Skip to main content
Springer Nature Link
Log in

On a Decomposition Model for Optical Flow

  • Conference paper
Energy Minimization Methods in Computer Vision and Pattern Recognition (EMMCVPR 2009)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 5681))

  • 1442 Accesses

Abstract

In this paper we present a variational method for determining cartoon and texture components of the optical flow of a noisy image sequence. The method is realized by reformulating the optical flow problem first as a variational denoising problem for multi-channel data and then by applying decomposition methods. Thanks to the general formulation, several norms can be used for the decomposition. We study a decomposition for the optical flow into bounded variation and oscillating component in greater detail. Numerical examples demonstrate the capabilities of the proposed approach.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. http://vision.middlebury.edu/flow/

  2. Amann, H.: Compact embeddings of sobolev and besov spaces. Glasnik Matematicki 35(55), 161–177 (2000)

    MathSciNet  MATH  Google Scholar 

  3. Aujol, J.-F., Aubert, G., Blanc-Feraud, L., Chambolle, A.: Image decomposition into a bounded variation component and an oscillating component. Journal of Mathematical Imaging and Vision 22(1), 71–88 (2005)

    Article  MathSciNet  Google Scholar 

  4. Aujol, J.-F., Chambolle, A.: Dual norms and image decomposition models. International Journal of Computer Vision 63(1), 85–104 (2005)

    Article  Google Scholar 

  5. Aujol, J.-F., Kang, S.-H.: Color image decomposition and restoration. Journal of Visual Communication and Image Representation 17(4), 916–928 (2006)

    Article  Google Scholar 

  6. Brox, T., Bruhn, A., Papenberg, N., Weickert, J.: High accuracy optical flow estimation based on a theory for warping. In: Pajdla, T., Matas, J(G.) (eds.) ECCV 2004. LNCS, vol. 3024, pp. 25–36. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  7. Bruhn, A.: Variational optic flow computation: Accurate modeling and efficient numerics. PhD thesis, Saarland University, Germany (2006)

    Google Scholar 

  8. Chambolle, A.: An algorithm for total variation minimization and applications. Journal of Mathematical Imaging and Vision 20(1-2), 89–97 (2004)

    MathSciNet  Google Scholar 

  9. Cohen, I.: Nonlinear variational method for optical flow computation. In: Proc. Eigth Scandinavian Conference on Image Analysis, Tromso, Norway, May 1993, vol. 1, pp. 523–530 (1993)

    Google Scholar 

  10. Deriche, R., Kornprobst, P., Aubert, G.: Optical flow estimation while preserving its discontinuities. In: Proc. Second Asian Conference on Computer Vision, Singapore, December 1995, vol. 2, pp. 290–295 (1995)

    Google Scholar 

  11. Fleet, D.J., Weiss, Y.: Optical Flow Estimation. In: Mathematical Models of Computer Vision: The Handbook, ch. 15, pp. 239–258. Springer, Heidelberg (2005)

    Google Scholar 

  12. Horn, B.K.P., Schunck, B.G.: Determining optical flow. Artificial Intelligence 17, 185–203 (2004)

    Article  Google Scholar 

  13. Kohlberger, T., Memin, E., Schnoerr, C.: Variational dense motion estimation using helmholtz decomposition. In: Griffin, L.D., Lillholm, M. (eds.) Scale-Space 2003. LNCS, vol. 2695, pp. 432–448. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  14. Meyer, Y.: Oscillating patterns in image processing and in some nonlinear evolution equations. In: The Fifteenth Dean Jaqueline B. Lewis Memorial Lectures (March 2001)

    Google Scholar 

  15. Starck, J.L., Elad, M., Donoho, D.L.: Image decomposition via the combination of sparse representations and a variational approach. IEEE Transactions on Image Processing 14(10), 1570–1582 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  16. Vese, L.A., Osher, S.: Modeling textures with total variation minimization and oscillating patterns in image processing. Journal of Scientific Computing 19, 553–572 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  17. Weickert, J., Bruhn, A., Brox, T., Papenberg, N.: A Survey on Variational Optic Flow Methods for Small Displacements. In: Mathematical Models for Registration and Applications to Medical Imaging, ch. 1, pp. 103–136. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  18. Weickert, J., Schnoerr, C.: A theoretical framework for convex regularizers in pde-based computation of image motion. International Journal of Computer Vision 45(3), 245–264 (2001)

    Article  MATH  Google Scholar 

  19. Weickert, J., Schnoerr, C.: Variational optic flow computation with a spatio-temporal smoothness constraint. Journal of Mathematical Imaging and Vision 14(3), 245–255 (2001)

    Article  MATH  Google Scholar 

  20. Yuan, J., Schnoerr, C., Steidl, G.: Simultaneous higher-order optical flow estimation and decomposition. SIAM J. Scientfic Computing 29(6), 2283–2304 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  21. Yuan, J., Schnörr, C., Steidl, G., Becker, F.: A study of non-smooth convex flow decomposition. In: Paragios, N., Faugeras, O., Chan, T., Schnörr, C. (eds.) VLSM 2005. LNCS, vol. 3752, pp. 1–12. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  22. Zach, C., Pock, T., Bischof, H.: A duality based approach for realtime TV-shape L 1 optical flow. In: Hamprecht, F.A., Schnörr, C., Jähne, B. (eds.) DAGM 2007. LNCS, vol. 4713, pp. 214–223. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Innsbruck, Technikerstrasse 21a, A-6020, Innsbruck, Austria

    Jochen Abhau

  2. Laboratoire de Mathématiques LMAM, UMR 7122, Université UPV-Metz, ISGMP, Batiment A, Ile du Saulcy, 57045, Metz, France

    Zakaria Belhachmi

  3. Department of Mathematics, University of Vienna, Nordbergstrasse 15, A-1090, Wien, Austria

    Otmar Scherzer

  4. Radon Institute of Computational and Applied Mathematics, Altenberger Strasse 69, A-4040, Linz, Austria

    Otmar Scherzer

Authors
  1. Jochen Abhau
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zakaria Belhachmi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Otmar Scherzer
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institut für Informatik III, Rö, Universität Bonn, merstraße 164, 53117, Bonn, Germany

    Daniel Cremers

  2. Computer Science Department, University of Western Ontario, N6A 5A5, London, ON, Canada

    Yuri Boykov

  3. Microsoft Research, J.J. Thomson Avenue, CB3 OFB, Cambridge, United Kingdom

    Andrew Blake

  4. Institut für Informatik III, Universität Bonn, Römerstraße 164, 53117, Bonn, Germany

    Frank R. Schmidt

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Abhau, J., Belhachmi, Z., Scherzer, O. (2009). On a Decomposition Model for Optical Flow. In: Cremers, D., Boykov, Y., Blake, A., Schmidt, F.R. (eds) Energy Minimization Methods in Computer Vision and Pattern Recognition. EMMCVPR 2009. Lecture Notes in Computer Science, vol 5681. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03641-5_10

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-03641-5_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03640-8

  • Online ISBN: 978-3-642-03641-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics