Fast and numerically stable circle fit

H. Abdul-Rahman; N. Chernov

doi:10.1007/s10851-013-0461-4

Fast and numerically stable circle fit

H. Abdul-Rahman, N. Chernov

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English (US)
Pages (from-to)	289-295
Number of pages	7
Journal	Journal of Mathematical Imaging and Vision
Volume	49
Issue number	2
DOIs	https://doi.org/10.1007/s10851-013-0461-4
State	Published - Jun 2014

Keywords

Fitting circles
Gauss-Newton
Geometric fit
Levenberg-Marquardt

ASJC Scopus subject areas

Statistics and Probability
Modeling and Simulation
Condensed Matter Physics
Computer Vision and Pattern Recognition
Geometry and Topology
Applied Mathematics

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10.1007/s10851-013-0461-4

Cite this

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title = "Fast and numerically stable circle fit",

abstract = "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.",

keywords = "Fitting circles, Gauss-Newton, Geometric fit, Levenberg-Marquardt",

author = "H. Abdul-Rahman and N. Chernov",

note = "Funding Information: Acknowledgement N.C. was partially supported by National Science Foundation, grant DMS-0969187.",

year = "2014",

month = jun,

doi = "10.1007/s10851-013-0461-4",

language = "English (US)",

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AU - Abdul-Rahman, H.

AU - Chernov, N.

N1 - Funding Information: Acknowledgement N.C. was partially supported by National Science Foundation, grant DMS-0969187.

PY - 2014/6

Y1 - 2014/6

N2 - 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.

AB - 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.

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KW - Gauss-Newton

KW - Geometric fit

KW - Levenberg-Marquardt

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ER -

Fast and numerically stable circle fit

Abstract

Keywords

ASJC Scopus subject areas

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