The Community for Technology Leaders
RSS Icon
Issue No.06 - June (2013 vol.35)
pp: 1343-1356
Patrick Héas , INRIA, Rennes
Cédric Herzet , INRIA, Rennes
Etienne Mémin , INRIA, IRSTEA, Rennes
Dominique Heitz , IRSTEA, Rennes
Pablo D. Mininni , University of Buenos-Aires, Buenos Aires and National Center for Atmospheric Research, Buenos Aires
Based on physical laws describing the multiscale structure of turbulent flows, this paper proposes a regularizer for fluid motion estimation from an image sequence. Regularization is achieved by imposing some scale invariance property between histograms of motion increments computed at different scales. By reformulating this problem from a Bayesian perspective, an algorithm is proposed to jointly estimate motion, regularization hyperparameters, and to select the most likely physical prior among a set of models. Hyperparameter and model inference are conducted by posterior maximization, obtained by marginalizing out non--Gaussian motion variables. The Bayesian estimator is assessed on several image sequences depicting synthetic and real turbulent fluid flows. Results obtained with the proposed approach exceed the state-of-the-art results in fluid flow estimation.
Bayesian methods, Optimization, Vectors, Estimation, Motion estimation, Computational modeling, Optical imaging, Bayesian model selection, Optic flow, turbulence, robust estimation, constrained optimization
Patrick Héas, Cédric Herzet, Etienne Mémin, Dominique Heitz, Pablo D. Mininni, "Bayesian Estimation of Turbulent Motion", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol.35, no. 6, pp. 1343-1356, June 2013, doi:10.1109/TPAMI.2012.232
[1] S. Baker, D. Scharstein, J. Lewis, S. Roth, M. Black, and R. Szeliski, "A Database and Evaluation Methodology for Optical Flow," Proc. 11th IEEE Int'l Conf. Computer Vision, 2007.
[2] F. Becker, B. Wieneke, S. Petra, A. Schroeder, and C. Schnoerr, "Variational Adaptive Correlation Method for Flow Estimation," IEEE Trans. Image Processing, vol. 21, no. 6, pp. 3053-3065, June 2012.
[3] J. Bergen, P. Burt, R. Hingorani, and S. Peleg, "A 3-Frame Algorithm for Estimating Two-Component Image Motion," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 14, no. 9, pp. 886-895, Sept. 1992.
[4] M.J. Beal and Z. Ghahramani, "The Variational Bayesian EM Algorithm for Incomplete Data: With Application to Scoring Graphical Model Structures," Bayesian Statistics, vol. 7, pp. 453-464, 2003.
[5] Convex Analysis and Optimization, D. Bertsekas, A. Nedic, and A. Ozdaglar eds. Athena Scientific 2003.
[6] M. Black and P. Anandan, "The Robust Estimation of Multiple Motions: Parametric and Piecewise-Smooth Flow Fields," Computer Vision and Image Understanding, vol. 63, no. 1, pp. 75-104, 1996.
[7] J. Carlier and B. Wieneke, "Report 1 on Production and Diffusion of Fluid Mechanics Images and Data," Fluid Project Deliverable 1.2, http:/, 2005.
[8] T. Corpetti, E. Mémin, and P. Pérez, "Dense Estimation of Fluid Flows," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 24, no. 3, pp. 365-380, Mar. 2002.
[9] P. Dérian, P. Héas, C. Herzet, and E. Mémin, "Wavelet-Based Fluid Motion Estimation," Proc. Third Int'l Conf. Scale Space and Variational Methods in Computer Vision, June 2011.
[10] U. Frisch, Turbulence: The Legacy of A.N. Kolmogorov. Cambridge Univ. Press, 1995.
[11] D. Geman and G. Reynolds, "Constrained Restoration and the Recovery of Discontinuities," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 14, no. 3, pp. 367-383, Mar. 1992.
[12] P. Héas, C. Herzet, and E. Mémin, "Bayesian Inference of Models and Hyper-Parameters for Robust Optic-Flow Estimation," IEEE Trans. Image Processing, vol. 21, no. 4, pp. 1437-1451, Apr. 2012.
[13] P. Héas, E. Mémin, D. Heitz, and P. Mininni, "Bayesian Selection of Scaling Laws for Motion Modeling in Images," Proc. 12th IEEE Int'l Conf. Computer Vision, Oct. 2009.
[14] P. Héas, E. Mémin, D. Heitz, and P. Mininni, "Power Laws and Inverse Motion Modeling: Application to Turbulence Measurements from Satellite Images," TellusA, vol. 64, 2012, doi: 10.3402/tellusA.v64i0.10962.
[15] P. Héas, E. Mémin, N. Papadakis, and A. Szantai, "Layered Estimation of Atmospheric Mesoscale Dynamics from Satellite Imagery," IEEE Trans. Geoscience and Remote Sensing, vol. 45, no. 12, pp. 4087-4104, Dec. 2007.
[16] D. Heitz, E. Mémin, and C. Schnörr, "Variational Fluid Flow Measurements from Image Sequences: Synopsis and Perspectives," Experiments in Fluids, vol. 48, no. 3, pp. 369-393, 2010.
[17] B. Horn and B. Schunck, "Determining Optical Flow," Artificial Intelligence, vol. 17, pp. 185-203, 1981.
[18] J. Idier, "Convex Half-Quadratic Criteria and Interacting Auxiliary Variables for Image Restoration," IEEE Trans. Image Processing, vol. 10, no. 7, pp. 1001-1009, July 2001.
[19] E.T. Jaynes, "Bayesian Methods: General Background," Maximum-Entropy and Bayesian Methods in Applied Statistics, Cambridge Univ. Press, 1986.
[20] S.K. Harouna, P. Dérian, P. Héas, and E. Memin, "Divergence-Free Wavelets and High Order Regularization," hal-00646104, Jan. 2012.
[21] A. Kolmogorov, "The Local Structure of Turbulence in Incompressible Viscous Fluid for Very Large Reynolds Number," Dolk. Akad. Nauk SSSR, vol. 30, pp. 301-305, 1941.
[22] R. Kraichnan, "Inertial Ranges in Two-Dimensional Turbulence," Physics Fluids, vol. 10, pp. 1417-1423, 1967.
[23] K. Krajsek and R. Mester, "Bayesian Model Selection for Optical Flow Estimation," Proc. DAGM Symp., pp. 142-151, 2007.
[24] P. Lavoie, L. Djenidi, and R.A. Antonia, "Effects of Initial Conditions in Decaying Turbulence Generated by Passive Grids," J. Fluid Mechanics, vol. 585, no. 1, pp. 395-420, 2007.
[25] E. Lindborg and J. Cho, "Horizontal Velocity Structure Functions in the Upper Troposphere and Lower Stratosphere: 2. Theoretical Considerations," J. Geophysical Research, vol. 106, pp. 233-241, 2001.
[26] T. Liu and L. Shen, "Fluid Flow and Optical Flow," J. Fluid Mechanics, vol. 614, pp. 253-291, Oct. 2008.
[27] B. Lucas and T. Kanade, "An Iterative Image Registration Technique with an Application to Stereovision," Proc. Int'l Joint Conf. Artificial Intelligence, pp. 674-679, 1981.
[28] D.J.C. MacKay, "Bayesian Interpolation," Neural Computation, vol. 4, no. 3, pp. 415-447, 1992.
[29] P.D. Mininni, D.O. Gomez, and S.M. Mahajan, "Direct Simulations of Helical Hall-MHD Turbulence and Dynamo Action," The Astrophysical J., vol. 619, pp. 1019-1027, 2005.
[30] R. Molina, A.K. Katsaggelos, and J. Mateos, "Bayesian and Regularization Methods for Hyperparameter Estimation in Image Restoration," IEEE Trans. Image Processing, vol. 8, no. 2, pp. 231-246, Feb. 1999.
[31] A. Monin and A. Yaglom, Statistical Fluid Mechanics: Mechanics of Turbulence. Dover, 1971.
[32] N. Papadakis and E. Memin, "Variational Assimilation of Fluid Motion from Image Sequences," SIAM J. Imaging Science, vol. 1, no. 4, pp. 343-363, 2008.
[33] C.P. Robert, The Bayesian Choice: From Decision-Theoretic Foundations to Computational Implementation, second ed. Springer Verlag, June 2007.
[34] P. Ruhnau and C. Schnörr, "Optical Stokes Flow Estimation: An Imaging-Based Control Approach," Experiments in Fluids, vol. 42, pp. 61-78, 2007.
[35] P. Ruhnau, A. Stahl, and C. Schnörr, "Variational Estimation of Experimental Fluid Flows with Physics-Based Spatioc-Temporal Regularization," Measurement Science and Technology, vol. 18, pp. 755-763, 2007.
[36] J. Skilling, "The Eigenvalues of Mega-Dimensional Matrices," Maximum Entropy and Bayesian Methods, pp. 455-466, Springer, 1989.
[37] J. Yuan, C. Schnörr, and E. Mémin, "Discrete Orthogonal Decomposition and Variational Fluid Flow Estimation," J. Math. Imaging & Vision, vol. 28, pp. 67-80, 2007.
7 ms
(Ver 2.0)

Marketing Automation Platform Marketing Automation Tool