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

Point cloud registration critically depends on local featuresthat are both distinctive and robust to arbitrary 3D rotations. Existinglearning-based methods typically approximate rotation invariance viafragile local reference frames or extensive data augmentation, providingonly empirical invariance and often degrading under unseen rotationaltransformations. In this paper, we propose SHReg, a strictly rotation-equivariant point cloud registration framework grounded in the repre-sentation theory of SO(3). By representing local geometric features asirreducible representations of SO(3), SHReg guarantees exact equivari-ance under arbitrary rotations without relying on local reference frames.Built upon a spherical-harmonics-based equivariant backbone, SHRegjointly learns rotation-invariant descriptors for robust correspondencematching and rotation-equivariant features that preserve fine-grained ori-entation information. The preserved equivariant structure enables eachcorrespondence to directly hypothesize a rigid transformation, reducingreliance on large-scale hypothesis sampling in conventional RANSAC-based pipelines and leading to improved robustness under challengingrotational variations. Extensive experiments on 3DMatch, 3DLoMatch,and KITTI demonstrate that SHReg consistently outperforms state-of-the-art methods in registration accuracy, particularly under large rota-tional perturbations.