Template-Type: ReDIF-Paper 1.0
Author-Name: van Deun, K.
Author-Name-Last: van Deun
Author-Name: Groenen, P.J.F.
Author-Name-Last: Groenen
Author-Name-First: Patrick
Author-Person: pgr229
Title: Majorization algorithms for inspecting circles, ellipses, squares, rectangles, and rhombi
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 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.
Creation-Date: 2003-09-26
File-URL: https://repub.eur.nl/pub/944/ei200335.pdf
File-Format: application/pdf
Series: RePEc:ems:eureir
Number: EI 2003-35
Keywords: iterative majorization, location, optimization, shape analysis
Handle: RePEc:ems:eureir:944