Skip to main content

Optical Flow Computation with Locally Quadratic Assumption

  • Conference paper
  • First Online:
Computer Analysis of Images and Patterns (CAIP 2015)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 9256))

Included in the following conference series:

Abstract

The purpose of this paper is twofold. First, we develop a quadratic tracker which computes a locally quadratic optical flow field by solving a model-fitting problem for each point in its local neighbourhood. This local method allows us to select a region of interest for the optical flow computation. Secondly, we propose a method to compute the transportation of a motion field in long-time image sequences using the Wasserstein distance for cyclic distributions. This measure evaluates the motion coherency in an image sequence and detects collapses of smoothness of the motion vector field in an image sequence.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Horn, B.K.P., Schunck, B.G.: Determining optical flow. Artificial Intelligence 17, 185–204 (1981)

    Article  Google Scholar 

  2. Rubner, Y., Tomasi, C., Guibas, L.J.: A metric for distributions with applications to image databases. In: Proceedings of ICCV 1998, pp. 59–66 (1998)

    Google Scholar 

  3. Fisher, N.I.: Statistical Analysis of Circular Data. Cambridge University Press (1993)

    Google Scholar 

  4. Wedel, A., Cremers, D.: Stereo Scene Flow for 3D Motion Analysis. Springer (2011)

    Google Scholar 

  5. Vogel, Ch., Schindler, K., Roth, S.L.: Piecewise rigid scene flow. In: Proceedings of ICCV 2013, pp. 1377–1384 (2013)

    Google Scholar 

  6. Vogel, Ch., Schindler, K., Roth, S.: 3D scene flow estimation with a rigid motion prior. In: Proceedings of ICCV 2011, pp. 1291–1298 (2011)

    Google Scholar 

  7. Rabin, J., Delon, J., Gousseau, Y.: Transportation distances on the circle. JMIV 41, 147–167 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  8. Hwang, S.-H., Lee, U.-K.: A hierarchical optical flow estimation algorithm based on the interlevel motion smoothness constraint. Pattern Recognition 26, 939–952 (1993)

    Article  Google Scholar 

  9. Amiaz, T., Lubetzky, E., Kiryati, N.: Coarse to over-fine optical flow estimation. Pattern Recognition 40, 2496–2503 (2007)

    Article  MATH  Google Scholar 

  10. Villani, C.: Optimal Transport, Old and New. Springer (2009)

    Google Scholar 

  11. Baker, S., Matthews, I.: Lucas-Kanade 20 years On: A unifying framework. IJCV 56, 221–255 (2004)

    Article  Google Scholar 

  12. Lucas, B.D., Kanade, T.: An iterative image registration technique with an application to stereo vision. In: Proceedings of IJCAI 1981, pp. 674–679 (1981)

    Google Scholar 

  13. Shi, J., Tomasi, C.: Good features to track. In: Proceedings of CVPR 1994, pp. 593–600 (1994)

    Google Scholar 

  14. Dalal, N., Triggs, B.: Histograms of oriented gradients for human detection. In: Proceedings of CVPR 2005 (2005)

    Google Scholar 

  15. Ustundag, B.C., Unel, M.: Human action recognition using histograms of oriented optical flows from depth. In: Bebis, G., et al. (eds.) ISVC 2014, Part I. LNCS, vol. 8887, pp. 629–638. Springer, Heidelberg (2014)

    Google Scholar 

  16. Chaudhry, R., Ravichandran, A., Hager, G.D., Vidal, R.: Histograms of oriented optical flow and binet-cauchy kernels on nonlinear dynamical systems for the recognition of human actions. In: Proceedings of CVPR 2009, pp. 1932–1939 (2009)

    Google Scholar 

  17. Mileva, Y., Bruhn, A., Weickert, J.: Illumination-robust variational optical flow with photometric invariants. In: Hamprecht, F.A., Schnörr, C., Jähne, B. (eds.) DAGM 2007. LNCS, vol. 4713, pp. 152–162. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  18. Bruhn, A., Weickert, J., Schnörr, C.: Lucas/Kanade meets Horn/Schunck: Combining local and global optic flow methods. IJCV 61, 211–231 (2005)

    Article  Google Scholar 

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

    Chapter  Google Scholar 

  20. Papenberg, N., Bruhn, A., Brox, T., Didas, S., Weickert, J.: Highly accurate optic flow computation with theoretically justified warping. IJCV 67, 141–158 (2006)

    Article  Google Scholar 

  21. Shin, Y.-Y., Chang, O.-S., Xu, J.: Convergence of fixed point iteration for deblurring and denoising problem. Applied Mathematics and Computation 189, 1178–1185 (2007)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Atsushi Imiya .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Kato, T., Itoh, H., Imiya, A. (2015). Optical Flow Computation with Locally Quadratic Assumption. In: Azzopardi, G., Petkov, N. (eds) Computer Analysis of Images and Patterns. CAIP 2015. Lecture Notes in Computer Science(), vol 9256. Springer, Cham. https://doi.org/10.1007/978-3-319-23192-1_19

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-23192-1_19

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-23191-4

  • Online ISBN: 978-3-319-23192-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics