The motion estimation problem for image sequences
depicting fluid flows has many important applications in
oceanography, meteorology, climatology, or experimental
The problem is to recover a dense motion field (one vector
per pixel) from two consecutive images.
The method we propose allows to represent and estimate
optical flow with a reduced number of
parameters. The method is based on a discrete smooth
representation of the vorticity and divergence of the 2D
The vorticity is written as a sum of
vortex particles, and the divergence as a sum of
source particles (regularized Dirac measures).
The motion field (obtained by Biot-Savart integration) is finally described by a set
of basis functions and their associated parameters.
The motion estimation problem becomes then a minimization
problem with respect to the basis functions
parameters. The minimization functional relies on an
integrated version of mass conservation principle of fluid
|Vortex launch at tipe of airplane wing
(image sequence provided by ONERA)
|Estimated motion field
|Particles transported by 2D turbulent
(simulation provided by CEMAGREF)
|True synthetic motion field
||Estimated motion field
A. Cuzol, P. Hellier, E. Mémin. A low dimensional
fluid motion estimator. submitted.
A. Cuzol, E. Mémin.
Vortex and source particles for fluid motion estimation. In
5th Int. Conf. on Scale-Space and PDE methods in Computer Vision, Scale-Space'05, Hofgeismar, Germany, Apr. 2005.