Advertisement

Mixed OLS-TLS for the Estimation of Dynamic Processes with a Linear Source Term

  • Christoph S. Garbe
  • Hagen Spies
  • Bernd Jähne
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2449)

Abstract

We present a novel technique to eliminate strong biases in parameter estimation were part of the data matrix is not corrupted by errors. Problems of this type occur in the simultaneous estimation of optical flow and the parameter of linear brightness change as well as in range flow estimation. For attaining highly accurate optical flow estimations under real world situations as required by a number of scientific applications, the standard brightness change constraint equation is violated. Very often the brightness change has to be modelled by a linear source term. In this problem as well as in range flow estimation, part of the data term consists of an exactly known constant. Total least squares (TLS) assumes the error in the data terms to be identically distributed, thus leading to strong biases in the equations at hand. The approach presented in this paper is based on a mixture of ordinary least squares (OLS) and total least squares, thus resolving the bias encountered in TLS alone. Apart from a thorough performance analysis of the novel estimator, a number of applications are presented.

Keywords

parameter estimation least squares dynamic processes brightness change optical flow 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A. Bab-Hadiashar and D. Suter. Robust optic flow computation. IJCV, 29(1):59–77, 1998.CrossRefGoogle Scholar
  2. 2.
    J.L. Barron, D. J. Fleet, and S. Beauchemin. Performance of optical flow techniques. International Journal of Computer Vision, 12(1):43–77, 1994.CrossRefGoogle Scholar
  3. 3.
    S.S. Beauchemin and J. L. Barron. The computation of optical flow. ACM Computing Surveys, 27(3):433–467, 1995.CrossRefGoogle Scholar
  4. 4.
    A Björck. Least squares methods. In P. G. Ciarlet and J. L. Lions, editors, Finite Difference Methods (Part 1), volume 1 of Handbook of Numerical Analysis, pages 465–652. Elesvier Science Publishers, North-Holland, 1990.Google Scholar
  5. 5.
    P.P. Gallo. Consistency of regression estimates when some variables are subject to error. Communications in statistics / Theory and methods, 11:973–983, 1982.zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    C.S. Garbe. Measuring Heat Exchange Processes at the Air-Water Interface from Thermographic Image Sequence Analysis. PhD thesis, University of Heidelberg, Heidelberg, Germany, 2001.Google Scholar
  7. 7.
    C.S. Garbe, H. Haußecker, and B. Jähne. Measuring the sea surface heat flux and probability distribution of surface renewal events. In E. Saltzman, M. Donelan, W. Drennan, and R. Wanninkhof, editors, Gas Transfer at Water Surfaces, Geophysical Monograph. American Geophysical Union, 2001.Google Scholar
  8. 8.
    C.S. Garbe and B. Jähne. Reliable estimates of the sea surface heat flux from image sequences. In Proc. of the 23rd DAGM Symposium, Lecture Notes in Computer Science, LNCS 2191, pages 194–201, Munich, Germany, 2001. Springer-Verlag.Google Scholar
  9. 9.
    L.J. Gleser. Estimation in a multivariate “error in variables” regression model: Large sample results. Annals of Statistics, 9:24–44, 1981.zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    G.H. Golub and C. F. van Loan. Matrix Computations. The Johns Hopkins University Press, Baltimore and London, 3 edition, 1996.zbMATHGoogle Scholar
  11. 11.
    F.R. Hampel, E. M. Ronchetti, P. J. Rousseeuw, and W. A. Stahel. Robust Statistics: The Approach Based on Influence Functions. John Wiley and Sons, New York, 1986.zbMATHGoogle Scholar
  12. 12.
    H. Haußecker and D. J. Fleet. Computing optical flow with physical models of brightness variation. PAMI, 23(6):661–673, June 2001.Google Scholar
  13. 13.
    H. Haußecker, C. S. Garbe, H. Spies, and B. Jähne. A total least squares for low-level analysis of dynamic scenes and processes. In DAGM, pages 240–249, Bonn, Germany, 1999. Springer.Google Scholar
  14. 14.
    H. Haußecker and H. Spies. Motion. In B. Jähne, H. Haußecker, and P. Geißler, editors, Handbook of Computer Vision and Applications, volume 2, chapter 13, pages 309–396. Academic Press, San Diego, 1999.Google Scholar
  15. 15.
    R. Mester and M. Mühlich. Improving motion and orientation estimation using an equilibrated total least squares approach. In ICIP, Greece, October 2001.Google Scholar
  16. 16.
    M. Mühlich and R. Mester. The role of total least squares in motion analysis. In ECCV, pages 305–321, Freiburg, Germany, 1998.Google Scholar
  17. 17.
    M. Mühlich and R. Mester. Subspace methods and equilibration in computer vision. Technical Report XP-TR-C-21, Institute for Applied Physics, Goethe-Universitaet, Frankfurt, Germany, November 1999.Google Scholar
  18. 18.
    H. Scharr. Optimale Operatoren in der Digitalen Bildverarbeitung. PhD thesis, University of Heidelberg, Heidelberg, Germany, 2000.Google Scholar
  19. 19.
    H. Spies, H. Haußecker, B. Jähne, and J. L. Barron. Differential range flow estimation. In DAGM, pages 309–316, Bonn, Germany, September 1999.Google Scholar
  20. 20.
    S. Van Huffel and J. Vandewalle. The Total Least Squares Problem: Computational Aspects and Analysis. Society for Industrial and Applied Mathematics, Philadelphia, 1991.zbMATHGoogle Scholar
  21. 21.
    M. Yamamoto, P. Boulanger, J. Beraldin, and M. Rioux. Direct estimation of range flow on deformable shape from a video rate range camera. PAMI, 15(1):82–89, January 1993.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Christoph S. Garbe
    • 1
  • Hagen Spies
    • 2
  • Bernd Jähne
    • 1
  1. 1.Interdisciplinary Center for Scientific Computing, INF 368HeidelbergGermany
  2. 2.ICG-III (Phytosphere) Forschungszentrum Jülich GmbHJülichGermany

Personalised recommendations