caa a22 4500 467914478 CHVBK 20180406152858.0 cr unu---uuuuu 170328e20060501xx s 000 0 eng 10.1007/s11263-006-5167-2 doi (NATIONALLICENCE)springer-10.1007/s11263-006-5167-2 Geometry and Convergence Analysis of Algorithms for Registration of 3D Shapes [Elektronische Daten] [Helmut Pottmann, Qi-Xing Huang, Yong-Liang Yang, Shi-Min Hu] 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, 1992) or tangent planes at closest points (Chen and Medioni, 1991) and for a recently developed approach based on quadratic approximants of the squared distance function (Pottmann et al., 2004). 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 (Pottmann et al., 2004). 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. Springer Science + Business Media, Inc, 2006 registration nationallicence rigid registration nationallicence kinematics nationallicence optimization nationallicence ICP algorithm nationallicence distance function nationallicence convergence analysis nationallicence Pottmann Helmut Institute of Discrete Mathematics and Geometry, Vienna University of Technology, Austria aut Huang Qi-Xing Department of Computer Science and Technology, Tsinghua University, China aut Yang Yong-Liang Department of Computer Science and Technology, Tsinghua University, China aut Hu Shi-Min Department of Computer Science and Technology, Tsinghua University, China aut International Journal of Computer Vision Kluwer Academic Publishers 67/3(2006-05-01), 277-296 0920-5691 67:3<277 2006 67 11263 https://doi.org/10.1007/s11263-006-5167-2 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11263-006-5167-2 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Pottmann Helmut Institute of Discrete Mathematics and Geometry, Vienna University of Technology, Austria aut NATIONALLICENCE 700 1- Huang Qi-Xing Department of Computer Science and Technology, Tsinghua University, China aut NATIONALLICENCE 700 1- Yang Yong-Liang Department of Computer Science and Technology, Tsinghua University, China aut NATIONALLICENCE 700 1- Hu Shi-Min Department of Computer Science and Technology, Tsinghua University, China aut NATIONALLICENCE 773 0- International Journal of Computer Vision Kluwer Academic Publishers 67/3(2006-05-01), 277-296 0920-5691 67:3<277 2006 67 11263 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer