Fluid Motion Estimation

Contact: Thomas Corpetti, Etienne Mémin, Patrick Pérez

Fluid motion estimation has many important applications: in meteorology, climatology, oceanography and experimental fluid mechanics. Due to the great deal of spatial and temporal distortions that luminance patterns exhibit in images describing fluid phenomenon, the analysis of motion in such sequences is particularly challenging and can hardly be handled with standard generic models relying on the brightness constancy assumption and a first order regularization.  Even if robust versions have been successfully used for sequences involving deformable objects or fluid phenomenon, such generic methods are completely inefficient in crucial areas revealing high variations of matter density.

In this context, we  investigate  a specialized energy -based motion estimator.  The considered  functional  to be minimized includes an original flow constraint relying on  the continuity equation of fluid mechanics. This new data model specifically designed to be embedded in an incremental multiresolution framework is associated to  an original div-curl type  smoothness constraint regularization. The  optimization  of the global  energy function  is performed within an efficient multigrid scheme.
Experimental results
We present results obtained for two kinds of Meteosat sequences. The first one is an infra-red sequence of 13 images. The second one is a water-vapor sequence of 22 images.  For both sequences we present  the results provided by a robust generic motion estimator and the results obtained with the fluid motion estimator. We show a movie of the successive recovered velocity fields, the associated vorticity and divergence maps, and an animation representing reconstructed trajectories of some points (Lagrangian drifters) obtained with a standard fourth-order Runge-Kutta integration method.

Infra-red sequence

Water-vapor sequence

  A last example is given, tracking the two singular points of an infra-red sequence , using Runge-Kutta integrations at fourth order.

T. Corpetti, D. Heitz, G. Arroyo, E. Mémin, A. Santa Cruz. Estimating fluid optical flow. - Experiments in Fluids, 40(1):80-97, 2006.
T. Corpetti, E. Mémin, P. Pérez. Extraction of Singular Points from Dense Motion Fields: an Analytic Approach. - Journal of Mathematical Imaging and Vision,, 19(3):175-198, 2003.
T. Corpetti, E. Mémin, P. Pérez. Dense Estimation of Fluid Flows. - IEEE Transactions on Pattern Analysis and Machine Intelligence,24(3):365-380, March 2002.


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