Circle fitting by linear and nonlinear least squares
- I. D. Coope
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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.
- Gruntz, D.,Finding the Best Fit Circle, The MathWorks Newsletter, Vol. 1, p. 5, 1990.
- Fletcher, R.,Practical Methods of Optimization, 2nd Edition, John Wiley and Sons, New York, New York, 1987.
- Coope, I. D.,Circle Fitting by Linear and Nonlinear Least Squares, University of Canterbury, Mathematics Department, Report No. 69, 1992.
- Sylvester, J. J.,A Question in the Geometry of Situation, Quarterly Journal of Pure and Applied Mathematics, Vol. 1, p. 79, 1857.
- 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.
- Hearn, D. W., andVijay, J.,Efficient Algorithms for the (Weighted) Minimum Circle Problem, Operations Research, Vol. 30, pp. 777–795, 1982.
- Circle fitting by linear and nonlinear least squares
Journal of Optimization Theory and Applications
Volume 76, Issue 2 , pp 381-388
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers-Plenum Publishers
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- Curve fitting
- circle fitting
- total least squares
- nonlinear least squares
- Industry Sectors
- I. D. Coope (1)
- Author Affiliations
- 1. Department of Mathematics, University of Canterbury, Christchurch, New Zealand