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Reseach Article

A Study on the Effect of Regularization Matrices in Motion Estimation

by Alessandra Martins Coelho, Vania V. Estrela
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 51 - Number 19
Year of Publication: 2012
Authors: Alessandra Martins Coelho, Vania V. Estrela
10.5120/8151-1886

Alessandra Martins Coelho, Vania V. Estrela . A Study on the Effect of Regularization Matrices in Motion Estimation. International Journal of Computer Applications. 51, 19 ( August 2012), 17-24. DOI=10.5120/8151-1886

@article{ 10.5120/8151-1886,
author = { Alessandra Martins Coelho, Vania V. Estrela },
title = { A Study on the Effect of Regularization Matrices in Motion Estimation },
journal = { International Journal of Computer Applications },
issue_date = { August 2012 },
volume = { 51 },
number = { 19 },
month = { August },
year = { 2012 },
issn = { 0975-8887 },
pages = { 17-24 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume51/number19/8151-1886/ },
doi = { 10.5120/8151-1886 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T20:50:48.670482+05:30
%A Alessandra Martins Coelho
%A Vania V. Estrela
%T A Study on the Effect of Regularization Matrices in Motion Estimation
%J International Journal of Computer Applications
%@ 0975-8887
%V 51
%N 19
%P 17-24
%D 2012
%I Foundation of Computer Science (FCS), NY, USA
Abstract

Inverse problems are very frequent in computer vision and machine learning applications. Since noteworthy hints can be obtained from motion data, it is important to seek more robust models. The advantages of using a more general regularization matrix such as ?=diag{?1,…,?K} to robustify motion estimation instead of a single parameter ? (?=?I) are investigated and formally stated in this paper, for the optical flow problem. Intuitively, this regularization scheme makes sense, but it is not common to encounter high-quality explanations from the engineering point of view. The study is further confirmed by experimental results and compared to the nonregularized Wiener filter approach.

References
  1. Biemond, J. , Looijenga, L. , Boekee, D. E. , and Plompen, R. H. J. M. 1987. A pel-recursive Wiener-based displacement estimation algorithm, Signal Processing, 13, 399-412.
  2. Estrela, V. V. , Rivera, L. A. , Beggio, P. C. , and Lopes, R. T. 2003. Regularized pel-recursive motion estimation using generalized cross-validation and spatial adaptation, In Proc. of SIBGRAPI 2003 XVI Brazilian Symp. Comp. Grap. and Image Processing, 331-338.
  3. Galatsanos, N. P. , and Katsaggelos, A. K. 1992. Methods for choosing the regularization parameter and estimating the noise variance in image restoration and their relation, IEEE Trans. Image Proc. , Vol. 1, No. 3, 322-336.
  4. Golub, G. H. , Heath, M. and Wahba, G. 1979. Generalized cross-validation as a method for choosing a good ridge parameter, Technometrics, Vol. 21, No. 2, 215-223.
  5. Hoerl, E. , and Kennard, R. W. 1970. Ridge regression: biased estimation for nonorthogonal problems, Technometrics, 55-67.
  6. Katsaggelos, A. K. 1991. Image Restoration, Springer-Verlag, Berlin-Heidelberg, Germany.
  7. Kay, S. 1993. Fundamentals of Statistical Signal Processing: Estimation Theory, Prentice Hall.
  8. Reeves, S. J. 1992. A cross-validation framework for solving image restoration problems, J. Vis. Comm. Im. Repres. , Vol. 3, No. 4, 433-445.
  9. Tekalp, M. 1995. Digital Video Processing, Prentice Hall.
  10. Tikhonov, A. , and Arsenin, V. 1977. Solution of Ill-Posed Problems, John Wiley and Sons, 1977.
  11. Thompson, A. M. , Brown, J. C. , Kay, J. W. , and Titterington, D. M. 1991. A study of methods for choosing the smoothing parameter in image restoration by regularization, IEEE Trans. P. A. M. I. , Vol. 13, No. 4, 326-339.
  12. Van Loan, C. F. , and Golub, G. H. 1993. Matrix Computations, The John Hopkins University Press.
  13. Wiener, N. 1948. Cybernetics, MIT Press, Cambridge, MA.
  14. Coelho, A. M. and Estrela, V. V. 2012. Data-driven motion estimation with spatial adaptation, International Journal of Image Processing (IJIP), vol. 6, no. 1. http://www. cscjournals. org/csc/manuscript/Journals/IJIP/volume6/Issue1/IJIP-513. pdf
  15. Bharathi P. T. and Subashini, P. 2012. Automatic identification of noise in ice images using statistical features, Proc. SPIE 8334, 83340G http://dx. doi. org/10. 1117/12. 946038
  16. Padmavathi, V. , Subashini, P. and Krishnaveni, M. 2011. A generic framework for landmine detection using statistical classifier based on IR images, International Journal on Computer Science and Engineering (IJCSE), Vol. 3 No. 1, 254-261, ISSN : 0975-3397 http://www. enggjournals. com/ijcse/doc/IJCSE11-03-01-164. pdf
  17. Franz, M. O. , and Schölkopf, B. 2006. A unifying view of Wiener and Volterra theory and polynomial kernel regression. Neural Computation 18(12): 3097-3118. http://keck. ucsf. edu/~craig/Franz_Scholkopf_2006_A_Unifying_View_of_Wiener_and_Volterra_Theory_and_Polynomial_Kernel_Regression. pdf
  18. Kienzle, W. , Bakir, G. H. , Franz, M. O. and Scholkopf, B. 2005. Face detection — efficient and rank deficient. In Y. W. Saul, L. K. and L. Bottou, editors, Advances in Neural Information Processing Systems 17, MIT Press, 673–680. http://eprints. pascal-network. org/archive/00000370/01/pdf2776. pdf
Index Terms

Computer Science
Information Sciences

Keywords

Regularization inverse problems motion estimation image analysis computer vision optical flow machine learning