Hyper least squares fitting of circles and ellipses

Authors:
Kenichi Kanatani;Prasanna Rangarajan
Affiliations:
Department of Computer Science, Okayama University, Okayama 700-8530, Japan;Department of Electrical Engineering, Southern Methodist University, Dallas, TX 75205, USA
Venue:
Computational Statistics & Data Analysis
Year:
2011

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Abstract

This work extends the circle fitting method of Rangarajan and Kanatani (2009) to accommodate ellipse fitting. Our method, which we call HyperLS, relies on algebraic distance minimization with a carefully chosen scale normalization. The normalization is derived using a rigorous error analysis of least squares (LS) estimators so that statistical bias is eliminated up to second order noise terms. Numerical evidence suggests that the proposed HyperLS estimator is far superior to the standard LS and is slightly better than the Taubin estimator. Although suboptimal in comparison to maximum likelihood (ML), our HyperLS does not require iterations. Hence, it does not suffer from convergence issues due to poor initialization, which is inherent in ML estimators. In this sense, the proposed HyperLS is a perfect candidate for initializing the ML iterations.