A Low Dimensional Fluid Motion Estimator

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.

DOI: 10.1007/s11263-007-0037-0

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@article{Cuzol2007ALD, title={A Low Dimensional Fluid Motion Estimator}, author={Anne Cuzol and Pierre Hellier and {\'E}tienne M{\'e}min}, journal={International Journal of Computer Vision}, year={2007}, volume={75}, pages={329-349} }