Journal of Mathematical Imaging and Vision

, Volume 23, Issue 3, pp 239–252

Least Squares Fitting of Circles

  • N. Chernov
  • C. Lesort

DOI: 10.1007/s10851-005-0482-8

Cite this article as:
Chernov, N. & Lesort, C. J Math Imaging Vis (2005) 23: 239. doi:10.1007/s10851-005-0482-8


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.


least squares fit circle fitting Levenberg-Marquardt algorithm 

Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  • N. Chernov
    • 1
  • C. Lesort
    • 1
  1. 1.Department of MathematicsUniversity of Alabama at BirminghamBirminghamUSA

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