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 Navier-Stokes equation.

The tracking is solved by a particle filter (sequential Monte-Carlo 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 Monte-Carlo 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