Helmut Pottmann, Qixing Huang, Yongliang Yang, Shimin Hu: Geometry and Convergence Analysis of Algorithms for Registration of 3D Shapes. International Journal of Computer Vision 67(3): 277-296 (2006)

Abstract:

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 { if enhanced by regularization and step size control { comes close to quadratic convergence in many realistic scenarios. Quadratically convergent algorithms are based on the approach in [24]. The theoretical results are supported by a number of experiments; there, we also compare the algorithms with respect to global convergence behavior, stability and running time.

Bibtex: 

@article{phyh-gcar-06,
 author = {H. Pottmann and Q. Huang and Y. Yang and S. Hu},
 title = {Geometry and Convergence Analysis of Algorithms for Registration of 3D Shapes},
 journal = {Int. J. Comput. Vision},
 volume = {67},
 number = {3},
 year = {2006},
 issn = {0920-5691},
 pages = {277--296},
 }