Electronic Journal of Statistics

Error analysis for circle fitting algorithms

Ali Al-Sharadqah and Nikolai Chernov

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We study the problem of fitting circles (or circular arcs) to data points observed with errors in both variables. A detailed error analysis for all popular circle fitting methods – geometric fit, Kåsa fit, Pratt fit, and Taubin fit – is presented. Our error analysis goes deeper than the traditional expansion to the leading order. We obtain higher order terms, which show exactly why and by how much circle fits differ from each other. Our analysis allows us to construct a new algebraic (non-iterative) circle fitting algorithm that outperforms all the existing methods, including the (previously regarded as unbeatable) geometric fit.

Article information

Electron. J. Statist. Volume 3 (2009), 886-911.

First available in Project Euclid: 24 August 2009

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Zentralblatt MATH identifier

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Least squares fit curve fitting circle fitting algebraic fit error analysis variance bias functional model


Al-Sharadqah, Ali; Chernov, Nikolai. Error analysis for circle fitting algorithms. Electron. J. Statist. 3 (2009), 886--911. doi:10.1214/09-EJS419. http://projecteuclid.org/euclid.ejs/1251119958.

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