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Robust Parameter Estimation

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Image Registration

Part of the book series: Advances in Computer Vision and Pattern Recognition ((ACVPR))

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Abstract

The problem of robust parameter estimation in image registration is discussed and various robust methods for estimating registration parameters under outliers and inaccurate correspondences are reviewed and compared. After reviewing ordinary least-squares and weighted least-squares estimation, robust estimators such as maximum likelihood (M), repeated median (RM), scale (S), least median of squares (LMS), least trimmed square (LTS), and rank (R) estimators are described and compared.

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References

  1. Abdi, H.: Least squares. In: Lewis-Beck, M., Bryman, A., Futing, T. (eds.) The Sage Encyclopedia of Social Sciences Research Methods, Thousand Oaks, CA, pp. 1–4 (2003)

    Google Scholar 

  2. Aitken, A.C.: On least squares and linear combinations of observations. Proc. R. Soc. Edinb. 55, 42–48 (1935)

    Google Scholar 

  3. Andrews, D.F., Bickel, P.J., Hampel, F.R., Huber, P.J., Rogers, W.H., Tukey, J.W.: Robust Estimates of Location: Survey and Advances. Princeton University Press, Princeton (1972)

    MATH  Google Scholar 

  4. Golub, G., Kahan, W.: Calculating the singular values and pseudo-inverse of a matrix. J. SIAM Numer. Anal., Ser. B 2(2), 205–224 (1965)

    Article  MathSciNet  Google Scholar 

  5. Hampel, F.R.: A general qualitative definition of robustness. Ann. Math. Stat. 42(6), 1887–1896 (1971)

    Article  MathSciNet  MATH  Google Scholar 

  6. Hampel, F.R.: The influence curve and its role in robust estimation. J. Am. Stat. Assoc. 69(346), 383–393 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  7. Hampel, F.R., Ronchetti, E.M., Rousseeuw, P.J., Stahel, W.A.: Robust Statistics: The Approach Based on Influence Functions. Wiley, New York (1986)

    MATH  Google Scholar 

  8. Hodges, V.J., Austin, J.: A survey of outlier detection methodologies. Artif. Intell. Rev. 22, 85–126 (2004)

    Article  Google Scholar 

  9. Hossjer, P.: Rank-based estimates in the linear model with high breakdown point. J. Am. Stat. Assoc. 89(425), 149–158 (1994)

    MathSciNet  Google Scholar 

  10. Hotelling, H.: Analysis of a complex of statistical variables into principal components. J. Educ. Psychol. 24, 417–441 (1933), also see pp. 498–520

    Article  Google Scholar 

  11. Huber, P.J.: Robust regression: Asymptotics, conjectures and Monte Carlo. Ann. Stat. 1(5), 799–821 (1973)

    Article  MATH  Google Scholar 

  12. Huber, P.J.: Robust Statistics. Wiley, New York (1981)

    Book  MATH  Google Scholar 

  13. Jaeckel, L.A.: Regression coefficients by minimizing the dispersion of the residuals. Ann. Math. Stat. 43(5), 1449–1458 (1972)

    Article  MathSciNet  MATH  Google Scholar 

  14. Jolliffe, I.T.: Discarding variables in a principal component analysis. I: Artificial data. J. R. Stat. Soc., Ser. C, Appl. Stat. 21(2), 160–173 (1972)

    MathSciNet  Google Scholar 

  15. Jolliffe, I.T.: Discarding variables in a principal component analysis. II: Real data. J. R. Stat. Soc., Ser. C, Appl. Stat. 22(1), 21–31 (1973)

    Google Scholar 

  16. Jolliffee, I.T.: Principal Component Analysis. Springer, New York (2002)

    Google Scholar 

  17. Kendall, M.G.: A Course in Multivariate Analysis, 4th Impression. Hafner, New York (1968)

    Google Scholar 

  18. Kittler, J., Young, P.C.: A new approach to feature selection based on the Karhunen–Loève expansion. Pattern Recognit. 5, 335–352 (1973)

    Article  MathSciNet  Google Scholar 

  19. Mao, K.Z.: Identifying critical variables of principal components for unsupervised feature selection. IEEE Trans. Syst. Man Cybern., Part B, Cybern. 35(2), 334–339 (2005)

    Article  Google Scholar 

  20. McElroy, F.W.: A necessary and sufficient condition that ordinary least-squares estimators be best linear unbiased. J. Am. Stat. Assoc. 62(320), 1302–1304 (1967)

    Article  MathSciNet  Google Scholar 

  21. Pearson, K.: On lines and planes of closest fit to systems of points in space. Philos. Mag. 2(6), 559–572 (1901)

    Google Scholar 

  22. Penrose, R.: A generalized inverse for matrices. Math. Proc. Camb. Philos. Soc. 51(3), 406–413 (1955)

    Article  MathSciNet  MATH  Google Scholar 

  23. Rao, C.R.: The use of interpretation of principal component analysis in applied research. Indian J. Stat., Ser. A 26(4), 329–358 (1964)

    MATH  Google Scholar 

  24. Rousseeuw, P.J.: Least median of squares regression. J. Am. Stat. Assoc. 79(388), 871–880 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  25. Rousseeuw, P.J., Croux, C.: Alternatives to the median absolute deviation. J. Am. Stat. Assoc. 88(424), 1273–1283 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  26. Rousseeuw, P.J., Hubert, M.: Recent developments in PROGRESS. In: Lecture Notes on L 1-Statistical Procedures and Related Topics, vol. 31, pp. 201–214 (1997)

    Chapter  Google Scholar 

  27. Rousseeuw, P.J., Leroy, A.M.: Robust Regression and Outlier Detection. Wiley, New York (1987)

    Book  MATH  Google Scholar 

  28. Rousseeuw, P., Yohai, V.: Robust regression by means of S-estimators. In: Franke, J., Hördle, W., Martin, R.D. (eds.) Robust and Nonlinear Time Series Analysis. Lecture Notes in Statistics, vol. 26, pp. 256–274. Springer, New York (1984)

    Chapter  Google Scholar 

  29. Roweis, S.T., Saul, L.K.: Nonlinear dimensionality reduction by locally linear embedding. Science 290, 2323–2326 (2000)

    Article  Google Scholar 

  30. Scholkopf, B., Smola, A., Muller, K.-R.: Nonlinear component analysis as a kernel eigenvalue problem. Neural Comput. 10, 1299–1319 (1998)

    Article  Google Scholar 

  31. Seal, H.L.: Studies in the history of probability and statistics XV: The historical development of the Gauss linear model. Biometrika 54(1–2), 1–24 (1967)

    MathSciNet  MATH  Google Scholar 

  32. Siegel, A.F.: Robust regression using repeated medians. Biometrika 69(1), 242–244 (1982)

    Article  MATH  Google Scholar 

  33. Tenenbaum, J.B., de Silva, V., Langford, J.C.: A global geometric framework for nonlinear dimensionality reduction. Science 290, 2319–2323 (2000)

    Article  Google Scholar 

  34. Theodoridis, S., Koutroumbas, K.: Pattern Recognition, 4th edn. Academic Press, San Diego (2009), pp. 602, 605, 606

    Google Scholar 

  35. Watanabe, S.: Karhunen–Loève expansion and factor analysis theoretical remarks and applications. In: Trans. Prague Conf. Information Theory, Statistical Decision Functions, Random Processes, pp. 9–26 (1965)

    Google Scholar 

  36. Wilcox, R.R.: Introduction to Robust Estimation and Hypothesis Testing. Academic Press, San Diego (1997)

    MATH  Google Scholar 

Download references

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Correspondence to A. Ardeshir Goshtasby .

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Goshtasby, A.A. (2012). Robust Parameter Estimation. In: Image Registration. Advances in Computer Vision and Pattern Recognition. Springer, London. https://doi.org/10.1007/978-1-4471-2458-0_8

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  • DOI: https://doi.org/10.1007/978-1-4471-2458-0_8

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-2457-3

  • Online ISBN: 978-1-4471-2458-0

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