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Circle fitting by linear and nonlinear least squares. (English) Zbl 0790.65012
Summary: The problem of determining the circle of the best fit to a set of points in the plane (or the obvious generalization to $$n$$-dimensions) is easily formulated as a nonlinear total least squares problem which may be solved using a Gauss-Newton minimization algorithm. This straightforward 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.

##### MSC:
 65D10 Numerical smoothing, curve fitting 65K05 Numerical mathematical programming methods 90C30 Nonlinear programming
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##### References:
 [1] Gruntz, D.,Finding the Best Fit Circle, The MathWorks Newsletter, Vol. 1, p. 5, 1990. [2] Fletcher, R.,Practical Methods of Optimization, 2nd Edition, John Wiley and Sons, New York, New York, 1987. · Zbl 0905.65002 [3] Coope, I. D.,Circle Fitting by Linear and Nonlinear Least Squares, University of Canterbury, Mathematics Department, Report No. 69, 1992. · Zbl 0790.65012 [4] Sylvester, J. J.,A Question in the Geometry of Situation, Quarterly Journal of Pure and Applied Mathematics, Vol. 1, p. 79, 1857. [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. [6] Hearn, D. W., andVijay, J.,Efficient Algorithms for the (Weighted) Minimum Circle Problem, Operations Research, Vol. 30, pp. 777-795, 1982. · Zbl 0486.90039
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