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

arXiv: https://arxiv.org/abs/2607.23096 · HTML: https://mlsanity.com/paper/2607.23096/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 42 references that are in the map.
- First posted on arXiv 25 Jul 2026.

## Builds on (most cited first, 4 of 4)

- [GRM: Large Gaussian Reconstruction Model for Efficient 3D Reconstruction and Generation](https://mlsanity.com/paper/2403.14621/) (2024)
- [PPF-FoldNet: Unsupervised Learning of Rotation Invariant 3D Local Descriptors](https://mlsanity.com/paper/1808.10322/) (2018)
- [3DFeat-Net: Weakly Supervised Local 3D Features for Point Cloud Registration](https://mlsanity.com/paper/1807.09413/) (2018)
- [Cultural Heritage 3D Reconstruction with Diffusion Networks](https://mlsanity.com/paper/2410.10927/) (2024)

## Abstract (arXiv)

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.