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.
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.