Skip to main content
SpringerLink
Log in

Optical flow for incompressible turbulence motion estimation

  • Research Article
  • Published:
Experiments in Fluids Aims and scope Submit manuscript

Abstract

We propose in this paper a new formulation of optical flow dedicated to 2D incompressible turbulent flows. It consists in minimizing an objective function constituted by an observation term and a regularization one. The observation term is based on the transport equation of the passive scalar field. For non-fully resolved scalar images, we propose to use the mixed model in large eddy simulation to determine the interaction between large scales and unresolved ones. The regularization term is based on the continuity equation of 2D incompressible flows. Compared to prototypical method, this regularizer preserves more vortex structures by eliminating constraints over the vorticity field. The evaluation of the proposed formulation is done over synthetic and experimental images, and the improvements in term of estimation are discussed.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

Notes

  1. http://fluid.irisa.fr/data-eng.htm.

References

  • Adrian RJ (1991) Particle-imaging techniques for experimental fluid mechanics. Annu Rev Fluid Mech 23(1):261–304

    Article  Google Scholar 

  • Baker S, Scharstein D, Lewis J, Roth S, Black MJ, Szeliski R (2011) A database and evaluation methodology for optical flow. Int J Comput Vis 92(1):1–31

    Article  Google Scholar 

  • Bardina J, Ferziger J, Reynold W (1980) Improved subgrid-scale models for large-eddy simulation. In: American institute of aeronautics and astronautics, fluid and plasma dynamics conference, 13th, Snowmass, Colo., July 14–16, 1980, 10 p., vol 1

  • Bardina J, Ferziger J, Reynold W (1983) Improved turbulence models based on large eddy simulation of homogeneous, incompressible turbulent flows. Stanford Univ, Report 1

  • Barron JL, Fleet DJ, Beauchemin SS (1994) Performance of optical flow techniques. Int J Comput Vis 12(1):43–77

    Article  Google Scholar 

  • Batchelor G et al (1959) Small-scale variation of convected quantities like temperature in turbulent fluid. J Fluid Mech 5(1):113–133

    Article  MATH  MathSciNet  Google Scholar 

  • Becker F, Wieneke B, Petra S, Schroder A, Schnorr C (2012) Variational adaptive correlation method for flow estimation. Image Process IEEE Trans 21(6):3053–3065

    Article  MathSciNet  Google Scholar 

  • Bergen JR, Burt PJ, Hingorani R, Peleg S (1992) A three-frame algorithm for estimating two-component image motion. IEEE Trans Pattern Anal Mach Intell 14(9):886–896

    Article  Google Scholar 

  • Bertoglio JP (1985) A stochastic subgrid model for sheared turbulence. In: macroscopic modelling of turbulent flows. Springer, Berlin, pp 100–119

    Book  Google Scholar 

  • Brox T, Bruhn A, Papenberg N, Weickert J (2004) High accuracy optical flow estimation based on a theory for warping. Springer, Berlin, pp 25–36

    Google Scholar 

  • Burt P (1988) Smart sensing within a pyramid vision machine. Proc IEEE 76(8):1006–1015

    Article  Google Scholar 

  • Carlier J, Wieneke B (2005) Report 1 on production and diffusion of fluid mechanics images and data. fluid project deliverable 1.2. European ProjectFluid image analisys and description(FLUID)-http://www fluid irisa fr 47

  • Cassisa C, Simoëns S, Prinet V, Shao L (2011) Subgrid scale formulation of optical flow for the study of turbulent flow. Exp Fluids 51(6):1739–1754

    Article  Google Scholar 

  • Corpetti T, Mémin É, Pérez P (2002) Dense estimation of fluid flows. Pattern Anal Mach Intell IEEE Trans 24(3):365–380

    Article  Google Scholar 

  • Corpetti T, Heitz D, Arroyo G, Memin E, Santa-Cruz A (2006) Fluid experimental flow estimation based on an optical-flow scheme. Exp Fluids 40(1):80–97

    Article  Google Scholar 

  • Deardorff JW (1970) A numerical study of three-dimensional turbulent channel flow at large reynolds numbers. J Fluid Mech 41(2):453–480

    Article  MATH  Google Scholar 

  • Dérian P, Héas P, Herzet C, Mémin É (2012) Wavelet-based fluid motion estimation. In: scale space and variational methods in computer vision. Springer, Berlin, pp 737–748

    Book  Google Scholar 

  • Deriche R (1993) Recursively implementating the Gaussian and its derivatives, Research report 1893, INRIA, France

  • Fleet D, Weiss Y (2006) Optical flow estimation. In: handbook of mathematical models in computer vision. Springer, Berlin, pp 237–257

    Book  Google Scholar 

  • Guichard F, Rudin L (1996) Accurate estimation of discontinuous optical flow by minimizing divergence related functionals. In: image processing, 1996. Proceedings., international conference on, IEEE, vol 1, pp 497–500

  • Héas P, Herzet C, Memin E, Heitz D, Mininni PD (2013) Bayesian estimation of turbulent motion. Pattern Anal Mach Intell 35(6):1343–1356

    Article  Google Scholar 

  • Heitz D, Héas P, Mémin E, Carlier J (2008) Dynamic consistent correlation-variational approach for robust optical flow estimation. Exp Fluids 45(4):595–608

    Article  Google Scholar 

  • Heitz D, Mémin E, Schnörr C (2010) Variational fluid flow measurements from image sequences: synopsis and perspectives. Exp Fluids 48(3):369–393

    Article  Google Scholar 

  • Horn B, Schunck B (1981) Determining optical flow. Artif Intell 17(1):185–203

    Article  Google Scholar 

  • Jullien MC, Castiglione P, Tabeling P (2000) Experimental observation of Batchelor dispersion of passive tracers. Phys Rev Lett 85(17):3636

    Article  Google Scholar 

  • Kadri-Harouna S, Dérian P, Héas P, Memin E (2013) Divergence-free wavelets and high order regularization. Int J Comput Vis 103(1):80–99

    Article  MATH  MathSciNet  Google Scholar 

  • Kolmogorov AN (1941) The local structure of turbulence in incompressible viscous fluid for very large reynolds numbers. In: Dokl. Akad. Nauk SSSR, vol 30, pp 299–303

  • Liu T, Shen L (2008) Fluid flow and optical flow. J Fluid Mech 614(253):1

    MathSciNet  Google Scholar 

  • Mallat SG (1989) A theory for multiresolution signal decomposition: the wavelet representation. IEEE Trans Pattern Anal Mach Intell 11:674–693

    Article  MATH  Google Scholar 

  • Papadakis N, Mémin É (2008) Variational assimilation of fluid motion from image sequence. SIAM J Imaging Sci 1(4):343–363

    Article  MATH  Google Scholar 

  • Paret J, Tabeling P (1998) Intermittency in the two-dimensional inverse cascade of energy: experimental observations. Phys Fluids 10:3126

    Article  Google Scholar 

  • Pope SB (2000) Turbulent flows. Cambridge university press, Cambridge

    Book  MATH  Google Scholar 

  • Ruhnau P, Kohlberger T, Schnörr C, Nobach H (2005) Variational optical flow estimation for particle image velocimetry. Exp Fluids 38(1):21–32

    Article  Google Scholar 

  • Sagaut P (2000) Large eddy simulation for incompressible flows, vol 3. Springer, Berlin

    Google Scholar 

  • Shao L, Sarkar S, Pantano C (1999) On the relationship between the mean flow and subgrid stresses in large eddy simulation of turbulent shear flows. Phys Fluids (1994-present) 11(5):1229–1248

    Article  MATH  Google Scholar 

  • Smagorinsky J (1963) General circulation experiments with the primitive equations: I. The basic experiment*. Mon Weather Rev 91(3):99–164

    Article  Google Scholar 

  • Su LK, Dahm WJA (1996) Scalar imaging velocimetry measurements of the velocity gradient tensor field in turbulent flows. II. Experimental results. Phys Fluids 8(7):1883–1906

    Article  Google Scholar 

  • Yuan J, Schnörr C, Mémin E (2007) Discrete orthogonal decomposition and variational fluid flow estimation. J Math Imaging Vis 28(1):67–80

    Article  Google Scholar 

  • Zille P, Corpetti T, Shao L, Xu C (2014) Observation models based on scale interactions for optical flow estimation. IEEE Trans Image Process 23(8):3281–3293

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgments

This work is supported by the National Natural Science Foundation of China (51420105008) and Xu Chen is sponsored by the China Scholarship Council.

Author information

Authors and Affiliations

  1. Laboratoire de Mécanique des Fluides et d’Acoustique, Lyon, France

    Xu Chen, Pascal Zillé & Liang Shao

  2. Laboratoire COSTEL UMR 6554 LETG, Rennes, France

    Thomas Corpetti

Authors
  1. Xu Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Pascal Zillé
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Liang Shao
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Thomas Corpetti
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xu Chen.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chen, X., Zillé, P., Shao, L. et al. Optical flow for incompressible turbulence motion estimation. Exp Fluids 56, 8 (2015). https://doi.org/10.1007/s00348-014-1874-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00348-014-1874-6

Keywords

Search

Navigation