Training-Free Coarse Point Cloud Registration via Axis-Projected Surface Area Matching

Abstract

Point cloud registration is a fundamental problem in three-dimensional computer vision, underpinning robotics, autonomous driving and 3D reconstruction. The Iterative Closest Point (ICP) algorithm dominates fine registration but diverges under large rotational misalignment, while feature-based coarse methods such as Fast Point Feature Histograms demand high scan overlap. This paper introduces a training-free coarse registration method based on axis-projected surface area minimization. The method operates on triangulated (meshed) scans; raw point clouds are handled after a surface-reconstruction step. Given two partial scans and an estimate of their shared region, the method computes exact projected surface areas and area-weighted centroids on the three coordinate planes and recovers the rigid transform by minimizing a normalized area-plus-centroid objective over the rotation group. The method is placed on a formal footing: the projected signal is exact at alignment, its area-only invariance group is characterized, the objective gradient on the rotation group is derived, and translation is solved in closed form. A two-stage coarse-to-fine optimizer combines grid search with Nelder–Mead refinement. On the Stanford Bunny and Armadillo the method restores ICP performance where cold-start ICP collapses, and a controlled synthetic study over many random shapes confirms the predicted reflection ambiguity and graceful degradation to ten per cent overlap.