发表机构
College of Mathematics and Systems Science, Shandong University of Science and Technology; School of Artificial Intelligence, Shandong Women’s University（山东科技大学数学与系统科学学院; 山东女子学院人工智能学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究提出基于$SO(3)$表示理论的SHReg框架，将局部几何特征表示为$SO(3)$不可约表示，基于球谐函数等变主干联合学习旋转不变描述符与等变特征，减少对大规模假设采样依赖，在点云配准精度上优于现有方法。
AI 中文摘要
点云配准严重依赖于对任意3D旋转具有独特性和鲁棒性的局部特征。现有基于学习的方法通常通过脆弱的局部参考框架或大量数据增强来近似旋转不变性，仅提供经验不变性，且在未见旋转变换下常性能下降。本文提出SHReg，一个基于$SO(3)$表示理论的严格旋转等变点云配准框架。通过将局部几何特征表示为$SO(3)$的不可约表示，SHReg保证在任意旋转下的精确等变性，无需局部参考框架。基于球谐函数的等变主干构建，联合学习旋转不变描述符用于鲁棒对应匹配和保留细粒度方向信息的旋转等变特征。保留的等变结构使每个对应关系能直接假设刚性变换，减少对传统基于RANSAC管道中大规模假设采样的依赖，在具有挑战性的旋转变化下提高鲁棒性。在3DMatch、3DLoMatch和KITTI上的大量实验表明，SHReg在配准精度上始终优于现有方法，特别是在大旋转扰动下。
英文摘要
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.
