## A low dimensional fluid motion estimator

Venue: | Int. J. Comp. Vision |

Citations: | 16 - 8 self |

### BibTeX

@ARTICLE{Cuzol_alow,

author = {Anne Cuzol and Pierre Hellier and Etienne Mémin},

title = {A low dimensional fluid motion estimator},

journal = {Int. J. Comp. Vision},

year = {},

volume = {75},

pages = {2007}

}

### OpenURL

### 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 vorticity free component. The objective is to provide a low-dimensional parametric representation of optical flows by depicting them as deformations generated by a reduced number of vortex and source particles. Both components are approximated using a discretization of the vorticity and divergence maps through regularized Dirac measures. The resulting so called irrotational and solenoidal fields consist of 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 by minimization of a functional relying on an integrated version of mass conservation principle of fluid mechanics. Results are provided on synthet-ic examples and real world sequences. 1