Vortex and source particles for fluid motion estimation

acuzol,memin¡ Abstract. In this paper we propose a new motion estimator for image sequences depicting fluid flows. The proposed estimator is based on the Helmholtz decomposition of vector fields. This decomposition consists in representing the velocity field as a sum of a divergence free component and a curl free component. In order to provide a low dimensional solution, both components are approximated using a discretization of the vorticity and divergence maps through regularized Dirac measure. The resulting so called irrotational and solenoidal fields consist then in linear combinations of basis functions obtained through a convolution product of the Green kernel gradient and the vorticity map or the divergence map respectively. The coefficient values and the basis function parameters are obtained as the minimizer of a functional relying on an integrated version of mass conservation principle of fluid mechanics. Results are provided on real world sequences.