuned annealing schedules. In this paper, we propose Sinkhorn-CPD, which replaces CPD's target-side marginal constraint with dual Kullback-Leibler penalties, allowing the algorithm to discard outliers on both sides. The resulting formulation is a fully unbalanced entropic optimal transport problem, which can be efficiently solved by generalized Sinkhorn iterations. Moreover, Sinkhorn-CPD preserves the closed-form Procrustes and variance updates of CPD. In our method, the variance sigma^2 plays the role of the entropic regularization parameter, which induces an automatic annealing schedule from diffuse to sharp correspondences without manual temperature tuning. Experiments on synthetic, cross-category, and scan-to-CAD benchmarks show that Sinkhorn-CPD achieves state-of-the-art accuracy, with strong robustness to outliers and partial overlap.

We propose a fast and correspondence-free local point cloud registration method that leverages geometric surface structure and reproducing kernel Hilbert space (RKHS) embeddings. The method represents point clouds as continuous functions with point-wise anisotropic kernels that encode local geometry. This formulation improves alignment along surface normals while relaxing alignment along tangential directions. To solve the resulting registration problem, we propose a second-order on-manifold optimization scheme with approximate Riemannian Hessians, achieving a speedup of up to 10x over the first-order solvers used in prior correspondence-free RKHS-based methods. We demonstrate improved frame-to-frame LiDAR and RGB-D tracking accuracy across diverse indoor and outdoor datasets. On a LiDAR tracking registration task in the driving domain, we achieve a reduction of $>55\%$ in both translational and rotational drift in challenging feature-sparse environments. On object registration benchmarks, we show improved robustness over ICP-based methods and further gains when refining global initialization, particularly under moderate misalignment.

Multiview point cloud registration is particularly challenging in low-overlap scenes, where reliable correspondences are limited and incorrect pairwise transformations can affect global pose estimation. In addition, registering all scan pairs is computationally expensive because many pairs provide weak geometric information. To address these problems, we propose GMPCR, a non-learning-based spectral consistency-guided framework for efficient and robust multiview point cloud registration. GMPCR builds a refined second-order compatibility structure from initial correspondences and uses its dominant spectral response to evaluate both correspondence reliability and scan-pair confidence. This allows unreliable correspondences to be filtered and informative scan pairs to be selected before relative transformation estimation, leading to a sparse pose graph and reduced pairwise registration cost. For each retained scan pair, maximal-clique-based hypothesis generation is used to estimate reliable relative transformations. The resulting pose graph is further refined by an adaptive history-aware synchronization scheme, in which the effect of residual history is adjusted according to changes in the global rotation residual. A recovery mechanism also allows down-weighted edges to regain confidence when their global consistency improves. Experiments on 3DMatch, 3DLoMatch, ScanNet, and ETH demonstrate the effectiveness of GMPCR. It achieves registration recalls of 97.2% and 89.6% on 3DMatch and 3DLoMatch, respectively, while maintaining competitive performance on ScanNet and ETH. The results show that GMPCR provides a favorable balance among registration accuracy, robustness to low overlap, and computational efficiency. The code is publicly available at https://github.com/swccj/gmpcr.