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

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Bibliographic Details
Title:	Geometry and Convergence Analysis of Algorithms for Registration of 3D Shapes.
Authors:	Pottmann, Helmut¹ pottmann@geometrie.tuwien.ac.at, Huang, Qi-Xing², Yang, Yong-Liang², Hu, Shi-Min² shimin@tsinghua.edu.cn
Source:	International Journal of Computer Vision. May2006, Vol. 67 Issue 3, p277-296. 20p. 3 Diagrams, 3 Charts, 5 Graphs.
Subjects:	Contact transformations, Geometry, Mathematical optimization, Program transformation, Structural optimization, Algorithms, Evolutionary computation, Stiff computation (Differential equations)
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, 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. [ABSTRACT FROM AUTHOR]
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Database:	Engineering Source

Description
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, 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. [ABSTRACT FROM AUTHOR]
ISSN:	09205691
DOI:	10.1007/s11263-006-5167-2