Journal of Mathematical Imaging and Vision
, Volume 23, Issue 3, pp 239252
First online:
Least Squares Fitting of Circles
 N. ChernovAffiliated withDepartment of Mathematics, University of Alabama at Birmingham
 , C. LesortAffiliated withDepartment of Mathematics, University of Alabama at Birmingham
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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.
Keywords
least squares fit circle fitting LevenbergMarquardt algorithm Title
 Least Squares Fitting of Circles
 Journal

Journal of Mathematical Imaging and Vision
Volume 23, Issue 3 , pp 239252
 Cover Date
 200511
 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