A Stochastic Filter for Fluid Motion Tracking

Abstract

In this paper, we present a method for the tracking of fluid flows velocity fields. The technique we propose is formalized within sequential Bayesian filter framework. The filter we propose here combines an Ito diffusion process coming from a stochastic formulation of the vorticity-velocity form of Navier-Stokes equation and discrete measurements extracted from an image sequence. The resulting tracker provides robust and consistent estimations of instantaneous motion fields along the whole image sequence. In order to handle a state space of reasonable dimension for the stochastic filtering problem, we represent the motion field as a combination of adapted basis functions. The used basis functions ensue from a mollification of Biot-Savart integral and a discretization of the vorticity and divergence maps of the fluid vector field. The efficiency of the method is demonstrated on a long real world sequence showing a vortex launch at tip of airplane wing.