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Least Squares Fitting of Circles
 N. Chernov,
 C. Lesort
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Fitting standard shapes or curves to incomplete data (which represent only a small part of the curve) is a notoriously difficult problem. Even if the curve is quite simple, such as an ellipse or a circle, it is hard to reconstruct it from noisy data sampled along a short arc. Here we study the least squares fit (LSF) of circular arcs to incomplete scattered data. We analyze theoretical aspects of the problem and reveal the cause of unstable behavior of conventional algorithms. We also find a remedy that allows us to build another algorithm that accurately fits circles to data sampled along arbitrarily short arcs.
Nikolai Chernov PhD in mathematics from Moscow University in 1984, scientist in Joint Institute for Nuclear Research (Dubna, Russia) 1983–1991, professor of mathematics in UCLA 1991–92, Georgia Tech 1992–93, Princeton University 1993–94, University of Alabama at Birmingham since 1994.
Claire Lesort MS in mathematics from University of Limoges in 1994, MS in mathematics from University of Alabama at Birmingham 2000, PhD in Statistics from University of Alabama at Birmingham 2004. Statistician at BellSouth Telecommunication Inc. since 2003.
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 Title
 Least Squares Fitting of Circles
 Journal

Journal of Mathematical Imaging and Vision
Volume 23, Issue 3 , pp 239252
 Cover Date
 20051101
 DOI
 10.1007/s1085100504828
 Print ISSN
 09249907
 Online ISSN
 15737683
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 least squares fit
 circle fitting
 LevenbergMarquardt algorithm
 Industry Sectors
 Authors

 N. Chernov ^{(1)}
 C. Lesort ^{(1)}
 Author Affiliations

 1. Department of Mathematics, University of Alabama at Birmingham, Birmingham, AL, 35294, USA