Majorization Algorithms for Inspecting Circles, Ellipses, Squares, Rectangles, and Rhombi

K. Van Deun () and Patrick Groenen ()
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K. Van Deun: Department of Psychology, Catholic University of Leuven, Tiensestraat 102, B-3000 Leuven, Belgium

Operations Research, 2005, vol. 53, issue 6, 957-967

Abstract: In several disciplines as diverse as shape analysis, location theory, quality control, archaeology, and psychometrics, it can be of interest to fit a circle through a set of points. We use the result that it suffices to locate a center for which the variance of the distances from the center to a set of given points is minimal. In this paper, we propose a new algorithm based on iterative majorization to locate the center. This algorithm is guaranteed to yield a series of nonincreasing variances until a stationary point is obtained. In all practical cases, the stationary point turns out to be a local minimum. Numerical experiments show that the majorizing algorithm is stable and fast. In addition, we extend the method to fit other shapes, such as a square, an ellipse, a rectangle, and a rhombus by making use of the class of l p distances and dimension weighting. In addition, we allow for rotations for shapes that might be rotated in the plane. We illustrate how this extended algorithm can be used as a tool for shape recognition.

Keywords: mathematics: functions: majorizing functions; facilities: location: continuous; engineering: shape analysis (search for similar items in EconPapers)
Date: 2005
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http://dx.doi.org/10.1287/opre.1050.0253 (application/pdf)

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Working Paper: Majorization algorithms for inspecting circles, ellipses, squares, rectangles, and rhombi (2003)
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Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:53:y:2005:i:6:p:957-967

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