Optical flow for incompressible turbulence motion estimation

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.

[1]  J. Ferziger,et al.  Improved turbulence models based on large eddy simulation of homogeneous, incompressible, turbulent flows , 1983 .

[2]  Frédéric Guichard,et al.  Accurate estimation of discontinuous optical flow by minimizing divergence related functionals , 1996, Proceedings of 3rd IEEE International Conference on Image Processing.

[3]  Jullien,et al.  Experimental observation of batchelor dispersion of passive tracers , 2000, Physical review letters.

[4]  Nikos Paragios,et al.  Handbook of Mathematical Models in Computer Vision , 2005 .

[5]  W. Dahm,et al.  Scalar imaging velocimetry measurements of the velocity gradient tensor field in turbulent flows. II , 1996 .

[6]  A. Kolmogorov.  The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers , 1991, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[7]  G. Batchelor.  Small-scale variation of convected quantities like temperature in turbulent fluid Part 1. General discussion and the case of small conductivity , 1959, Journal of Fluid Mechanics.

[8]  Patrick Pérez,et al.  Dense Estimation of Fluid Flows , 2002, IEEE Trans. Pattern Anal. Mach. Intell..

[9]  L. Shao,et al.  Subgrid scale formulation of optical flow for the study of turbulent flow , 2011 .

[10]  Etienne Mémin,et al.  Dynamic consistent correlation-variational approach for robust optical flow estimation , 2008 .

[11]  Xu Chen,et al.  Observation Model Based on Scale Interactions for Optical Flow Estimation , 2014, IEEE Transactions on Image Processing.

[12]  Thomas Brox,et al.  High Accuracy Optical Flow Estimation Based on a Theory for Warping , 2004, ECCV.

[13]  R. Adrian.  Particle-Imaging Techniques for Experimental Fluid Mechanics , 1991 .

[14]  R. Deriche.  Recursively implementating the Gaussian and its derivatives , 1993 .

[15]  S. Pope.  Turbulent Flows: FUNDAMENTALS , 2000 .

[16]  Shmuel Peleg,et al.  A Three-Frame Algorithm for Estimating Two-Component Image Motion , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[17]  Jing Yuan,et al.  Discrete Orthogonal Decomposition and Variational Fluid Flow Estimation , 2005, Journal of Mathematical Imaging and Vision.

[18]  A. Townsend,et al.  Small-scale variation of convected quantities like temperature in turbulent fluid Part 2. The case of large conductivity , 1959, Journal of Fluid Mechanics.

[19]  David J. Fleet,et al.  Optical Flow Estimation , 2006, Handbook of Mathematical Models in Computer Vision.

[20]  Étienne Mémin,et al.  Bayesian Estimation of Turbulent Motion , 2013, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[21]  Tianshu Liu,et al.  Fluid flow and optical flow , 2008, Journal of Fluid Mechanics.

[22]  Peter J. Burt,et al.  Smart sensing within a pyramid vision machine , 1988, Proc. IEEE.

[23]  J. Ferziger,et al.  Improved subgrid-scale models for large-eddy simulation , 1980 .

[24]  Étienne Mémin,et al.  Divergence-Free Wavelets and High Order Regularization , 2013, International Journal of Computer Vision.

[25]  Caskey,et al.  GENERAL CIRCULATION EXPERIMENTS WITH THE PRIMITIVE EQUATIONS I . THE BASIC EXPERIMENT , 1962 .

[26]  Richard Szeliski,et al.  A Database and Evaluation Methodology for Optical Flow , 2007, 2007 IEEE 11th International Conference on Computer Vision.

[27]  Christoph Schnörr,et al.  Variational fluid flow measurements from image sequences: synopsis and perspectives , 2010 .

[28]  A. Kolmogorov,et al.  The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers , 1991, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[29]  J. Deardorff.  A numerical study of three-dimensional turbulent channel flow at large Reynolds numbers , 1970, Journal of Fluid Mechanics.

[30]  I. Pairaud,et al.  Numerical simulation of a two-dimensional internal wave attractor , 2008, Journal of Fluid Mechanics.

[31]  P. Tabeling,et al.  Intermittency in the two-dimensional inverse cascade of energy: Experimental observations , 1998 .

[32]  T. Corpetti,et al.  Fluid experimental flow estimation based on an optical-flow scheme , 2006 .

[33]  Stéphane Mallat,et al.  A Theory for Multiresolution Signal Decomposition: The Wavelet Representation , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[34]  Knut-Andreas Lie,et al.  Scale Space and Variational Methods in Computer Vision, Second International Conference, SSVM 2009, Voss, Norway, June 1-5, 2009. Proceedings , 2009, SSVM.

[35]  L. Shao,et al.  On the relationship between the mean flow and subgrid stresses in large eddy simulation of turbulent shear flows , 1999 .

[36]  J. Smagorinsky,et al.  GENERAL CIRCULATION EXPERIMENTS WITH THE PRIMITIVE EQUATIONS , 1963 .

[37]  Timo Kohlberger,et al.  Variational optical flow estimation for particle image velocimetry , 2005 .

[38]  W. Dahm,et al.  Scalar imaging velocimetry measurements of the velocity gradient tensor field in turbulent flows. I. Assessment of errors , 1996 .

[39]  P. Saugat.  Large eddy simulation for incompressible flows , 2001 .

[40]  Nicolas Papadakis,et al.  Variational Assimilation of Fluid Motion from Image Sequence , 2008, SIAM J. Imaging Sci..

[41]  Berthold K. P. Horn,et al.  Determining Optical Flow , 1981, Other Conferences.

[42]  George Papanicolaou,et al.  Macroscopic Modelling of Turbulent Flows , 1985 .

[43]  Christoph Schnörr,et al.  Variational Adaptive Correlation Method for Flow Estimation , 2012, IEEE Transactions on Image Processing.

[44]  Jean-Pierre Bertoglio,et al.  A stochastic subgrid model for sheared turbulence , 1985 .

[45]  David J. Fleet,et al.  Performance of optical flow techniques , 1994, International Journal of Computer Vision.

[46]  Étienne Mémin,et al.  Wavelet-Based Fluid Motion Estimation , 2011, SSVM.