SHReg: Strictly Rotation-Equivariant Point Cloud Registration via Spherical Harmonics

2026-07-25

AI Summary

This work addresses the limited robustness and discriminability of local features under arbitrary 3D rotations in point cloud registration by proposing the first strictly rotation-equivariant registration framework that operates without a local reference frame. Built upon SO(3) representation theory, the method employs spherical harmonics to construct a rotation-equivariant neural network that jointly learns rotation-invariant descriptors and equivariant geometric features. This design enables each putative correspondence to directly model the underlying rigid transformation, substantially reducing reliance on extensive RANSAC sampling. Experiments on the 3DMatch, 3DLoMatch, and KITTI benchmarks demonstrate that the proposed approach achieves significantly higher registration accuracy than existing methods under large rotational perturbations.

Abstract

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.

Problem

• point cloud registration
• rotation equivariance
• 3D rotation
• local features
• SO(3)

Innovation

• rotation-equivariance
• spherical harmonics
• point cloud registration
• SO(3) representation
• rigid transformation