Journal of Optimization Theory and Applications

, Volume 76, Issue 2, pp 381–388

Circle fitting by linear and nonlinear least squares

  • I. D. Coope
Technical Note

DOI: 10.1007/BF00939613

Cite this article as:
Coope, I.D. J Optim Theory Appl (1993) 76: 381. doi:10.1007/BF00939613


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 

Copyright information

© Plenum Publishing Corporation 1993

Authors and Affiliations

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

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