A doubly optimal ellipse fit

A. Al-Sharadqah and N. Chernov

Computational Statistics & Data Analysis, 2012, vol. 56, issue 9, 2771-2781

Abstract: We study the problem of fitting ellipses to observed points in the context of Errors-In-Variables regression analysis. The accuracy of fitting methods is characterized by their variances and biases. The variance has a theoretical lower bound (the KCR bound), and many practical fits attend it, so they are optimal in this sense. There is no lower bound on the bias, though, and in fact our higher order error analysis (developed just recently) shows that it can be eliminated, to the leading order. Kanatani and Rangarajan recently constructed an algebraic ellipse fit that has no bias, but its variance exceeds the KCR bound; so their method is optimal only relative to the bias. We present here a novel ellipse fit that enjoys both optimal features: the theoretically minimal variance and zero bias (both to the leading order). Our numerical tests confirm the superiority of the proposed fit over the existing fits.

Keywords: Errors-In-Variables regression; Ellipse fitting; Conic fitting; Cramer–Rao bound; Bias reduction (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:56:y:2012:i:9:p:2771-2781

DOI: 10.1016/j.csda.2012.02.028

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