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An impartial trimming algorithm for robust circle fitting

Author

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  • Greco, Luca
  • Pacillo, Simona
  • Maresca, Piera

Abstract

Accurate circle fitting can be seriously compromised by the occurrence of even few anomalous points. Then, it is proposed to resort to a robust fitting strategy based on the idea of impartial trimming. Malicious data are supposed to be deleted, whereas estimation only relies on a set of genuine observations. The procedure is impartial in that trimmed points are not decided in advance but they are detected simultaneously to parameters estimation, according to an iterative algorithm: in each step a fixed proportion of the data is trimmed after sorting their geometric distances from the current fitted circle in non decreasing order. A reweighting step is also considered to improve the quality of the fit and make it less dependent on the selected trimming level. The global robustness properties of the method are established. The finite sample behavior of the proposed estimator has been investigated according to some numerical studies and real data examples.

Suggested Citation

  • Greco, Luca & Pacillo, Simona & Maresca, Piera, 2023. "An impartial trimming algorithm for robust circle fitting," Computational Statistics & Data Analysis, Elsevier, vol. 181(C).
    • Handle: RePEc:eee:csdana:v:181:y:2023:i:c:s0167947322002663
    DOI: 10.1016/j.csda.2022.107686
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    References listed on IDEAS

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    1. Marco Riani & Andrea Cerioli & Francesca Torti, 2014. "On consistency factors and efficiency of robust S-estimators," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 356-387, June.
    2. Kanatani, Kenichi & Rangarajan, Prasanna, 2011. "Hyper least squares fitting of circles and ellipses," Computational Statistics & Data Analysis, Elsevier, vol. 55(6), pages 2197-2208, June.
    3. Agostinelli, Claudio, 2007. "Robust estimation for circular data," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5867-5875, August.
    4. García-Escudero, Luis A. & Mayo-Iscar, Agustín & Sánchez-Gutiérrez, Clara I., 2017. "Fitting parabolas in noisy images," Computational Statistics & Data Analysis, Elsevier, vol. 112(C), pages 80-87.
    5. Giovanni Saraceno & Claudio Agostinelli & Luca Greco, 2021. "Robust estimation for multivariate wrapped models," METRON, Springer;Sapienza Università di Roma, vol. 79(2), pages 225-240, August.
    6. Torti, Francesca & Perrotta, Domenico & Atkinson, Anthony C. & Riani, Marco, 2012. "Benchmark testing of algorithms for very robust regression: FS, LMS and LTS," Computational Statistics & Data Analysis, Elsevier, vol. 56(8), pages 2501-2512.
    7. Cerioli, Andrea & Farcomeni, Alessio, 2011. "Error rates for multivariate outlier detection," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 544-553, January.
    8. Luca Greco & Antonio Lucadamo & Claudio Agostinelli, 2021. "Weighted likelihood latent class linear regression," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(2), pages 711-746, June.
    9. Andrea Cerioli & Marco Riani & Anthony C. Atkinson & Aldo Corbellini, 2018. "The power of monitoring: how to make the most of a contaminated multivariate sample," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(4), pages 559-587, December.
    10. Willems, Gert & Van Aelst, Stefan, 2005. "Fast and robust bootstrap for LTS," Computational Statistics & Data Analysis, Elsevier, vol. 48(4), pages 703-715, April.
    11. Luca Greco & Giovanni Saraceno & Claudio Agostinelli, 2021. "Robust Fitting of a Wrapped Normal Model to Multivariate Circular Data and Outlier Detection," Stats, MDPI, vol. 4(2), pages 1-18, June.
    12. Alessio Farcomeni, 2009. "Robust Double Clustering: A Method Based on Alternating Concentration Steps," Journal of Classification, Springer;The Classification Society, vol. 26(1), pages 77-101, April.
    13. 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.
    14. 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.
    15. Andrea Cerioli & Marco Riani & Anthony C. Atkinson & Aldo Corbellini, 2018. "Rejoinder to the discussion of “The power of monitoring: how to make the most of a contaminated multivariate sample”," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(4), pages 661-666, December.
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