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Multicriteria Robust Fitting of Elliptical Primitives

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Abstract

Geometric fitting is present in different fields of science, engineering and astronomy. In particular, ellipse shapes are some of the most commonly employed geometric features in digital image analysis and visual pattern recognition. Most geometric and algebraic methods are sensitive to noise and outlier points and so the results are not usually acceptable. In this paper, a robust geometric multicriteria method based on the mean absolute geometric error and the eccentricity to fit an ellipse to set of points is proposed. It is well known that the least mean absolute error criterion leads to robust estimations.

The experimental results on different real and synthetic data have shown that the proposed algorithm is robust to outliers. Moreover, it allows us to identify outliers and remove them.

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Acknowledgements

The authors wish to thank the Coordinating Editor and the referees for their valuable comments and suggestions. This work is partially supported by Junta de Andalucía (Spain) under contract TIC-6213, project name DERENA.

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Authors and Affiliations

  1. E.T.S. de Ingenieros de Informática, University of Malaga, Malaga, Spain

    J. Muñoz-Pérez

  2. E.T.S. de Ingenieros Industriales, University of Malaga, Malaga, Spain

    I. Ladrón de Guevara-López

  3. Escuela Politécnica Superior, University of Malaga, Malaga, Spain

    O. D. de Cózar-Macías & E. B. Blázquez-Parra

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  1. J. Muñoz-Pérez
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  2. O. D. de Cózar-Macías
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Correspondence to E. B. Blázquez-Parra.

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Muñoz-Pérez, J., de Cózar-Macías, O.D., Blázquez-Parra, E.B. et al. Multicriteria Robust Fitting of Elliptical Primitives. J Math Imaging Vis 49, 492–509 (2014). https://doi.org/10.1007/s10851-013-0480-1

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