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.
Communicated by L. C. W. Dixon
This work was completed while the author was visiting the Numerical Optimisation Centre, Hatfield Polytechnic and benefitted from the encouragement and helpful suggestions of Dr. M. C. Bartholomew-Biggs and Professor L. C. W. Dixon.
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- 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
- Additional Links
- 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