Geometry and Convergence Analysis of Algorithms for Registration of 3D Shapes

The computation of a rigid body transformation which optimally aligns a set of measurement points with a surface and related registration problems are studied from the viewpoint of geometry and optimization. We provide a convergence analysis for widely used registration algorithms such as ICP, using either closest points (Besl and McKay [2]) or tangent planes at closest points (Chen and Medioni [4]), and for a recently developed approach based on quadratic approximants of the squared distance function [24]. ICP based on closest points exhibits local linear convergence only. Its counterpart which minimizes squared distances to the tangent planes at closest points is a Gauss-Newton iteration; it achieves local quadratic convergence for a zero residual problem and

• Type: Journal
• Year: 2006
• Where: IJCV
• Authors: Helmut Pottmann, Qi-Xing Huang, Yong-Liang Yang, Shi-Min Hu
• Keywords: Closest Points, Convergence, IJCV 2006, Tangent Planes