SHReg: Strictly Rotation-Equivariant Point Cloud Registration via Spherical Harmonics
Authors: Chongjian Wang, Junjie Gao
Organizations: College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, China · School of Artificial Intelligence, Shandong Women’s University, Jinan, China
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.
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.
Point-cloud (PC) registration is fundamental to three-dimensional (3D) perception in robotic systems. However, classic registration algorithms falter when aligning a source PC containing limited, incomplete, or ambiguous geometric cues against a reference. This challenge of registering a small, partial PC to a significantly larger global reference is pervasive in real-world deployment yet remains insufficiently addressed by existing learning-based approaches, which typically assume comparable scales and significant overlap. To bridge this gap, we propose the Region-based Small-to-Large Point-cloud Registra- tion framework (R-SLPR), a novel three-stage architecture that fundamentally reformulates the scale-mismatched registration problem into a sequence of region proposal, regional matching, and iterative refinement. Unlike conventional methods that fail to localize specific regions, R-SLPR explicitly identifies candidate regions prior to estimating rigid transformations, ensuring robust alignment even under severe scale mismatch. The framework introduces a Fibonacci Grid Segmentation method coupled with a contrastive learning objective to effectively generate and match local geometric patches. Building on this, a novel Cascade Anchor Selection and Refinement algorithm iteratively aligns the source with the target region to maximize precision. Extensive evaluation on ModelNet40 demonstrates that R-SLPR establishes a new state-of-the-art accuracy standard, outperforming prior approaches and significantly reducing position and rotation Mean Absolute Error (MAE) to 0.009 and 1.104, respectively.
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.