Abstract
We present in this paper a novel combined scheme dedicated to the measurement of velocity in fluid experimental flows through image sequences. The proposed technique satisfies the Navier–Stokes equations and combines the robustness of correlation techniques with the high density of global variational methods. It can be considered either as a reenforcement of fluid dedicated optical-flow methods towards robustness, or as an enhancement of correlation approaches towards dense information. This results in a physics-based technique that is robust under noise and outliers, while providing a dense motion field. The method was applied on synthetic images and on real experiments in turbulent flows carried out to allow a thorough comparison with a state of the art variational and correlation methods.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Alvarez L, Castano C, García M, Krissian K, Mazorra L, Salgado A, Sánchez J (2008) Variational second order flow estimation for PIV sequences. Exp Fluids 44(2):291–304
Bergen J, Anadan P, Anna K, Hingorani R (1992) Hierarchical model-based motion estimation. In: Sandini G (ed) Proceedings of European conference on computer vision. Springer, Heidelberg, pp 237–252
Bigün J, Granlund G (1988) Optical flow based on the inertia matrix in the frequency domain. In: Proceedings of SSAB symposium on picture processing. Lund, Sweden
Black M, Anandan P (1996) The robust estimation of multiple motions: parametric and piecewise-smooth flow fields 63(1):75–104
Bruhn A, Weickert J, Schnörr C (2005) Lucas/Kanade meets Horn/Schunck: combining local and global optic flow methods. Int J Comput Vis 63(3):211–231
Carlier J, Wieneke B (2005) Report 1 on production and diffusion of fluid mechanics images and data, Fluid project deliverable 1.2. European Project ‘Fluid image analisys and description’ (FLUID). http://www.fluid.irisa.fr/
Corpetti T, Mémin E, Pérez P (2002) Dense estimation of fluid flows. IEEE Trans Pattern Anal Mach Intell 24(3):365–380
Corpetti T, Heitz D, Arroyo G, Mémin E, Santa-Cruz A (2006) Fluid experimental flow estimation based on an optical-flow scheme. Exp Fluids 40:80–97
Cuzol A, Hellier P, Mémin E (2007) A low dimensional fluid motion estimator. Int J Comput Vis 75(3):329–349
Hain R, Kähler C (2007) Fundamentals of multiframe particle image velocimetry (PIV). Exp Fluids 42:575–587
Héas P, Mémin E, Papadakis N, Szantai A (2007) Layered estimation of atmospheric mesoscale dynamics from satellite imagery. IEEE Trans Geosci Remote Sens (in press)
Heitz D, Mémin E, Schnörr C (2008) Fluid flow motion measurements from image sequence: a review and some perspectives. Exp Fluids (submitted)
Horn B, Schunck B (1981) Determining optical flow. Artif Intell 17:185–203
Kohlberger T, Mémin E, Schnörr C (2003) Variational dense motion estimation using the Helmholtz decomposition. In: Griffin L, Lillholm M (eds) Scale space methods in computer vision LNCS, vol 2695. Springer, Berlin, pp 432–448
Lecordier B, Westerweel J (2003) The EUROPIV synthetic image generator (SIG). In: Stanislas M, Westerweel J, Kompenhans J (eds) Particle image velocimetry: recent improvements. EUROPIV 2 workshop, Springer, pp 145–162
Liu T, Shen L (2008) Fluid flow and optical flow. J Fluid Mech (in press)
Lucas B, Kanade T (1981) An iterative image registration technique with application to stereo vision. In: Proceedings of seventh international joint conference on artificial intelligence, Vancouver, Canada, pp 674–679
Mansour NN, Ferziger JH, Reynolds WC (1978) Large-eddy simulation of a turbulent mixing layer. Technical report. Report TF-11, Thermosciences Division, Department of Mechanical Engineering, Standford University
Okuno T, Sugii Y, Nishio S (2000) Image measurement of flow field using physics-based dynamic model. Meas Sci Technol 11:667–676
Papadakis N, Corpetti T, Mémin E (2007) Dynamically consistent optical flow estimation. In: IEEE international conference on computer vision, ICCV’07. Rio de Janeiro, Brazil
Parnaudeau P, Carlier J, Heitz D, Lamballais E (2008) Experimental and numerical studies of the flow over a circular cylinder at Reynolds number 3900. Phys Fluids 20(085101). doi:10.1063/1.2957018
Rhunau P, Schnörr C (2007) Optical Stokes flow estimation: an imaging based control approach. Exp Fluids 42:61–78
Rhunau P, Stahl A, Schnörr C (2007) Variational estimation of experimental fluid flows with physycs-based spatio-temporal regularization. Meas Sci Technol 18:755–763
Ruhnau P, Kohlberger T, Schnörr C, Nobach H (2005) Variational optical flow estimation for particle image velocimetry. Exp Fluids 38:21–32
Saint-Venant A (1871) Theorie du mouvement non-permanent des eaux, avec application aux crues des rivieres et l’introduction des marees dans leur lit. C R Acad Sci Paris 73:147–154
Stanislas M, Okamoto K, Kähler CJ, Westerweel J, Scarano F (2008) Main results of the third international PIV challenge. Exp Fluids 45(1):27–71
Stansby PK (1974) The effect of end plates on the pressure coefficient of a circular cylinder. R Aeronaut J 78:36–37
Suter D (1994) Motion estimation and vector splines. Seattle, USA, pp 939–942
Tikhonov AN, Arsenin VY (1977) Solutions of ill-posed problems. In: Scripta series in mathematics, chap II. ISBN 0470991240
Weickert J, Schnörr C (2001) Variational optic flow computation with a spatio-temporal smoothness constraint. J Math Imaging Vis 14(3):245–255
Westerweel J (1994) Efficient detection of spurious vectors in particle image velocimetry data sets. Exp Fluids 16:236–247
Yuan J, Schnörr C, Mémin E (2007) Discrete orthogonal decomposition and variational fluid flow estimation. J Math Imaging Vis 28:67–80
Acknowledgments
The financial support by the Region of Bretagne in France under Grant No. 20048347 and by the European Union under Grant No. FP6-513663 are gratefully acknowledged.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Heitz, D., Héas, P., Mémin, E. et al. Dynamic consistent correlation-variational approach for robust optical flow estimation. Exp Fluids 45, 595–608 (2008). https://doi.org/10.1007/s00348-008-0567-4
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00348-008-0567-4