CSDL Home IEEE Transactions on Pattern Analysis & Machine Intelligence 2009 vol.31 Issue No.07 - July

Subscribe

Issue No.07 - July (2009 vol.31)

pp: 1278-1293

Anne Cuzol , European University of Brittany-UBS, CNRS, UMR, France

ABSTRACT

In this paper, we present a method for the temporal tracking of fluid flow velocity fields. The technique we propose is formalized within a sequential Bayesian filtering framework. The filtering model combines an Itô diffusion process coming from a stochastic formulation of the vorticity-velocity form of the Navier-Stokes equation and discrete measurements extracted from the image sequence. In order to handle a state space of reasonable dimension, the motion field is represented as a combination of adapted basis functions, derived from a discretization of the vorticity map of the fluid flow velocity field. The resulting nonlinear filtering problem is solved with the particle filter algorithm in continuous time. An adaptive dimensional reduction method is applied to the filtering technique, relying on dynamical systems theory. The efficiency of the tracking method is demonstrated on synthetic and real-world sequences.

INDEX TERMS

Motion estimation, tracking, nonlinear stochastic filtering, fluid flows.

CITATION

Anne Cuzol, "A Stochastic Filtering Technique for Fluid Flow Velocity Fields Tracking",

*IEEE Transactions on Pattern Analysis & Machine Intelligence*, vol.31, no. 7, pp. 1278-1293, July 2009, doi:10.1109/TPAMI.2008.152REFERENCES

- [2] E. Arnaud, E. Mémin, R. Sosa, and G. Artana, “A Fluid Motion Estimator for Schlieren Imaging Velocimetry,”
Proc. European Conf. Comp. Vision, May 2006.- [5] M. Bossy, “Some Stochastic Particle Methods for Nonlinear Parabolic PDEs,”
Proc. European Series in Applied and Industrial Math., vol. 15, pp. 18-57, 2005.- [6] C. Canuto, M. Hussaini, A. Quarteroni, and T. Zang,
Spectral Methods in Fluid Dynamics. Springer, 1988.- [7] A.J. Chorin, “Numerical Study of Slightly Viscous Flow,”
J. Fluid Mechanics, vol. 57, pp. 785-796, 1973.- [8] A.J. Chorin and P. Krause, “Dimensional Reduction for a Bayesian Filter,”
Proc. Nat'l Academy of Sciences USA, vol. 101, no. 42, 2004.- [9] A.J. Chorin and J.E. Marsden,
A Mathematical Introduction to Fluid Mechanics. Springer-Verlag, 1993.- [11] T. Corpetti, E. Mémin, and P. Pérez, “Extraction of Singular Points from Dense Motion Fields: An Analytic Approach,”
J. Math. Imaging and Vision, vol. 19, no. 3, pp. 175-198, 2003.- [12] G.-H. Cottet and P. Koumoutsakos,
Vortex Methods: Theory and Practice. Cambridge Univ. Press, 2000.- [14] A. Cuzol and E. Mémin, “A Stochastic Filter for Fluid Motion Tracking,”
Proc. Int'l Conf. Computer Vision, Oct. 2005.- [15] A. Cuzol and E. Mémin, “Vortex and Source Particles for Fluid Motion Estimation,”
Proc. Fifth Int'l Conf. Scale-Space and PDE Methods in Computer Vision, Apr. 2005.- [16] P. Del Moral, J. Jacod, and Ph. Protter, “The Monte-Carlo Method for Filtering with Discrete-Time Observations,”
Probability Theory and Related Fields, vol. 120, pp. 346-368, 2001.- [17] A. Doucet, S. Godsill, and C. Andrieu, “On Sequential Monte Carlo Sampling Methods for Bayesian Filtering,”
Statistics and Computing, vol. 10, no. 3, pp. 197-208, 2000.- [19] G. Farnebäck, “Very High Accuracy Velocity Estimation Using Orientation Tensors, Parametric Motion, and Segmentation of the Motion Field,”
Proc. Int'l Conf. Computer Vision, pp. 5-26, 1999.- [20] P. Héas and E. Mémin, “3D Motion Estimation of Atmospheric Layers from Image Sequences,”
IEEE Trans. Geoscience and Remote Sensing, 2007.- [21] P. Héas, E. Mémin, and N. Papadakis, “Time-Consistent Estimators of 2D/3D Motion of Atmospheric Layers from Pressure Images,” Technical Report 6292, INRIA, 2007.
- [23] M. Isard and A. Blake, “Condensation—Conditional Density Propagation for Visual Tracking,”
Int'l J. Computer Vision, vol. 29, no. 1, pp. 5-28, 1998.- [24] P.E. Kloeden and E. Platen,
Numerical Solution of Stochastic Differential Equations. Springer-Verlag, 1991.- [29] N. Papadakis and E. Mémin, “A Variational Method for Joint Tracking of Curve and Motion,” Technical Report 6283, INRIA, Sept. 2007.
- [31] P. Pérez, J. Vermaak, and A. Blake, “Data Fusion for Visual Tracking,”
Proc. IEEE, vol. 92, no. 3, pp. 495-513, 2004.- [33] P. Ruhnau and C. Schnoerr, “Optical Stokes Flow Estimation: An Imaging-Based Control Approach,”
Experiments in Fluids, vol. 42, pp. 61-78, 2007.- [34] P. Ruhnau, A. Stahl, and C. Schnoerr, “On-Line Variational Estimation of Dynamical Fluid Flows with Physics-Based Spatio-Temporal Regularization,”
Proc. 28th Ann. Symp. German Assoc. for Pattern Recognition, Sept. 2006.- [36] J. Weickert and C. Schnoerr, “Variational Optic-Flow Computation with a Spatio-Temporal Smoothness Constraint,”
J. Math. Imaging and Vision, vol. 14, no. 3, pp. 245-255, 2001.- [37] J. Yuan, P. Ruhnau, E. Mémin, and C. Schnoerr, “Discrete Orthogonal Decomposition and Variational Fluid Flow Estimation,”
Proc. Fifth Int'l Conf. Scale-Space and PDE Methods in Computer Vision, Apr. 2005. |