Fluid motion estimation (back)

Description

The motion estimation problem for image sequences depicting fluid flows has many important applications in oceanography, meteorology, climatology, or experimental fluid dynamics.

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 this 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 vector field.

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 mechanics.

Results

Vortex launch at tipe of airplane wing (image sequence provided by ONERA)	Estimated motion field	Estimated vorticity

Particles transported by 2D turbulent flow (simulation provided by CEMAGREF)	True synthetic motion field	Estimated motion field

References

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. pdf