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Monte Carlo maximum likelihood circle fitting using circular density functions

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  • Ulric Lund

Abstract

Finding the “best-fitting” circle to describe a set of points in two dimensions is discussed in terms of maximum likelihood estimation. Several combinations of distributions are proposed to describe the stochastic nature of points in the plane, as the points are considered to have a common, typically unknown center, a random radius, and random angular orientation. A Monte Carlo search algorithm over part of the parameter space is suggested for finding the maximum likelihood parameter estimates. Examples are presented, and comparisons are drawn between circles fit by this proposed method, least squares, and other maximum likelihood methods found in the literature. Copyright Springer-Verlag 2013

Suggested Citation

  • Ulric Lund, 2013. "Monte Carlo maximum likelihood circle fitting using circular density functions," Computational Statistics, Springer, vol. 28(2), pages 393-411, April.
    • Handle: RePEc:spr:compst:v:28:y:2013:i:2:p:393-411
    DOI: 10.1007/s00180-012-0307-3
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    References listed on IDEAS

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    1. Mark Berman, 1983. "Estimating the Parameters of a Circle When Angular Differences are Known," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 32(1), pages 1-6, March.
    2. K. V. Mardia, 1999. "Directional statistics and shape analysis," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(8), pages 949-957.
    3. Y. T. Chan & B. H. Lee & S. M. Thomas, 2005. "Approximate Maximum Likelihood Estimation of Circle Parameters," Journal of Optimization Theory and Applications, Springer, vol. 125(3), pages 723-734, June.
    4. Chernov, N. & Sapirstein, P.N., 2008. "Fitting circles to data with correlated noise," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5328-5337, August.
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