Majorization algorithms for inspecting circles, ellipses, squares, rectangles, and rhombi

K. van Deun and Patrick Groenen ()

No EI 2003-35 Revision_Date: 2009-09-15, Econometric Institute Report from Erasmus University Rotterdam, Econometric Institute

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.

Keywords: optimization; iterative majorization; location; shape analysis (search for similar items in EconPapers)
Date: 2003-09-26

Downloads: (external link)
http://hdl.handle.net/1765/944 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: http://EconPapers.repec.org/RePEc:dgr:eureir:1765000944

Access Statistics for this paper

More papers in Econometric Institute Report from Erasmus University Rotterdam, Econometric Institute
Series data maintained by Anneke Kop ().