Journal of Optimization Theory and Applications

, Volume 76, Issue 2, pp 381–388 | Cite as

Circle fitting by linear and nonlinear least squares

  • I. D. Coope
Technical Note


The problem of determining the circle of best fit to a set of points in the plane (or the obvious generalization ton-dimensions) is easily formulated as a nonlinear total least-squares problem which may be solved using a Gauss-Newton minimization algorithm. This straight-forward approach is shown to be inefficient and extremely sensitive to the presence of outliers. An alternative formulation allows the problem to be reduced to a linear least squares problem which is trivially solved. The recommended approach is shown to have the added advantage of being much less sensitive to outliers than the nonlinear least squares approach.

Key Words

Curve fitting circle fitting total least squares nonlinear least squares 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Gruntz, D.,Finding the Best Fit Circle, The MathWorks Newsletter, Vol. 1, p. 5, 1990.Google Scholar
  2. 2.
    Fletcher, R.,Practical Methods of Optimization, 2nd Edition, John Wiley and Sons, New York, New York, 1987.Google Scholar
  3. 3.
    Coope, I. D.,Circle Fitting by Linear and Nonlinear Least Squares, University of Canterbury, Mathematics Department, Report No. 69, 1992.Google Scholar
  4. 4.
    Sylvester, J. J.,A Question in the Geometry of Situation, Quarterly Journal of Pure and Applied Mathematics, Vol. 1, p. 79, 1857.Google Scholar
  5. 5.
    Kuhn, H. W.,Nonlinear Programming: A Historical View, Nonlinear Programming IX, SIAM-AMS Proceedings in Applied Mathematics, Edited by R. W. Cottle and C. E. Lemke, Vol. 9, pp. 1–26, 1975.Google Scholar
  6. 6.
    Hearn, D. W., andVijay, J.,Efficient Algorithms for the (Weighted) Minimum Circle Problem, Operations Research, Vol. 30, pp. 777–795, 1982.Google Scholar

Copyright information

© Plenum Publishing Corporation 1993

Authors and Affiliations

  • I. D. Coope
    • 1
  1. 1.Department of MathematicsUniversity of CanterburyChristchurch

Personalised recommendations