Temporal tracking
(back)
Description
We propose a method to track fluid flows velocity
fields.
The method is formalized within a
sequential filtering framework, in order to be robust to
noise acquisition or illumination conditions. We obtain
then a temporal coherence for the velocity fields along
the sequence. This temporal coherence would not be
garanted by a succession of motion estimations between
pairs of images.
The evolution of the fluid structure is described by a
continous dynamical law. This dynamic is represented by
a stochastic differential equation, corresponding to a
stochastic formulation of the 2D NavierStokes equation.
The tracking is solved by a particle filter (sequential
MonteCarlo method), where the continous non linear
evolution law is associated to discrete measurements
(extracted from the image sequence).
In order to handle a state space of reduced dimension
(so that the MonteCarlo method is applicable), we use a
low order representation of fluid flows velocity
fields. This representation allows to describe a dense
motion field with a reasonable number of basis
functions.
Results
Vortices
at the tip of an airplane wing



Initial field
(estimated from the first pair of images) 
Tracked
velocity fields 
Corresponding vorticity 
Meteorological sequence: cyclone over
the Indian Ocean


Tracking result 
Evolution of
the vorticity map 
Reference
A. Cuzol, E. Mémin.
A stochastic filter for fluid motion tracking. In
10th IEEE International Conference on Computer Vision, ICCV'05, Beijing, China,
Oct. 2005. pdf