International Journal of Computer Vision

, Volume 75, Issue 3, pp 329–349 | Cite as

A Low Dimensional Fluid Motion Estimator



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.


fluid motion optical flow parametric model radial basis functions 


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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.IRISAUniversité de Rennes 1Rennes CedexFrance

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