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://parte.pages.dev.
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.
Partial-to-full registration remains challenging due to varying overlap ratios, fluctuating point densities, and the presence of noise. While transformers have shown strong potential for point cloud processing, prior methods typically confine them to global context aggregation, overlooking fine-grained local geometry crucial for accurate correspondence. We propose \emph{GAPR-Net}, a learning-based point cloud registration framework with a coarse-to-fine architecture that combines convolution and transformer modules, in which local and global information is fused between the partial and full point clouds using a cross-attention mechanism. To achieve this, a transformation-invariant point-wise geometric feature representation is proposed, which can robustly capture relative geometric features for individual points with respect to their neighboring points. To evaluate the effectiveness of the proposed approach, experiments are conducted on four geometrically distinct bones, including the tibia, femur, pelvis, and thoracic cartilage. The overall registration recall reaches 94.2%, the method results in a low RMSE of 1.992 mm and R2 values of 0.908 and 0.974 for rotation and translation, respectively. The results demonstrate that the proposed method effectively addresses the partial-to-full point cloud registration problem. The proposed method enables highly accurate 3D point cloud registration using partial observation, providing a critical foundation for precise surgical navigation and robotic interventions in computer-assisted surgery. The code will be accessed after the double-blind review process.
Point cloud registration critically depends on local features that are both distinctive and robust to arbitrary 3D rotations. Existing learning-based methods typically approximate rotation invariance via fragile local reference frames or extensive data augmentation, providing only empirical invariance and often degrading under unseen rotational transformations. In this paper, we propose SHReg, a strictly rotation-equivariant point cloud registration framework grounded in the representation theory of SO(3). By representing local geometric features as irreducible representations of SO(3), SHReg guarantees exact equivariance under arbitrary rotations without relying on local reference frames. Built upon a spherical-harmonics-based equivariant backbone, SHReg jointly learns rotation-invariant descriptors for robust correspondence matching and rotation-equivariant features that preserve fine-grained orientation information. The preserved equivariant structure enables each correspondence to directly hypothesize a rigid transformation, reducing reliance on large-scale hypothesis sampling in conventional RANSAC-based pipelines and leading to improved robustness under challenging rotational variations. Extensive experiments on 3DMatch, 3DLoMatch, and KITTI demonstrate that SHReg consistently outperforms state-of-the-art methods in registration accuracy, particularly under large rotational perturbations.