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The Diverging Definition of Robustness in Statistics and Computer Vision

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Robust and Multivariate Statistical Methods

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Abstract

Statistics and computer vision have a different role for robustness. Statisticians are primarily concerned with the theoretical properties of estimators when models are only approximately true. In computer vision, performance takes precedence over theoretical considerations. This divergence is exemplified in statistics by the robust M-estimator in contrast to the RANdom SAmple Consensus (RANSAC) and the Multiple Input Structures with Robust Estimator (MISRE) in computer vision. All three have defined algorithms, but the M-estimator is based on theoretical results, while RANSAC and MISRE only emphasize recovering significant inlier structures. I offer suggestions for how the theory of the M-estimator can be further applied to MISRE, or MISRE can be applied to M-estimator.

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References

  • Beder, C., & Förstner, W. (2006). Direct solutions for computing cylinders from minimal sets of 3D points. In 2006 European Conference on Computer Vision (vol. 3952, pp. 135–146). Springer.

    Google Scholar 

  • Chen, H., Meer, P., & Tyler, D. E. (2001). Robust regression for data with multiple structures. In 2001 IEEE Computer Vision and Pattern Recognition (pp. 1069–1075).

    Google Scholar 

  • Comaniciu, D., & Meer, P. (2002). Mean shift: A robust approach toward feature space analysis. IEEE Transactions on Pattern Analysis and Machine Intelligence, 24, 603–619.

    Article  Google Scholar 

  • Comaniciu, D., Meer, P., & Tyler, D. E. (2003). Dissimilarity computation through low rank corrections. Pattern Recognition Letters, 24, 227–236.

    Article  MATH  Google Scholar 

  • Fischler, M. A., & Bolles, R. C. (1981). Random sample consensus: A paradigm for model fitting with applications to image analysis and automated cartography. Communications of the ACM, 24, 381–395.

    Article  MathSciNet  Google Scholar 

  • Hald, A. (2007). A history of parametric statistical inference from Bernoulli to Fisher, 1713 to 1935. Springer.

    MATH  Google Scholar 

  • Hough, P. (1959). Machine analysis of bubble chamber pictures. In International Conference on High Energy Accelerators and Instrumentation. CERN.

    Google Scholar 

  • Huber, P. J. (1964). Robust estimation of a location parameter. Annals of Mathematical Statistics, 35, 73–101.

    Article  MathSciNet  MATH  Google Scholar 

  • Jin, Y., Mishkin, D., Mishchuk, A., Matas, J., Fua, P., Yi, K. M., & Trulls, E. (2021). Image matching across wide baselines: From paper to practice. International Journal of Computer Vision, 129, 517–547.

    Article  Google Scholar 

  • Matei, B., Meer, P., & Tyler, D. E. (1998). Performance assessment by resampling: Rigid motion estimators. In K. W. Bowyer & P. J. Phillips (Eds.), Empirical Evaluation Techniques in Computer Vision (pp. 72–95). IEEE CS Press.

    Google Scholar 

  • Morgenthaler, S. (2007). A survey of robust statistics. Discussion. Statistical Methods and Applications, 15, 271–293.

    Article  MathSciNet  MATH  Google Scholar 

  • Rousseeuw, P. J. (1984). Least median of squares regression. Journal of the American Statistical Association, 79, 871–880.

    Article  MathSciNet  MATH  Google Scholar 

  • Rousseeuw, P. J., & Leroy, A. (1987). Robust Regression and Outlier Detection. John Viley & Sons.

    Google Scholar 

  • Stigler, S. M. (1973). Simon Newcomb, Percy Daniell, and the history of robust estimation 1885–1920. Journal of the American Statistical Association, 68, 872–879.

    MathSciNet  MATH  Google Scholar 

  • Stigler, S. M. (1986). The history of statistics. The measurement of uncertainty before 1900. Harvard University Press.

    MATH  Google Scholar 

  • Stigler, S. M. (2010). The changing history of robustness. The American Statistician, 64, 277–281.

    Article  MathSciNet  Google Scholar 

  • Tyler, D. E. (2013). A short course on robust statistics. http://www.stat.rutgers.edu/home/dtyler/ShortCourse.pdf. On-line, Rutgers University.

    Google Scholar 

  • Yang, X., Meer, P., & Meer, J. (2021). A new approach to robust estimation of parametric structures. IEEE Transactions on Pattern Analysis and Machine Intelligence, 43, 3754–3769.

    Article  Google Scholar 

Download references

Acknowledgements

I thank Jonathan Meer for all the suggestions which made this essay possible.

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Authors and Affiliations

  1. Department of Electrical Engineering, Rutgers University, Piscataway, NJ, USA

    Peter Meer

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  1. Peter Meer
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Correspondence to Peter Meer .

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Editors and Affiliations

  1. School of Statistics, Beijing Normal University, Beijing, China

    Mengxi Yi

  2. Department of Mathematics and Statistics, University of Jyväskylä, Jyväskylä, Finland

    Klaus Nordhausen

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Meer, P. (2023). The Diverging Definition of Robustness in Statistics and Computer Vision. In: Yi, M., Nordhausen, K. (eds) Robust and Multivariate Statistical Methods. Springer, Cham. https://doi.org/10.1007/978-3-031-22687-8_18

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