Skip to main content
SpringerLink
Log in

On Variational Methods for Fluid Flow Estimation

  • Conference paper
Complex Motion (IWCM 2004)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 3417))

Included in the following conference series:

Abstract

We present global variational approaches that are capable of extracting high-resolution velocity vector fields from image sequences of fluids. Starting points are existing variational approaches from image processing that we adapt to the requiremements of particle image sequences, paying particular attention to a multiscale representation of the image data.

Additionally, we combine a discrete non-differentiable particle matching term with a continuous regularization term and thus achieve a variational particle tracking approach.

As higher-order regularization can be used to preserve important flow structures, we finally sketch a motion estimation scheme based on the decomposition of motion vector fields into components of orthogonal subspaces.

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

Access this chapter

Log in via an institution
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. Raffel, M., Willert, C., Kompenhans, J.: Particle Image Velocimetry. A Practical Guide. Springer, Heidelberg (1999)

    Google Scholar 

  2. Kawamura, T., Hiwada, M., Hibino, T., Mabuchi, I., Kumada, M.: Flow around a finite circular cylinder on a flat plate. Bulletin of the JSME 27, 2142–2151 (1984)

    Google Scholar 

  3. Scarano, F.: Iterative image deformation methods in piv. Meas. Sci. Technol. 13, R1–R19 (2002)

    Article  Google Scholar 

  4. Kobayashi, T., Saga, T., Segawa, S.: Multipoint velocity measurement for unsteady flow field by digital image processing. Journal of Visualization 5, 197–202 (1989)

    Google Scholar 

  5. Hassan, Y., Canaan, R.: Full-field bubbly flow velocity measurements using a multiframe particle trackingg technique. Exp. Fluids 12, 49–60 (1991)

    Article  Google Scholar 

  6. Uemura, T., Yamamoto, F., Ohmi, K.: A high speed algorithm of image analysis for real time measurement of two-dimensional velocity distribution. Flow Visualization, pp. 129–133 (1989)

    Google Scholar 

  7. Ohmi, K., Li, H.Y.: Particle-tracking velocimetry with new algorithms. Meas. Sci. Technol. 11, 603–616 (2000)

    Article  Google Scholar 

  8. Keane, R., Adrian, R., Zhang, Y.: Super-resolution particle image velocimetry. Meas. Sci. Technol. 6, 754–768 (1995)

    Article  Google Scholar 

  9. Cowen, E., Monismith, S.: A hybrid digital particle tracking velocimetry technique. Exp. Fluids 22, 199–211 (1997)

    Article  Google Scholar 

  10. Horn, B., Schunck, B.: Determining optical flow. Artificial Intelligence 17, 185–203 (1981)

    Article  Google Scholar 

  11. Nagel, H.H.: On the estimation of optical flow: Relations between different approaches and some new results. Artificial Intelligence 33, 299–324 (1987)

    Article  Google Scholar 

  12. Schnörr, C.: Determining optical flow for irregular domains by minimizing quadratic functionals of a certain class. International Journal of Computer Vision 6, 25–38 (1991)

    Article  Google Scholar 

  13. 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)

    Article  Google Scholar 

  14. Schnörr, C.: Segmentation of visual motion by minimizing convex non-quadratic functionals. In: 12th Int. Conf. on Pattern Recognition, vol. A, Jerusalem, Israel, pp. 661–663. IEEE Computer Society Press, Los Alamitos (1994)

    Google Scholar 

  15. Schnörr, C.: Convex variational segmentation of multi-channel images. In: 12th Int. Conf. on Analysis and Optimization of Systems: Images, Wavelets and PDE’s. Lect. Notes in Control and Information Sciences, vol. 219, pp. 201–207 (1996)

    Google Scholar 

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

    Article  MATH  Google Scholar 

  17. Weickert, J., Schnörr, C.: A theoretical framework for convex regularizers in pde-based computation of image motion. Int. J. Computer Vision 45, 245–264 (2001)

    Article  MATH  Google Scholar 

  18. Ruhnau, P., Kohlberger, T., Nobach, H., Schnörr, C.: Variational optical flow estimation for particle image velocimetry. Exp. Fluids (in press, 2004)

    Google Scholar 

  19. Kohlberger, T., Mémin, E., Schnörr, C.: Variational dense motion estimation using the helmholtz decomposition. In: Griffin, L.D, Lillholm, M. (eds.) Scale Space Methods in Computer Vision. LNCS, vol. 2695, pp. 432–448. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  20. Krishnamurthy, R., Moulin, P., Woods, J.: Multiscale motion models for scalable video coding. In: Proc. IEEE Int. Conf. Image Processing, Lausanne, Switzerland, pp. 965–968. IEEE Computer Society Press, Los Alamitos (1996)

    Chapter  Google Scholar 

  21. Simoncelli, E.P.: Distributed representation and analysis of visual motion. PhD thesis, Massachusetts Institute of Technology (1993)

    Google Scholar 

  22. Quénot, G.M., Pakleza, J.: Particle image velocimetry with optical flow (1998)

    Google Scholar 

  23. Brede, M., Leder, A., Westergaard, C.H.: Time-resolved piv investigation of the separated shear layer in the transitional cylinder wake. In: Proc. 5th Int. Symp. on Particle Image Velocimetry (PIV’03), Busan, Korea (2003)

    Google Scholar 

  24. Westergaard, C.H., Brede, M., Leder, A.: Time-space analysis of time resolved piv data. In: Proc. 5th Int. Symp. on Particle Image Velocimetry (PIV’03), Busan, Korea (2003)

    Google Scholar 

  25. Quénot, G.M.: The orthogonal algorithm for optical flow detection using dynamic programming. In: Proc. Intl. Conf. on Acoustics, Speech and Signal Proc., pp. 249–252 (1992)

    Google Scholar 

  26. Quénot, G.M.: Performance evaluation of an optical flow technique applied to piv using the vsj standard images. In: Third International Workshop on PIV, pp. 579–584 (1999)

    Google Scholar 

  27. Barron, J., Fleet, D., Beauchemin, S.: Performance of optical flow techniques. International Journal of Computer Vision 39, 43–77 (1994)

    Article  Google Scholar 

  28. Chetverikov, D.: Applying feature tracking to piv. International Journal of Pattern Recognition and Artificial Intelligence 17, 477–504 (2003)

    Article  Google Scholar 

  29. Brandt, A.: Multi-level adaptive solutions to boundary-value problems. Mathematics of Computation 31, 333–390 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  30. Hackbusch, W.: Iterative Solution of Large Sparse Systems of Equations. Applied Mathematical Sciences, vol. 95. Springer, Heidelberg (1993)

    MATH  Google Scholar 

  31. Bruhn, A., Weickert, J., Feddern, C., Kohlberger, T., Schnörr, C.: Variational optic flow computation in real-time. In: IEEE Trans. Image Proc. (in press, 2004)

    Google Scholar 

  32. Kohlberger, T., Schnörr, C., Bruhn, A., Weickert, J.: Parallel variational motion estimation by domain decomposition and cluster computing. In: Pajdla, T., Matas, J.(G.) (eds.) ECCV 2004. LNCS, vol. 3024, pp. 205–216. Springer, Heidelberg (2004)

    Google Scholar 

  33. Cohen, L.D.: Auxiliary variables and two-step iterative algorithms in computer vision problems. J. Math. Imaging Vis. 6, 59–83 (1996)

    Article  Google Scholar 

  34. Aurenhammer, F.: Voronoi diagrams – a survey of a fundamental geometric data structure (Habilitationsschrift. Report B 90-09, FU Berlin, Germany (1990)). ACM Computing Surveys 23, 345–405 (1991)

    Article  Google Scholar 

  35. Ruhnau, P., Gütter, C., Schnörr, C.: A variational approach for particle tracking velocimetry. Comp. science series, technical report, Dept. Math. and Comp. Science, University of Mannheim, Germany (2004)

    Google Scholar 

  36. Okamoto, K., Nishio, S., Kobayashi, T.: Standard images for particle-image velocimetry. Meas. Sci. Technol. 11, 685–691 (2000)

    Article  Google Scholar 

  37. Okamoto, K., Nishio, S., Kobayashi, T., Saga, T., Takehara, K.: Evaluation of the 3d-piv standard images (piv-std project). Journal of Visualization 3, 115–124 (2000)

    Article  Google Scholar 

  38. Hyman, J.M., Shashkov, M.J.: The orthogonal decomposition theorems for mimetic finite difference methods. SIAM J. Numer. Anal. 36, 788–818 (electronic) (1999)

    Article  MathSciNet  Google Scholar 

  39. Hyman, J.M., Shashkov, M.J.: Natural discretizations for the divergence, gradient, and curl on logically rectangular grids. Comput. Math. Appl. 33, 81–104 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  40. Hyman, J.M., Shashkov, M.J.: Adjoint operators for the natural discretizations of the divergence, gradient and curl on logically rectangular grids. Appl. Numer. Math. 25, 413–442 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  41. Yuan, J., Ruhnau, P., Mémin, E., Schnörr, C.: Discrete orthogonal decomposition and variational fluid flow estimation. In: 5th International Conference on Scale Space and PDE Methods in Computer Vision (in preparation, 2005)

    Google Scholar 

  42. Evans, L.C.: Partial differential equations. Graduate Studies in Mathematics, vol. 19. American Mathematical Society, Providence (1998)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, Computer Vision, Graphics, and Pattern Recognition Group, University of Mannheim, 68131 Mannheim, Germany

    Paul Ruhnau, Jing Yuan & Christoph Schnörr

Authors
  1. Paul Ruhnau
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jing Yuan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Christoph Schnörr
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Bernd Jähne Rudolf Mester Erhardt Barth Hanno Scharr

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer Berlin Heidelberg

About this paper

Cite this paper

Ruhnau, P., Yuan, J., Schnörr, C. (2007). On Variational Methods for Fluid Flow Estimation. In: Jähne, B., Mester, R., Barth, E., Scharr, H. (eds) Complex Motion. IWCM 2004. Lecture Notes in Computer Science, vol 3417. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69866-1_10

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-69866-1_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-69864-7

  • Online ISBN: 978-3-540-69866-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation