Optical Flow Computation with Fourth Order Partial Differential Equations

  • Xiaoxin Guo
  • Zhiwen Xu
  • Yueping Feng
  • Yunxiao Wang
  • Zhengxuan Wang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4109)


In this paper, we propose a new hybrid optical flow computation with fourth order partial differential equations (PDEs). The integration of local and global optical flow methods exploits fourth order PDEs rather than second order for the purpose of the improvement of smoothness and accuracy of the estimated optical flow field. Furthermore, we describe the implementation of the method in detail. The experiments show that the employment of fourth order PDEs benefits the improvement of the two aspects of the resulting optical flow field.


Optical Flow Smoothness Term Order PDEs Optical Flow Field Optical Flow Computation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Mitiche, A., Bouthemy, P.: Computation and analysis of image motion: A synopsis of current problems and methods. International Journal of Computer Vision 19(1), 29–55 (1996)CrossRefGoogle Scholar
  2. 2.
    Stiller, C., Konrad, J.: Estimating motion in image sequences. IEEE Signal Processing Magazine 16, 70–91 (1999)CrossRefGoogle Scholar
  3. 3.
    Schnörr, C.: On functionals with greyvalue-controlled smoothness terms for determining optical flow. IEEE Transactions on Pattern Analysis and Machine Intelligence 15, 1074–1079 (1993)CrossRefGoogle Scholar
  4. 4.
    Fleet, D.J., Jepson, A.D.: Computation of component image velocity from local phase information. International Journal of Computer Vision 5(1), 77–104 (1990)CrossRefGoogle Scholar
  5. 5.
    Tretiak, P.L.: Velocity estimation from image sequences with second order differential operators. In: Proc. Seventh International Conference on Pattern Recognition, Montreal, Canada, pp. 16–19 (1984)Google Scholar
  6. 6.
    Uras, S., Girosi, F., Verri, A.V., Torre, A.: Computational approach to motion perception. Biological Cybernetics 60, 79–87 (1988)CrossRefGoogle Scholar
  7. 7.
    Bainbridge-Smith, Lane, R.G.: Determining optical flow using a differential method. Image and Vision Computing 15(1), 11–22 (1997)CrossRefGoogle Scholar
  8. 8.
    Fermüller, Shulman, D., Aloimonos, Y.: The statistics of optical flow. Computer Vision and Image Understanding 82(1), 1–32 (2001)MATHCrossRefGoogle Scholar
  9. 9.
    Jähne: Digitale Bildverarbeitung. Springer, Berlin (2001)Google Scholar
  10. 10.
    Ohta, N.: Uncertainty models of the gradient constraint for optical flow computation. IEICE Transactions on Information and Systems E79-D(7), 958–962 (1996)Google Scholar
  11. 11.
    Simoncelli, E.P., Adelson, E.H., Heeger, D.J.: Probability distributions of optical flow. In: Proc. 1991 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pp. 310–315. IEEE Computer Society Press, Maui (1991)CrossRefGoogle Scholar
  12. 12.
    Galvin, B., McCane, B., Novins, K., Mason, D., Mills, S.: Recovering motion fields: An analysis of eight optical flow algorithms. In: Proc. 1998 British Machine Vision Conference, Southampton, England (1998)Google Scholar
  13. 13.
    Barron, J.L., Fleet, D.J., Beauchemin, S.S.: Performance of optical flow techniques. International Journal of Computer Vision 12(1), 43–77 (1994)CrossRefGoogle Scholar
  14. 14.
    Lucas, B., Kanade, T.: An iterative image registration technique with an application to stereo vision. In: Proc. Seventh International Joint Conference on Artificial Intelligence, Vancouver, Canada, pp. 674–679 (1981)Google Scholar
  15. 15.
    Lucas, B.D.: Generalized image matching by the method of differences. PhD thesis, School of Computer Science, Carnegie–Mellon University, Pittsburgh, PA (1984)Google Scholar
  16. 16.
    Horn, K.P., Schunk, B.G.: Determining optical flow. Aritificial Intelligence 17, 185–203 (1981)CrossRefGoogle Scholar
  17. 17.
    Young, D.M.: Iterative Solution of Large Linear Systems. Academic Press, New York (1971)MATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Xiaoxin Guo
    • 1
  • Zhiwen Xu
    • 1
  • Yueping Feng
    • 1
  • Yunxiao Wang
    • 1
  • Zhengxuan Wang
    • 1
  1. 1.Key Laboratory of Symbol Computation and Knowledge Engineering of the Ministry of Education, College of Computer Science and TechnologyJilin UniversityChangchunP.R. China

Personalised recommendations