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

Helmut Pottmann Vienna University of Technology, Austria Qi-Xing Huang Tsinghua University Yong-Liang Yang Tsinghua University Shi-Min Hu Tsinghua University

Geometric Modeling and Processing mathscidoc:1608.16058

International Journal of Computer Vision, 67, (3), 277-296, 2006
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.
Registration, Convergence Analysis, ICP
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@inproceedings{helmut2006geometry,
  title={Geometry and Convergence Analysis of Algorithms for Registration of 3D Shapes},
  author={Helmut Pottmann, Qi-Xing Huang, Yong-Liang Yang, and Shi-Min Hu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160824212955895384434},
  booktitle={International Journal of Computer Vision},
  volume={67},
  number={3},
  pages={277-296},
  year={2006},
}
Helmut Pottmann, Qi-Xing Huang, Yong-Liang Yang, and Shi-Min Hu. Geometry and Convergence Analysis of Algorithms for Registration of 3D Shapes. 2006. Vol. 67. In International Journal of Computer Vision. pp.277-296. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160824212955895384434.
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