Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
Introduction Read chapter Read first chapter

2012 | OriginalPaper | Chapter

8. Robust Parameter Estimation

Author : Prof. A. Ardeshir Goshtasby

Published in: Image Registration

Publisher: Springer London

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

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.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
previous chapter Point Pattern Matching
next chapter Transformation Functions
Literature
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)
2.
Aitken, A.C.: On least squares and linear combinations of observations. Proc. R. Soc. Edinb. 55, 42–48 (1935)
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
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) MathSciNetCrossRef
5.
6.
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
8.
Hodges, V.J., Austin, J.: A survey of outlier detection methodologies. Artif. Intell. Rev. 22, 85–126 (2004) CrossRef
9.
Hossjer, P.: Rank-based estimates in the linear model with high breakdown point. J. Am. Stat. Assoc. 89(425), 149–158 (1994) MathSciNet
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 CrossRef
11.
Huber, P.J.: Robust regression: Asymptotics, conjectures and Monte Carlo. Ann. Stat. 1(5), 799–821 (1973) MATHCrossRef
12.
13.
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
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)
16.
Jolliffee, I.T.: Principal Component Analysis. Springer, New York (2002)
17.
Kendall, M.G.: A Course in Multivariate Analysis, 4th Impression. Hafner, New York (1968)
18.
Kittler, J., Young, P.C.: A new approach to feature selection based on the Karhunen–Loève expansion. Pattern Recognit. 5, 335–352 (1973) MathSciNetCrossRef
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) CrossRef
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) MathSciNetCrossRef
21.
Pearson, K.: On lines and planes of closest fit to systems of points in space. Philos. Mag. 2(6), 559–572 (1901)
22.
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
24.
25.
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) CrossRef
27.
Rousseeuw, P.J., Leroy, A.M.: Robust Regression and Outlier Detection. Wiley, New York (1987) MATHCrossRef
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) CrossRef
29.
Roweis, S.T., Saul, L.K.: Nonlinear dimensionality reduction by locally linear embedding. Science 290, 2323–2326 (2000) CrossRef
30.
Scholkopf, B., Smola, A., Muller, K.-R.: Nonlinear component analysis as a kernel eigenvalue problem. Neural Comput. 10, 1299–1319 (1998) CrossRef
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) MathSciNetMATH
32.
Siegel, A.F.: Robust regression using repeated medians. Biometrika 69(1), 242–244 (1982) MATHCrossRef
33.
Tenenbaum, J.B., de Silva, V., Langford, J.C.: A global geometric framework for nonlinear dimensionality reduction. Science 290, 2319–2323 (2000) CrossRef
34.
Theodoridis, S., Koutroumbas, K.: Pattern Recognition, 4th edn. Academic Press, San Diego (2009), pp. 602, 605, 606
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)
36.
Wilcox, R.R.: Introduction to Robust Estimation and Hypothesis Testing. Academic Press, San Diego (1997) MATH
Metadata
Title
Robust Parameter Estimation
Author
Prof. A. Ardeshir Goshtasby
Copyright Year
2012
Publisher
Springer London
Book
Image Registration

Print ISBN: 978-1-4471-2457-3

Electronic ISBN: 978-1-4471-2458-0

Copyright Year: 2012

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

Premium Partner

    Image Credits