Experiments in Fluids

, Volume 44, Issue 2, pp 291–304 | Cite as

Variational second order flow estimation for PIV sequences

  • L. Alvarez
  • C. A. Castaño
  • M. García
  • K. Krissian
  • L. Mazorra
  • A. Salgado
  • J. Sánchez
Research Article
First Online:
Received:
Revised:
Accepted:

Abstract

We present in this paper a variational approach to accurately estimate simultaneously the velocity field and its derivatives directly from PIV image sequences. Our method differs from other techniques that have been presented in the literature in the fact that the energy minimization used to estimate the particles motion depends on a second order Taylor development of the flow. In this way, we are not only able to compute the motion vector field, but we also obtain an accurate estimation of their derivatives. Hence, we avoid the use of numerical schemes to compute the derivatives from the estimated flow that usually yield to numerical amplification of the inherent uncertainty on the estimated flow. The performance of our approach is illustrated with the estimation of the motion vector field and the vorticity on both synthetic and real PIV datasets.

Keywords

Vorticity Particle Image Velocimetry Particle Image Velocimetry Image Motion Vector Field Average Angular Error 
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.
This is a preview of subscription content, log in to check access

Notes

Acknowledgments

This work has been funded by the European Commission under the Specific Targeted Research Project FLUID (contract no. FP6-513663). We acknowledge the Research Institute CEMAGREF (Rennes, France) for providing to us the synthetic PIV image and the real PIV sequence we have used in the experiments.

References

  1. Abrahamson S, Lonnes S (1995) Uncertainty in calculating vorticity from 2d velocity fields using circultaion and least-squares approaches. Exp Fluids 20:10–20CrossRefGoogle Scholar
  2. Adrian R (1988) Statistical properties of particle image velocimetry measurements in turbulent flow. Laser Anemometry Fluid Mech 1:115–129Google Scholar
  3. Alemßn M, Alvarez L, Gonzßlez E, Mazorra L, Sßnchez J (2005) Optic flow estimation in fluid images i. Cuadernos Instituto Universitario de Ciencias y Tecnologfas CibernTticas 31:1–25Google Scholar
  4. Alvarez L, Weickert J, Sßnchez J (2000) Reliable estimation of dense optical flow fields with large displacements. Int J Comput Vis 39(1):41–56MATHCrossRefGoogle Scholar
  5. Anandan P (1989) A computational framework and an algorithm for the measurement of visual motion. Int J Comput Vis 2:283–310CrossRefGoogle Scholar
  6. Corpetti T, Memin E, Perez P (2002) Dense estimation of fluid flows. IEEE Trans Pattern Anal Mach Intell 24(3):365–380CrossRefGoogle Scholar
  7. Corpetti T, Heitz D, Arroyo G, MTmin E, Santa-Cruz A (2006) Fluid experimental flow estimation based on an optical-flow scheme. Exp Fluids 40(1):80–97CrossRefGoogle Scholar
  8. Etebari A, Vlachos P (2005) Improvements on the accuracy of derivative estimation from dpiv velocity measurements. Exp Fluids 39:1040–1050CrossRefGoogle Scholar
  9. Fletcher R, Reeves C (1964) Function minimization by conjugate gradients. Comput J 7:149–154MATHCrossRefMathSciNetGoogle Scholar
  10. Foucaut JM, Stanislas M (2002) Some considerations on the accuracy and frequency response of some derivative filters applied to particle image velocimetry vector fields. Meas Sci Technol 13:1058–1071CrossRefGoogle Scholar
  11. Fouras A, Soria J (1998) Accuracy of out-of-plane vorticity measurements derived from in-plane velocity field data. Exp Fluids 25:409–430CrossRefGoogle Scholar
  12. Hunt J (1987) Vorticity and vortex dynamics in complex turbulent flows. In: Transactions Canadian Society for Mechanical Engineering (ISSN 0315-8977), vol 11, pp 21–35Google Scholar
  13. Keane R, Adrian R (1990) Optimization of particle image velocimeters. I. double pulsed systems. Meas Sci Technol 1(10):1202–1215CrossRefGoogle Scholar
  14. Keane R, Adrian R (1992) Theory of cross-correlation analysis of piv images. Appl Sci Res 49(3):191–215CrossRefGoogle Scholar
  15. Kim J, Lee D (1996) Optimized compact finite difference schemes with maximum resolution. AIAA J 34(5):887–893MATHCrossRefGoogle Scholar
  16. Luff JD, Drouillard T, Rompage AM, Linne M, Hertzberg JR (1999) Experimental uncertainties associated with particle image velocimetry (PIV) based vorticity algorithms. Exp Fluids 26:36–54CrossRefGoogle Scholar
  17. Nogueira J, Lecuona A, Rodrfguez PA, Alfaro JA, Acosta A (2005) Limits on the resolution of correlation piv iterative methods. practical implementation and design of weighting functions. Exp Fluids 39:314–321CrossRefGoogle Scholar
  18. Parnaudeau P, Carlier J, Heitz D, Lamballais E (2006) Experimental and numerical studies of the flow over a circular cylinder at reynolds number 3900. Phys Fluids (submitted)Google Scholar
  19. Press W, Teukolsky S, Vetterling W, Flannery B (1992) Numerical recipes in C: The Art of Scientific Computing. Cambridge University Press, New York, NY, USAGoogle Scholar
  20. Raffel M, Willert C, Kompenhans J (1998) Particle image velocimetry. A practical guide. Springer, HeidelbergGoogle Scholar
  21. Ruhnau P, Guetter C, Putze T, Schnorr C (2005a) A variational approach for particle tracking velocimetry. Meas Sci Technol 16:1449–1458CrossRefGoogle Scholar
  22. Ruhnau P, Kohlberger T, Nobach H, Schnorr C (2005b) Variational optical flow estimation for particle image velocimetry. Exp Fluids 38:21–32CrossRefGoogle Scholar
  23. Scarano F (2002) Iterative image deformation methods in PIV. Meas Sci Technol 13:R1–R19CrossRefGoogle Scholar
  24. Senel H, Peters R, Dawant B (2002) Topological median filters. IEEE Trans Image Process 11(2):89–104CrossRefMathSciNetGoogle Scholar
  25. Soria J, Giles CL, Omlin C (1996) An investigation of the near wake of a circular cylinder using a video-based digital cross-correlation particle image velocimetry technique. Exp Thermal Fluid Sci 12(2):221–233CrossRefGoogle Scholar
  26. Thomas M, Misra S, Kambhamettu C, Kirby J (2005) A robust motion estimation algorithm for piv. Meas Sci Technol 16:865–877CrossRefGoogle Scholar
  27. Westerweel J (1993) Digital particle image velocimetry. Theory and application. Delft University Press, DelftGoogle Scholar
  28. Westerweel J (1997) Fundamentals of digital particle image velocimetry. Meas Sci Technol 8:1379–1392CrossRefGoogle Scholar
  29. Westerweel J, Dabiri D, Gharib M (1997) The effect of a discrete window offset on the accuracy of cross-correlation analysis of digital piv recordings. Exp Fluids 23:20–28CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • L. Alvarez
    • 1
  • C. A. Castaño
    • 1
  • M. García
    • 1
  • K. Krissian
    • 1
  • L. Mazorra
    • 1
  • A. Salgado
    • 1
  • J. Sánchez
    • 1
  1. 1.Departamento de Informática y SistemasUniversidad de Las Palmas de Gran CanariaLas Palmas de Gran CanariaSpain

Personalised recommendations