Unsigned Distance Maps on 2D Point Cloud Registration

2026-09-22

AI Summary

该论文提出基于无符号距离图的2D点云配准方法，通过预计算欧氏距离及其空间导数来替代迭代最近邻搜索，使用Gauss-Newton优化解决点到点和点到平面误差。

Abstract

2D point cloud registration arises in laser odometry and Simultaneous Localization and Mapping (SLAM) for mobile robots. Iterative Closest Point (ICP) is one of the most widely used approaches. Still, its iterative procedure recomputes correspondences via nearest-neighbor search at every iteration, whereas correspondence-free alternatives focus on scan-to-map alignment. This paper proposes a 2D point cloud registration approach based on unsigned distance maps, precomputing the Euclidean distance to the nearest reference point, along with its spatial derivatives, over a discrete grid, replacing the per-iteration search with O(1) lookups. Moreover, point-to-point and point-to-plane error formulations are derived on the SE(2) manifold and solved via Gauss-Newton optimization. On a synthetic benchmark and the real-world IILABS 3D dataset, the precomputed point-to-point variant outperforms its analytical counterparts, achieving competitive laser-odometry drift compared to point-to-plane formulations, as the precomputed gradient regularizes correspondences in the presence of sensor noise.

Problem

• 2D Point Cloud Registration
• Iterative Closest Point (ICP)
• Correspondence-free
• Sensor Noise

Innovation

• Unsigned Distance Maps
• 2D Point Cloud Registration
• Gauss-Newton Optimization
• Precomputed Gradient