Robust Point Cloud Registration via Geometric Overlapping Guided Rotation Search

2025-08-24

AI Summary

To address the challenge of balancing robustness and efficiency in point cloud registration under high outlier ratios, this paper proposes a geometric-overlap-guided, rotation-prior branch-and-bound (BnB) framework. Methodologically, it decouples rigid-body transformation via Chasles’ theorem into rotation-axis direction and 2D residual parameters, circumventing the quadratic complexity of conventional spatial graph construction. Rotation space is parameterized via cubic mapping over the hemisphere, enabling efficient 2D range maximum queries through interval piercing combined with a sweep-line algorithm augmented by a segment tree; only rotation is optimized via BnB. Translation and angular parameters are solved analytically. The method achieves polynomial time complexity and linear space complexity in the number of points. Extensive experiments on 3DMatch, 3DLoMatch, and KITTI demonstrate significant improvements over state-of-the-art methods, achieving both higher accuracy and real-time performance.

Technology Category

• Intelligent Robots: Localization, Mapping, and Navigation
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

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 3DMatch, 3DLoMatch, and KITTI 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.

Problem

• Reducing computational complexity in point cloud registration
• Improving accuracy by avoiding local optima in BnB search
• Developing polynomial-time method for robust rotation estimation

Innovation

• Rotation-only BnB search with geometric overlapping framework
• Decomposed transformation using Chasles' theorem and RMQ
• Polynomial-time sweep line algorithm for 2D registration