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

M. Elad and A. Feuer, Recursive Optical Flow Estimation???Adaptive Filtering Approach, Journal of Visual Communication and Image Representation, vol.9, issue.2, pp.119-138, 1996.
DOI : 10.1006/jvci.1998.0382

N. Papadakis and E. Mémin, A Variational Technique for Time Consistent Tracking of Curves and Motion, Journal of Mathematical Imaging and Vision, vol.28, issue.1, p.141, 2008.
DOI : 10.1007/s10851-008-0069-2
URL : https://hal.archives-ouvertes.fr/hal-00596154

G. Evensen, The Ensemble Kalman Filter: theoretical formulation and practical implementation, Ocean Dynamics, vol.53, issue.4, pp.343-367, 2003.
DOI : 10.1007/s10236-003-0036-9

B. K. Horn and B. G. Schunk, Determining optical flow, Artificial Intelligence, vol.17, issue.1-3, pp.185-203, 1981.
DOI : 10.1016/0004-3702(81)90024-2

A. N. Tikhonov, Regularization of incorrectly posed problems, Soviet Mathematics -Doklady, vol.4, issue.11, pp.1624-1627, 1963.

H. H. Nagel and W. Enkelmann, An Investigation of Smoothness Constraints for the Estimation of Displacement Vector Fields from Image Sequences, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.8, issue.5, pp.565-593, 1986.
DOI : 10.1109/TPAMI.1986.4767833

M. Nielsen, L. Florack, and R. Deriche, Regularisation and scale space, p.12, 1994.

M. Werlberger, T. Pock, and H. Bischof, Motion estimation with non-local total variation regularization, 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, p.12, 2010.
DOI : 10.1109/CVPR.2010.5539945

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

D. Fortun, P. Bouthemy, and C. Kervrann, Optical flow modeling and computation: A survey, Computer Vision and Image Understanding, vol.134, issue.12, pp.1-21, 2015.
DOI : 10.1016/j.cviu.2015.02.008
URL : https://hal.archives-ouvertes.fr/hal-01104081

S. Baker, D. Scharstein, J. P. Lewis, S. Roth, M. J. Black et al., A Database and Evaluation Methodology for Optical Flow, International Journal of Computer Vision, vol.27, issue.3, pp.1-31, 2011.
DOI : 10.1007/s11263-010-0390-2

D. J. Butler, J. Wulff, G. B. Stanley, and M. J. Black, A Naturalistic Open Source Movie for Optical Flow Evaluation, European Conference on Computer Vision Part IV, pp.611-625, 2012.
DOI : 10.1007/978-3-642-33783-3_44

S. Volz, A. Bruhn, L. Valgaerts, and H. Zimmer, Modeling temporal coherence for optical flow, 2011 International Conference on Computer Vision, pp.1116-1123, 2011.
DOI : 10.1109/ICCV.2011.6126359

C. Vogel, S. Roth, and K. Schindler, View-Consistent 3D Scene Flow Estimation over Multiple Frames, European Conference on Computer Vision, pp.263-278, 2014.
DOI : 10.1007/978-3-319-10593-2_18

A. Yilmaz, O. Javed, and M. Shah, Object tracking, ACM Computing Surveys, vol.38, issue.4, pp.13-25, 2006.
DOI : 10.1145/1177352.1177355

A. Smeulder, D. Chu, R. Cucchiara, S. Calderara, A. Deghan et al., Visual tracking: an experimental survey, Pattern Analysis and Machine Intelligence, p.12, 2014.

N. Peterfreund, Robust tracking of position and velocity with Kalman snakes, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.21, issue.6, pp.564-569, 1999.
DOI : 10.1109/34.771328

Y. Rathi, N. Vaswani, A. Tannenbaum, and A. J. Yezzi, Tracking Deforming Objects Using Particle Filtering for Geometric Active Contours, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.29, issue.8, pp.1470-1475, 2007.
DOI : 10.1109/TPAMI.2007.1081

C. Avenel, E. Mémin, and P. Pérez, Tracking Closed Curves with Non-linear Stochastic Filters, Conference on Space-Scale and Variational Methods, p.12, 2009.
DOI : 10.1007/3-540-48236-9_13
URL : https://hal.archives-ouvertes.fr/tel-00763157

F. Bouttier and P. Courtier, Data assimilation concepts and methods Training Course of European Centre for Medium-Range Weather Forecasts, Tech. Rep, p.13, 1999.

N. Papadakis, E. Mémin, A. Cuzol, and N. Gengembre, Data assimilation with the weighted ensemble Kalman filter Tellus Series A : Dynamic meteorology and oceanography, pp.673-697, 2010.

M. Ridal, M. Lindskog, N. Gustafsson, and G. Haase, Optimized advection of radar reflectivities, Atmospheric Research, vol.100, issue.2-3, pp.213-225, 2011.
DOI : 10.1016/j.atmosres.2010.12.016

R. E. Kalman, A New Approach to Linear Filtering and Prediction Problems, Journal of Basic Engineering, vol.82, issue.1, pp.35-45, 1960.
DOI : 10.1115/1.3662552

F. , L. Dimet, and O. Talagrand, Variational algorithms for analysis and assimilation of meteorological observations: theoretical aspects Tellus Series A : Dynamic meteorology and oceanography, pp.97-110, 1986.

R. Leveque, Numerical Methods for Conservative Laws, Lectures in Mathematics. ETH Zürich, p.25, 1992.

A. Robert, A stable numerical integration scheme for the primitive meteorological equations, Atmosphere-Ocean, vol.19, issue.1, pp.35-46, 1981.
DOI : 10.1111/j.2153-3490.1959.tb00019.x

A. Staniforth and J. Côté, Semi-Lagrangian Integration Schemes for Atmospheric Models???A Review, Monthly Weather Review, vol.119, issue.9, pp.2206-2223, 1991.
DOI : 10.1175/1520-0493(1991)119<2206:SLISFA>2.0.CO;2

J. Pudykiewicz and A. Staniforth, Some properties and comparative performance of the semi???Lagrangian method of Robert in the solution of the advection???diffusion equation, Atmosphere-Ocean, vol.12, issue.3, pp.283-308, 1984.
DOI : 10.1080/07055900.1984.9649200

R. H. Byrd, P. Lu, and J. Nocedal, A Limited Memory Algorithm for Bound Constrained Optimization, SIAM Journal on Scientific Computing, vol.16, issue.5, pp.1190-1208, 1995.
DOI : 10.1137/0916069

C. Zhu, R. H. Byrd, P. Lu, and J. Nocedal, Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization, ACM Transactions on Mathematical Software, vol.23, issue.4, pp.550-560, 1997.
DOI : 10.1145/279232.279236

R. Giering and T. Kaminski, Recipes for adjoint code construction, ACM Transactions on Mathematical Software, vol.24, issue.4, pp.437-474, 1998.
DOI : 10.1145/293686.293695

L. Nardi, C. Sorror, F. Badran, and S. Thiria, YAO: A Software for Variational Data Assimilation Using Numerical Models, Computational Science and Its Applications, pp.621-636, 2009.
DOI : 10.1121/1.2197790
URL : https://hal.archives-ouvertes.fr/hal-01125735

L. Hascoët and V. Pascual, Tapenade 2.1 user's guide, p.31, 2004.

D. Béréziat and I. Herlin, Solving ill-posed image processing problems using data assimilation, p.32, 2009.

D. S. Oliver, Calculation of the inverse of the covariance, Mathematical Geology, vol.30, issue.7, pp.911-933, 1998.
DOI : 10.1023/A:1021734811230

J. L. Morales and J. Nocedal, Remark on ???algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound constrained optimization???, ACM Transactions on Mathematical Software, vol.38, issue.1, pp.1-7, 2011.
DOI : 10.1145/2049662.2049669

P. Courtier, J. Thépaut, and A. Hollingsworth, A strategy for operational implementation of 4D-Var, using an incremental approach, Quarterly Journal of the Royal Meteorological Society, vol.45, issue.519, pp.1367-1387, 1994.
DOI : 10.1002/qj.49712051912

E. and V. Hólm, Lectures notes on assimilation algorithms European Centre for Medium-Range Weather Forecasts Reading, Tech. Rep, p.42, 2008.

D. Béréziat and I. Herlin, Image-based modelling of ocean surface circulation from satellite acquisitions, International Conference on Computer Vision Theory and Applications, p.141, 2014.

I. Herlin, D. Béréziat, and N. Mercier, Improvement of motion estimation by assessing the errors on the evolution equation, International Conference on Computer Vision Theory and Applications, pp.235-240, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00677662

R. Deriche, Using Canny's criteria to derive a recursively implemented optimal edge detector, International Journal of Computer Vision, vol.1, issue.2, pp.167-187, 1987.
DOI : 10.1007/BF00123164

J. Canny, A computational approach to edge detection, Pattern Analysis and Machine Intelligence, vol.8, issue.6, pp.679-698, 1986.

J. A. Sethian, Level Set Methods, p.48, 1996.

J. A. Sethian, Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science, p.48, 1999.

M. Sussman, E. Fatemi, P. Smereka, and S. Osher, An improved level set method for incompressible two-phase flows, Computers & Fluids, vol.27, issue.5-6, pp.663-680, 1998.
DOI : 10.1016/S0045-7930(97)00053-4

M. Sussman and E. Fatemi, An Efficient, Interface-Preserving Level Set Redistancing Algorithm and Its Application to Interfacial Incompressible Fluid Flow, SIAM Journal on Scientific Computing, vol.20, issue.4, p.49, 1999.
DOI : 10.1137/S1064827596298245

V. Chabot, M. Nodet, N. Papadakis, and A. Vidard, Accounting for observation errors in image data assimilation Tellus Series A : Dynamic meteorology and oceanography, pp.19-142, 2015.

A. T. Weaver and S. Ricci, Constructing a background-error correlation model using generalized diffusion operators ECWMF procreedings on " Recent developments in data assimilation for atmosphere and ocean, p.55, 2003.

J. Parent-du and . Châtelet, Aramis, le réseau franccais de radars pour la surveillance des précipitations, Société météorologique de France, p.79, 2003.

S. Mecklenburg, A. Jurczyk, J. Szturc, and K. Osrodka, Quantitative precipitation forecasts (QPF) based on radar data for hydrological models, COST action, p.80, 2002.

E. Ebert, L. Wilson, B. Brown, P. Nurmi, H. Brooks et al., Verification of Nowcasts from the WWRP Sydney 2000 Forecast Demonstration Project, Weather and Forecasting, vol.19, issue.1, pp.73-96, 2004.
DOI : 10.1175/1520-0434(2004)019<0073:VONFTW>2.0.CO;2

A. Neumann, Introduction d'outils de l'intelligence artificielle dans la prévision de pluie par radar, p.81, 1991.

M. Dixon and G. Wiener, TITAN: Thunderstorm Identification, Tracking, Analysis, and Nowcasting???A Radar-based Methodology, Journal of Atmospheric and Oceanic Technology, vol.10, issue.6, pp.785-797, 1993.
DOI : 10.1175/1520-0426(1993)010<0785:TTITAA>2.0.CO;2

D. Sempere-torres, R. Sánchez-diezma, M. Córdoba, R. Pascual, and I. Zawadzki, An operational methodology to control radar measurements stability from mountain returns, Conference on Radar Meteorology of the, pp.264-83, 2001.

J. S. Marshall and W. M. Palmer, THE DISTRIBUTION OF RAINDROPS WITH SIZE, Journal of Meteorology, vol.5, issue.4, pp.165-166, 1948.
DOI : 10.1175/1520-0469(1948)005<0165:TDORWS>2.0.CO;2

J. Van-baelen, F. Tridon, and Y. Pointin, Simultaneous X-band and K-band study of precipitation to derive specific Z???R relationships, Atmospheric Research, vol.94, issue.4, pp.596-605, 2009.
DOI : 10.1016/j.atmosres.2009.04.003

C. Temperton, M. Hortal, and A. Simmons, A two-time-level semi-Lagrangian global spectral model, Quarterly Journal of the Royal Meteorological Society, vol.125, issue.571, pp.111-127, 2001.
DOI : 10.1002/qj.49712757107

P. Sakov and P. R. Oke, A deterministic formulation of the ensemble Kalman filter: An alternative to ensemble square root filters Tellus Series A : Dynamic meteorology and oceanography, p.110, 2008.

P. L. Houtekamer and H. L. Mitchell, Data Assimilation Using an Ensemble Kalman Filter Technique, Monthly Weather Review, vol.126, issue.3, pp.796-811, 1998.
DOI : 10.1175/1520-0493(1998)126<0796:DAUAEK>2.0.CO;2

J. L. Anderson and S. L. Anderson, A Monte Carlo Implementation of the Nonlinear Filtering Problem to Produce Ensemble Assimilations and Forecasts, Monthly Weather Review, vol.127, issue.12, pp.2741-2758, 1999.
DOI : 10.1175/1520-0493(1999)127<2741:AMCIOT>2.0.CO;2

T. M. Hamill, J. S. Whitaker, and C. Snyder, Distance-Dependent Filtering of Background Error Covariance Estimates in an Ensemble Kalman Filter, Monthly Weather Review, vol.129, issue.11, pp.2776-2790, 2001.
DOI : 10.1175/1520-0493(2001)129<2776:DDFOBE>2.0.CO;2

P. R. Oke, P. Sakov, and S. P. Corney, Impacts of localisation in the EnKF and EnOI: experiments with a small model, Ocean Dynamics, vol.130, issue.1, pp.32-45, 2007.
DOI : 10.1007/s10236-006-0088-8

J. L. Anderson, An adaptive covariance inflation error correction algorithm for ensemble filters Tellus Series A : Dynamic meteorology and oceanography, pp.210-224, 2007.

G. Evensen, Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics, Journal of Geophysical Research, vol.109, issue.Part 4, p.104, 1994.
DOI : 10.1029/94JC00572

G. Evensen, Data Assimilation -The Ensemble Kalman Filter, p.115, 2006.

O. M. Aodha, G. J. Brostow, and M. Pollefeys, Segmenting video into classes of algorithmsuitability, Conference on Computer Vision and Pattern Recognition, pp.1054-1061, 2010.

T. Brox, A. Bruhn, N. Papenberg, and J. Weickert, High Accuracy Optical Flow Estimation Based on a Theory for Warping, European Conference on Computer Vision, pp.25-36, 2004.
DOI : 10.1007/978-3-540-24673-2_3

M. J. Black and P. Anandan, The Robust Estimation of Multiple Motions: Parametric and Piecewise-Smooth Flow Fields, Computer Vision and Image Understanding, vol.63, issue.1, pp.75-104, 1996.
DOI : 10.1006/cviu.1996.0006

Y. Li and S. Osher, A new median formula with applications to PDE based denoising, Communications in Mathematical Sciences, vol.7, issue.3, pp.741-753, 2009.
DOI : 10.4310/CMS.2009.v7.n3.a11

E. Agullo, J. Demmel, J. Dongarra, B. Hadri, J. Kurzak et al., Numerical linear algebra on emerging architectures: The PLASMA and MAGMA projects, Journal of Physics: Conference Series, vol.180, issue.1, pp.12037-115, 2009.
DOI : 10.1088/1742-6596/180/1/012037

P. L. Houtekamer and H. L. Mitchell, A Sequential Ensemble Kalman Filter for Atmospheric Data Assimilation, Monthly Weather Review, vol.129, issue.1, pp.123-137, 1998.
DOI : 10.1175/1520-0493(2001)129<0123:ASEKFF>2.0.CO;2

B. Hunt, E. J. Kostelich, and I. Szunyogh, Efficient data assimilation for spatiotemporal chaos: A local ensemble transform Kalman filter, Physica D: Nonlinear Phenomena, vol.230, issue.1-2, pp.112-126, 2007.
DOI : 10.1016/j.physd.2006.11.008

L. Nerger, S. Danilov, W. Hiller, and J. Schröter, Using sea-level data to constrain a finiteelement primitive-equation ocean model with a local SEIK filter, Ocean Dynamics, vol.56, pp.5-6, 2006.

S. L. Horowitz and T. Pavlidis, Picture Segmentation by a Tree Traversal Algorithm, Journal of the ACM, vol.23, issue.2, pp.368-388, 1976.
DOI : 10.1145/321941.321956

R. Ohlander, K. Price, and D. R. Reddy, Picture segmentation using a recursive region splitting method, Computer Graphics and Image Processing, vol.8, issue.3, pp.313-333, 1978.
DOI : 10.1016/0146-664X(78)90060-6

T. Janji?, L. Nerger, A. Albertella, J. Schröter, and S. Skachko, On Domain Localization in Ensemble-Based Kalman Filter Algorithms, Monthly Weather Review, vol.139, issue.7, pp.2046-2060, 2011.
DOI : 10.1175/2011MWR3552.1

C. H. Bishop, B. J. Etherton, and S. J. Majumdar, Adaptive Sampling with the Ensemble Transform Kalman Filter. Part I: Theoretical Aspects, Monthly Weather Review, vol.129, issue.3, pp.420-436, 2001.
DOI : 10.1175/1520-0493(2001)129<0420:ASWTET>2.0.CO;2

T. Miyoshi, S. Yamane, and T. Enomoto, Localizing the Error Covariance by Physical Distances within a Local Ensemble Transform Kalman Filter (LETKF), Scientific Online Letters on the Atmosphere, pp.89-92, 2007.
DOI : 10.2151/sola.2007-023