Robust Single-Parameter Point Cloud Registration using Truncated Lp Functions

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.

Global point-cloud registration remains challenging when limited overlap, repetitive geometry, and sensor noise produce correspondence sets dominated by outliers. Planar regions are particularly difficult for conventional point descriptors and are therefore often suppressed or discarded before matching. We present PARTE (Plane-Assisted Robust Transformation Estimation), a global registration method that instead treats planar structure as complementary registration evidence. PARTE extracts planar patches and represents them using our novel Plane Context Histogram (PCH), a descriptor that encodes the geometry surrounding each patch, while a two-level matching procedure identifies reliable plane correspondences. Candidate point and plane correspondences are combined in a confidence-weighted compatibility graph for joint outlier rejection, followed by rigid transformation estimation. When no usable plane correspondences are available, PARTE naturally reduces to point-only registration. We evaluate PARTE on 8,097 registration pairs across six indoor and outdoor benchmarks spanning dense RGB-D and sparse LiDAR measurements. Evaluations show PARTE achieves the highest overall success rate against 13 standard and state-of-the-art methods while maintaining low runtime. An open-source C++ implementation with Python bindings is provided at https://ariarobotics.github.io/parte/.

Point cloud registration (PCR) is a fundamental task in 3D vision and provides essential support for applications such as autonomous driving, robotics, and environmental modeling. Despite its widespread use, existing methods often fail when facing real-world challenges like heavy noise, significant occlusions, and large-scale transformations. These limitations frequently result in compromised registration accuracy and insufficient robustness in complex environments. In this paper, we propose IGASA as a novel registration framework constructed upon a Hierarchical Pyramid Architecture (HPA) designed for robust multi-scale feature extraction and fusion. The framework integrates two pivotal components consisting of the Hierarchical Cross-Layer Attention (HCLA) module and the Iterative Geometry-Aware Refinement (IGAR) module. The HCLA module utilizes skip attention mechanisms to align multi-resolution features and enhance local geometric consistency. Simultaneously, the IGAR module is designed for the fine matching phase by leveraging reliable correspondences established during coarse matching. This synergistic integration within the architecture allows IGASA to adapt effectively to diverse point cloud structures and intricate transformations. We evaluate the performance of IGASA on four widely recognized benchmark datasets including 3D(Lo)Match, KITTI, and nuScenes. Our extensive experiments consistently demonstrate that IGASA significantly surpasses state-of-the-art methods and achieves notable improvements in registration accuracy. This work provides a robust foundation for advancing point cloud registration techniques while offering valuable insights for practical 3D vision applications. The code for IGASA is available in https://github.com/DongXu-Zhang/IGASA.