arXiv 2508.174272026-01-30cs.CVcs.RO

GMOR: 一种通过几何最大重叠实现的轻量稳健点云配准框架

GMOR: A Lightweight Robust Point Cloud Registration Framework via Geometric Maximum Overlapping

Beijing Engineering Research Center of Mixed Reality and Advanced Display, School of Optics and Photonics, Beijing Institute of Technology（北京混合现实与先进显示工程研究中心，光学与 photonics 学院，北京理工大学）；Zhengzhou Research Institute, Beijing Institute of Technology（郑州研究院，北京理工大学）；School of Computer Science and Technology, Beijing Institute of Technology（计算机科学与技术学院，北京理工大学）；School of Medical Technology, Beijing Institute of Technology（医学技术学院，北京理工大学）

Zhao Zheng, Jingfan Fan, Long Shao, Hong Song, Danni Ai, Tianyu Fu, Deqiang Xiao, Yongtian Wang, Jian Yang

阅读 PDF

arXiv 页面 ↗HTML 原文 ↗

AI总结：

GMOR通过仅旋转BnB搜索和几何最大重叠方法，实现高效的点云配准，兼顾精度与效率。

摘要：

基于对应关系的点云配准计算在噪声阈值内最大化内点数的刚体变换。当前最先进的（SOTA）方法主要采用空间兼容图或分治搜索（BnB）搜索，主要集中在高异常比下的配准。然而，基于图的方法需要至少二次空间和时间复杂度进行图构建，而多阶段BnB搜索方法常因分解阶段之间的局部极值导致不准确。本文提出了一种通过仅旋转BnB搜索的几何最大重叠配准框架。刚体变换通过查尔斯定理分解为沿旋转轴的平移和二维刚体变换。通过BnB搜索寻找最优旋转轴和角度，残差参数被形式化为范围最大查询（RMQ）问题。首先，在由立方映射参数化的半球内搜索前k个候选旋转轴，并通过对应关系投影到该轴上的区间刺穿估计每个轴的平移。其次，二维配准被放松为一维旋转角搜索，利用几何重叠的二维RMQ对轴对齐矩形进行处理，使用扫面线算法配合线段树以多项式时间确定性解决。在室内3DMatch/3DLoMatch扫描和室外KITTI激光雷达数据集上的实验结果表明，相比SOTA方法，具有更高的精度和效率，时间复杂度为多项式，空间复杂度随点数线性增加，即使在最坏情况下也是如此。

英文摘要：

Point cloud registration based on correspondences computes the rigid transformation that maximizes the number of inliers constrained within the noise threshold. Current state-of-the-art (SOTA) methods employing spatial compatibility graphs or branch-and-bound (BnB) search mainly focus on registration under high outlier ratios. However, graph-based methods require at least quadratic space and time complexity for graph construction, while multi-stage BnB search methods often suffer from inaccuracy due to local optima between decomposed stages. This paper proposes a geometric maximum overlapping registration framework via rotation-only BnB search. The rigid transformation is decomposed using Chasles' theorem into a translation along rotation axis and a 2D rigid transformation. The optimal rotation axis and angle are searched via BnB, with residual parameters formulated as range maximum query (RMQ) problems. Firstly, the top-k candidate rotation axes are searched within a hemisphere parameterized by cube mapping, and the translation along each axis is estimated through interval stabbing of the correspondences projected onto that axis. Secondly, the 2D registration is relaxed to 1D rotation angle search with 2D RMQ of geometric overlapping for axis-aligned rectangles, which is solved deterministically in polynomial time using sweep line algorithm with segment tree. Experimental results on indoor 3DMatch/3DLoMatch scanning and outdoor KITTI LiDAR datasets demonstrate superior accuracy and efficiency over SOTA methods, while the time complexity is polynomial and the space complexity increases linearly with the number of points, even in the worst case.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。