D. Béréziat and I. Herlin, Solving ill-posed Image Processing problems using Data Assimilation, Numerical Algorithms, vol.14, issue.7, pp.219-252, 2011.
DOI : 10.1007/s11075-010-9383-z

E. Deriaz and V. Perrier, Divergence-free and curl-free wavelets in two dimensions and three dimensions: application to turbulent flows, Journal of Turbulence, vol.319, issue.4, pp.1-37, 2006.
DOI : 10.1080/14685240500260547

L. Dimet, F. X. Talagrand, and O. , Variational algorithms for analysis and assimilation of meteorological observations: theoretical aspects, Tellus A, vol.109, issue.2, pp.97-110, 1986.
DOI : 10.1111/j.1600-0870.1986.tb00459.x

D. Heitz, E. Mémin, and C. Schnörr, Variational fluid flow measurements from image sequences: synopsis and perspectives, Experiments in Fluids, vol.28, issue.4, pp.369-393, 2010.
DOI : 10.1007/s00348-009-0778-3
URL : https://hal.archives-ouvertes.fr/hal-00456162

B. Horn and B. Schunk, Determining optical flow, Artificial Intelligence, vol.17, issue.1-3, pp.185-203, 1981.
DOI : 10.1016/0004-3702(81)90024-2
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.185.1651

A. Amini, A scalar function formulation for optical flow, pp.125-131, 1994.
DOI : 10.1007/3-540-57956-7_13

R. Wildes and M. Amabile, Physically based fluid flow recovery from image sequences, Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pp.969-975, 1997.
DOI : 10.1109/CVPR.1997.609445
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.568.767

D. Bimbo, A. Nesi, P. Sanz, and J. , Optical flow computation using extended constraints, IEEE Transactions on Image Processing, vol.5, issue.5, pp.720-739, 1996.
DOI : 10.1109/83.495956

B. Schunck, The motion constraint equation for optical flow, In: ICPR, issue.2, 1984.

X. Vigan, C. Provost, R. Bleck, and P. Courtier, Sea surface velocities from sea surface temperature image sequences: 1. Method and validation using primitive equation model output, Journal of Geophysical Research: Oceans, vol.28, issue.C8, pp.19499-19514, 2000.
DOI : 10.1029/2000JC900027

D. Suter, Motion estimation and vector splines, Proceedings of IEEE Conference on Computer Vision and Pattern Recognition CVPR-94, pp.939-942, 1994.
DOI : 10.1109/CVPR.1994.323929
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.57.4768

T. Isambert, I. Herlin, and J. P. Berroir, Fast and stable vector spline method for fluid flow estimation, In: ICIP, vol.9, issue.10, pp.505-508, 2007.

T. Corpetti, E. Mémin, and P. Pérez, Dense estimation of fluid flows, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.24, issue.3, pp.365-380, 2002.
DOI : 10.1109/34.990137
URL : https://hal.archives-ouvertes.fr/hal-00329724

S. Song and R. Leahy, Computation of 3-D velocity fields from 3-D cine CT images of a human heart, IEEE Transactions on Medical Imaging, vol.10, issue.3, pp.295-306, 1991.
DOI : 10.1109/42.97579

S. N. Gupta and J. L. Prince, On div-curl regularization for motion estimation in 3-D volumetric imaging, Proceedings of 3rd IEEE International Conference on Image Processing, pp.929-932, 1996.
DOI : 10.1109/ICIP.1996.559652

P. Ruhnau and C. Schnörr, Optical Stokes flow estimation: an imaging-based control approach, Experiments in Fluids, vol.15, issue.3, pp.61-78, 2007.
DOI : 10.1007/s00348-006-0220-z

P. Ruhnau, A. Stahl, and C. Schnörr, Variational estimation of experimental fluid flows with physics-based spatio-temporal regularization, Measurement Science and Technology, vol.18, issue.3, pp.755-763, 2007.
DOI : 10.1088/0957-0233/18/3/027

E. Huot, I. Herlin, N. Mercier, and E. Plotnikov, Estimating Apparent Motion on Satellite Acquisitions with a Physical Dynamic Model, 2010 20th International Conference on Pattern Recognition, pp.41-44, 2010.
DOI : 10.1109/ICPR.2010.19
URL : https://hal.archives-ouvertes.fr/inria-00538317

N. Papadakis and E. Mémin, Variational Assimilation of Fluid Motion from Image Sequence, SIAM Journal on Imaging Sciences, vol.1, issue.4, pp.343-363, 2008.
DOI : 10.1137/080713896
URL : https://hal.archives-ouvertes.fr/hal-00596149

N. Papadakis, T. Corpetti, and E. Mémin, Dynamically consistent optical flow estimation, 2007 IEEE 11th International Conference on Computer Vision, pp.1-7, 2007.
DOI : 10.1109/ICCV.2007.4408889
URL : https://hal.archives-ouvertes.fr/hal-00596200

R. Mcowen, Chapter 4 In: Partial Differential Equations: Methods and Applications, p.5, 2003.

C. Zhu, R. Byrd, P. Lu, and J. Nocedal, L-BFGS-B: a limited memory FORTRAN code for solving bound constrained optimization problems, p.7, 1994.

R. Leveque, Numerical Methods for Conservative Laws, 1992.

W. Hundsdorfer and E. Spee, An Efficient Horizontal Advection Scheme for the Modeling of Global Transport of Constituents, Monthly Weather Review, vol.123, issue.12, pp.554-557, 1995.
DOI : 10.1175/1520-0493(1995)123<3554:AEHASF>2.0.CO;2

L. Hascoët and V. Pascual, Tapenade 2.1 user's guide, 2004.

D. Sun, S. Roth, and M. Black, Secrets of optical flow estimation and their principles, 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pp.2432-2439, 2010.
DOI : 10.1109/CVPR.2010.5539939