Skip to main content
SpringerLink
Log in

High accuracy optical flow estimation based on PDE decomposition

  • Original Paper
  • Published:
Signal, Image and Video Processing Aims and scope Submit manuscript

Abstract

Many optical flow estimation techniques are based on the differential optical flow equation. These algorithms involve solving over-determined systems of optical flow equations. Least-squares (LS) estimation is usually used to solve these systems even though the underlying noise does not conform to the model implied by LS estimation. To tackle this problem, work has been done combining the variational partial differential equation (PDE) methods with motion estimation. However, PDE methods demonstrated powerful tools to decompose an image into its structures, textures, and noise components. The noise is eliminated systematically in the proposed scheme, and the optical flow is computed separately on both components of the decomposition. We experimentally show that very precise and robust estimation of optical flow can be achieved with a total variational approach in real time. The implementation is described in a detailed way, which enables reimplementation of this high-end method. The proposed technique has been tested upon different dataset of both synthetic and real image sequences, and compared to both well-known and state-of-the-art differential optical flow methods.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  1. Zimmer, H., Bruhn, A., Weickert, J.: Optic flow in Harmony. Int. J. Comput. Vis. 93(3), 368–388 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  2. Wei, D., Li, Y.: Sampling reconstruction of N-dimensional bandlimited images after multilinear filtering in fractional Fourier domain. Optics Communica 295, 26–35 (2013)

    Article  Google Scholar 

  3. Xu, L., Jia, J., Matsushita, Y.: Motion detail preserving optical flow estimation. IEEE Trans. Pattern Anal. Mach. Intell. 34(9), 1744–1757 (2012)

    Article  Google Scholar 

  4. Jodoin, P.-M., Mignotte, M.: Optical-flow based on an edge-avoidance procedure. Comput. Vis. Image Underst. 113, 511–531 (2009)

    Article  Google Scholar 

  5. Liu, C.: Beyond Pixels: Exploring New Representations and Applications for Motion Analysis. In doctoral these. Massachusetts Institute of Technology (2009)

  6. Kristan, M., Perš, J., Kovačič, S., Leonardis, A.: A local-motion-based probabilistic model for visual tracking. Pattern Recogn. 40, 2160–2168 (2009)

    Article  Google Scholar 

  7. Lucas, B.D., Kanade, T.: An iterative image registration technique with an application in stereo vision. In: Proceedings of the International Joint Conference on Artificial Intelligence, pp. 674–679 (1981)

  8. Mahraz, M.A., Riffi, J., Hairi, H.: Motion estimation using the fast and adaptive bidimensional empirical mode decomposition. J. Real-Time Image Proc. (2012). doi:10.1007/s11554-012-0259-4

  9. Meyer, Y.: Oscillating patterns in image processing and in some nonlinear evolution equations. American Mathematical Society, The Fifteenth Dean Jacquelines B. Lewis Memorial Lectures (2001)

  10. Rudin, L., Osher, S., Fatimi, E.: Nonlinear total variation based noise removal algorithms. Physica D 60, 259–268 (1992)

    Article  MATH  Google Scholar 

  11. Aujol, J.-F., Chambolle, A.: Dual norms and image decomposition models. Int. J. Comput. Vis. 63(1), 85–104 (2005)

    Article  MathSciNet  Google Scholar 

  12. Chambolle, A.: An algorithm for total variation minimization and applications. JMIV 20, 89–97 (2004)

    Article  MathSciNet  Google Scholar 

  13. Aujol, J.-F., Aubert, G., Féraud, L.B., Chambolle, A.: Image decomposition into a bounded variation component and an oscillating component. J. Math. Imaging Vis. 22(1), 71–88 (2005)

    Google Scholar 

  14. Gilles, J.: Noisy image decomposition: a new structure, texture and noise model based on local adaptivity. J. Math. Imaging Vis. 28(3), 285–295 (2007b)

    Article  MathSciNet  Google Scholar 

  15. Brox, T., Bruhn, A., Papenberg, N., Weickert, J.: High accuracy optical flow estimation based on a theory for warping. In: Proceeding of the ECCV, pp. 25–36 (2004)

  16. Bruhn, A., Weickert, J., Schnörr, C.: Lucas/Kanade meets Horn/Schunk: combining local and global optical flow methods. IJCV 61(3), 211–231 (2005)

    Article  Google Scholar 

  17. Vese, L.A., Osher, S.J.: Modeling textures with total variation minimization and oscillating patterns in image processing. J. Sci Comput. 19(1–3), 553–572 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  18. Fabesa, E., Mendezb, O., Mitreab, M.: Boundary layers on Sobolev–Besov spaces and Poisson’s equation for the Laplacian in Lipschitz domains. J. Funct. Anal. 159(2), 323–368 (November 1998)

    Google Scholar 

  19. Chambolle, A., Vore, R.D., Lee, N., Lucier, B.: Nonlinear wavelet image processing: variational problems, compression, and noise removal through wavelet shrinkage. IEEE Trans. Image Process 7(3), 319–335 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  20. Aujol, J.-F., Gilboa, G., Chan, T., Osher, S.: Structure-texture image decomposition-modeling, algorithms, and parameter selection. IJCV 67(1), 111–136 (2006)

    Article  MATH  Google Scholar 

  21. Horn, B., Schunck, B.: Determining optical flow. Artif. Intell. 17, 185–203 (1981)

    Article  Google Scholar 

  22. Bruhn, A., Weickert, J.: Towards ultimate motion estimation: combining highest accuracy with real-time performance. In: ICCV, pp. 749–755 (2005)

  23. Baker, S., et al.: A database and evaluation methodology for optical flow. Int. J. Comput. Vis. 92(1), 1–31 (March 2011)

    Google Scholar 

  24. Bresson, X., Chan, T.F.: Fast minimization of the vectorial total variation norm and applications to color image processing. CAM, Report 07–25 2(4), 455–484 (2008)

    MathSciNet  MATH  Google Scholar 

  25. Dabov, K., Foi, A., Katkovnik, V., Egiazarian, K.: Image denoising by sparse 3D transform-domain collaborative filtering. IEEE Trans. Image Process. 16(8) (2007)

  26. Pock, T., Grabner, M., Bischof, H.: Real-time computation of variational methods on graphics hardware. In: 12th Computer Vision Winter Workshop (CVWW) (2007)

  27. Sun, D., Roth, S., Black, M.J.: Secrets of optical flow estimation and their principles. IEEE Int. Conf. on Comp. Vision Pattern Recogn. 2432–2439 (2010). doi:10.1109/CVPR.2010.5539939

  28. Sun, D., Roth, S., Black, M.J.: A quantitative analysis of current practices in optical flow estimation and the principles behind them. International Journal of Computer Vision (IJCV) (2013)

  29. Sun, D., Roth, S., Lewis, J.P., Michael Black, J.: Learning optical flow. In: Proceedings of the European Conference on Computer Vision (ECCV), vol. 3, pp. 83–97 (2008)

Download references

Author information

Authors and Affiliations

  1. LIIAN, Department of Computer Science, Faculty of Science, Dhar El Mahraz, University Sidi Mohamed Ben Abdellah, BP 1796, Fez, Morocco

    M. A. Mahraz, J. Riffi & H. Tairi

Authors
  1. M. A. Mahraz
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. Riffi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. H. Tairi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. A. Mahraz.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mahraz, M.A., Riffi, J. & Tairi, H. High accuracy optical flow estimation based on PDE decomposition. SIViP 9, 1409–1418 (2015). https://doi.org/10.1007/s11760-013-0594-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11760-013-0594-3

Keywords

Search

Navigation