Technical Note

Journal of Optimization Theory and Applications

, Volume 76, Issue 2, pp 381-388

First online:

Circle fitting by linear and nonlinear least squares

  • I. D. CoopeAffiliated withDepartment of Mathematics, University of Canterbury

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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