We presented in this section an algorithm to estimate the motion between two images. This algorithm is based on the constant brightness assumption. A multiscale approach allows us to perform a minimization of the cost function in nested subspaces, the Jacobian matrix of the cost function being rapidly assembled at each scale using a finite element method. The coarse estimation allows one to avoid local minima, while the fine scales give more precise details. Several regularization terms are discussed, and it appears that the 
norm of the gradient gives reliable results.
The results of this algorithm on both simulated data and real fluid flows are presented, and they are encouraging, both from their computational efficiency and from the quality of the estimated motion. Our algorithm has also been tested on full high-resolution movies provided by the Coriolis platform, confirming the efficiency of the proposed method.
As previously explained, the extracted velocity fields can be viewed as pseudo-observations of the fluid velocity, and the next step will be to consider the assimilation of these data. However, because of the time sampling of the images, these fields correpond to Lagrangian velocities, and a Lagrangian data assimilation method is then required. Note that if the time between the acquisition of two images is small, then the identified (or apparent) velocity can be directly assimilated as a standard Eulerian velocity.