A low dimensional fluid motion estimator

Anne Cuzol 1 Pierre Hellier 2, * Etienne Mémin 1
* Corresponding author
1 VISTA - Vision spatio-temporelle et active
IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires, Inria Rennes – Bretagne Atlantique
2 VisAGeS - Vision, Action et Gestion d'informations en Santé
INSERM - Institut National de la Santé et de la Recherche Médicale : U746, Inria Rennes – Bretagne Atlantique , IRISA-D5 - SIGNAUX ET IMAGES NUMÉRIQUES, ROBOTIQUE
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 synthetic examples and real world sequences.
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Submitted on : Friday, May 11, 2007 - 4:19:21 PM
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Anne Cuzol, Pierre Hellier, Etienne Mémin. A low dimensional fluid motion estimator. International Journal of Computer Vision, Springer Verlag, 2007, 75 (3), pp.329-349. ⟨10.1007/s11263-007-0037-0⟩. ⟨inserm-00140892⟩

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