Fast and Numerically Stable Circle Fit

We develop a new algorithm for fitting circles that does not have drawbacks commonly found in existing circle fits. Our fit achieves ultimate accuracy (to machine precision), avoids divergence, and is numerically stable even when fitting circles get arbitrary large. Lastly, our algorithm takes less...

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Bibliographic Details
Published in:	Journal of mathematical imaging and vision Vol. 49; no. 2; pp. 289 - 295
Main Authors:	Abdul-Rahman, H., Chernov, N.
Format:	Journal Article
Language:	English
Published:	Boston Springer US 01-06-2014 Springer
Subjects:	Algorithmics. Computability. Computer arithmetics Applications of Mathematics Applied sciences Computer Science Computer science; control theory; systems Exact sciences and technology Image Processing and Computer Vision Mathematical Methods in Physics Signal,Image and Speech Processing Theoretical computing Geometric fit Gauss–Newton Fitting circles Levenberg–Marquardt Levenberg-Marquardt Circle Computational geometry Divergence Levenberg Marquardt algorithm Gauss Newton method Curve fitting Gauss-Newton
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Summary:	We develop a new algorithm for fitting circles that does not have drawbacks commonly found in existing circle fits. Our fit achieves ultimate accuracy (to machine precision), avoids divergence, and is numerically stable even when fitting circles get arbitrary large. Lastly, our algorithm takes less than 10 iterations to converge, on average.
ISSN:	0924-9907 1573-7683
DOI:	10.1007/s10851-013-0461-4