Electronic Journal of Statistics

Improved algebraic methods for circle fitting

Prasanna Rangarajan and Kenichi Kanatani

Full-text: Open access

Abstract

Inspired by the circle fitting algorithm “Hyper” of Al-Sharadqah and Chernov [1], which eliminates the second order “essential bias” that excludes terms of O(σ2/N2), we extend their analysis and show that by a small modification the second order bias can be eliminated completely. By numerical experiments, we show that this results in better performance when the number N of points is small and the noise is large.

Article information

Source
Electron. J. Statist. Volume 3 (2009), 1075-1082.

Dates
First available in Project Euclid: 29 October 2009

Permanent link to this document
http://projecteuclid.org/euclid.ejs/1256822131

Digital Object Identifier
doi:10.1214/09-EJS488

Mathematical Reviews number (MathSciNet)
MR2557129

Zentralblatt MATH identifier
1263.68152

Subjects
Primary: 68T10: Pattern recognition, speech recognition {For cluster analysis, see 62H30} 68K45
Secondary: 68K40

Keywords
Circle fitting least squares algebraic fit error analysis bias removal

Citation

Rangarajan, Prasanna; Kanatani, Kenichi. Improved algebraic methods for circle fitting. Electronic Journal of Statistics 3 (2009), 1075--1082. doi:10.1214/09-EJS488. http://projecteuclid.org/euclid.ejs/1256822131.


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References

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