D. Adalsteinsson and J. A. Sethian, The Fast Construction of Extension Velocities in Level Set Methods, Journal of Computational Physics, vol.148, issue.1, pp.2-22, 1999.
DOI : 10.1006/jcph.1998.6090

J. An and Y. Chen, Region based image segmentation using a modified mumford-shah algorithm. Scale Space and Variational Methods in Computer Vision, pp.733-742, 2007.
DOI : 10.1007/978-3-540-72823-8_63
URL : http://www.ima.umn.edu/~jan/170AnChenSSVM07.pdf

P. L. Andrews, M. G. Cruz, and R. C. , Examination of the wind speed limit function in the Rothermel surface fire spread model, International Journal of Wildland Fire, vol.22, issue.7, pp.959-969, 2013.
DOI : 10.1071/WF12122

P. Arbogast, O. Pannekoucke, L. Raynaud, R. Lalanne, and E. Mémin, Object-oriented processing of CRM precipitation forecasts by stochastic filtering, Quarterly Journal of the Royal Meteorological Society, vol.105, issue.700, pp.2827-2838, 2016.
DOI : 10.1029/1999JD901087
URL : https://hal.archives-ouvertes.fr/hal-01378366

A. Armiento, P. Moireau, D. Martin, N. Lepejova, M. Doumic et al., The mechanism of monomer transfer between two structurally distinct PrP oligomers, PLOS ONE, vol.12, issue.11, p.180538, 2017.
DOI : 10.1371/journal.pone.0180538.s006
URL : https://hal.archives-ouvertes.fr/hal-01574346

T. Artes, A. Cencerrado, A. Cortes, T. Margalef, D. Rodriguez-aseretto et al., Towards a Dynamic Data Driven Wildfire Behavior Prediction System at European Level, Procedia Computer Science, vol.29, pp.1216-1226, 2014.
DOI : 10.1016/j.procs.2014.05.109

J. Beezley and J. Mandel, Morphing ensemble Kalman filters, pp.131-140, 2008.
DOI : 10.3402/tellusa.v60i1.15273
URL : http://arxiv.org/abs/0705.3693

I. Bloch, Fuzzy sets for image processing and understanding. Fuzzy Sets and Systems, pp.280-291, 2015.
DOI : 10.1016/j.fss.2015.06.017
URL : https://hal.archives-ouvertes.fr/hal-01219806

A. Bova, W. Mell, and C. Hoffman, A comparison of level set and marker methods for the simulation of wildland fire front propagation, International Journal of Wildland Fire, vol.25, issue.2, pp.229-241, 2015.
DOI : 10.1071/WF13178

T. F. Chan and L. A. Vese, A level set algorithm for minimizing the Mumford-Shah functional in image processing, Proceedings IEEE Workshop on Variational and Level Set Methods in Computer Vision, p.161, 2001.
DOI : 10.1109/VLSM.2001.938895

D. Chapelle, M. Fragu, V. Mallet, and P. Moireau, Fundamental principles of data assimilation underlying the Verdandi library: applications to biophysical model personalization within euHeart, Medical & Biological Engineering & Computing, vol.4, issue.7, pp.1221-1233, 2013.
DOI : 10.1016/j.jmbbm.2011.03.018
URL : https://hal.archives-ouvertes.fr/hal-00760887

S. Chen, G. Charpiat, and R. J. Radke, Converting Level Set Gradients to Shape Gradients, Computer Vision ? ECCV 2010, pp.715-728, 2010.
DOI : 10.1007/978-3-642-15555-0_52
URL : https://hal.archives-ouvertes.fr/inria-00497222

S. Clandillon and H. Yesou, GMES Emergency Response -Fire mapping experience within EO-based Rapid Mapping, In EGU General Assembly, vol.13, 2011.

A. Collin, Analyse asymptotique enélectrophysiologieenélectrophysiologie cardiaque : applicationsàapplications`applicationsà la modélisation etàetà l'assimilation de données, 2014.

A. Collin, D. Chapelle, and P. Moireau, A Luenberger observer for reaction???diffusion models with front position data, Journal of Computational Physics, vol.300, issue.C, pp.288-307, 2015.
DOI : 10.1016/j.jcp.2015.07.044
URL : https://hal.archives-ouvertes.fr/hal-01111675

A. Collin, D. Chapelle, and P. Moireau, Sequential State Estimation for Electrophysiology Models with Front Level-Set Data Using Topological Gradient Derivations, Proceedings of the 8th International Conference FIMH, volume LNCS 9126, pp.402-411, 2015.
DOI : 10.1007/978-3-319-20309-6_46
URL : https://hal.archives-ouvertes.fr/hal-01174916

M. G. Cruz and M. E. Alexander, Uncertainty associated with model predictions of surface and crown fire rates of spread. Environmental Modelling and Software, pp.16-28, 2013.

T. J. Duff, D. M. Chong, and K. G. Tolhurst, Quantifying spatio-temporal differences between fire shapes: Estimating fire travel paths for the improvement of dynamic spread models, Environmental Modelling & Software, vol.46, pp.33-43, 2013.
DOI : 10.1016/j.envsoft.2013.02.005

B. Engquist, A. Tornberg, and R. Tsai, Discretization of Dirac delta functions in level set methods, Journal of Computational Physics, vol.207, issue.1, pp.28-51, 2005.
DOI : 10.1016/j.jcp.2004.09.018

A. C. Fernandez-pello, Wildland fire spot ignition by sparks and firebrands, Fire Safety Journal, vol.91, p.2017
DOI : 10.1016/j.firesaf.2017.04.040

N. Feyeux, Transport optimal pour l'assimilation de données images, 2016.

N. Feyeux, M. Nodet, and A. Vidard, Optimal Transport for Data Assimilation. working paper or preprint, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01342193

J. B. Filippi, V. Mallet, and B. Nader, Evaluation of forest fire models on a large observation database, Natural Hazards and Earth System Science, vol.14, issue.11, pp.3077-3091, 2014.
DOI : 10.5194/nhess-14-3077-2014
URL : https://hal.archives-ouvertes.fr/hal-01108597

J. Filippi, F. Morandini, J. Balbi, and D. Hill, Discrete event front-tracking simulation of a physical fire-spread model. Simulation, Transactions of the Society for Modeling and Simulation International, pp.555-580, 2011.

M. Finney, FARSITE: Fire Area Simulator -Model Development and Evaluation, 1998.
DOI : 10.2737/RMRS-RP-4

B. Fisher, The product of distributions, The Quarterly Journal of Mathematics, 1971.

J. Glasa and L. Halada, On elliptical model for forest fire spread modeling and simulation, Mathematics and Computers in Simulation, vol.78, issue.1, pp.76-88, 2008.
DOI : 10.1016/j.matcom.2007.06.001

M. Gollner, A. Trouvé, I. Altintas, J. Block, R. De-callafon et al., Towards data-driven operational wildfire spread modeling -report of the nsf-funded wifire workshop, 2015.

L. He, C. Y. Kao, and S. Osher, Incorporating topological derivatives into shape derivatives based level set methods, Journal of Computational Physics, vol.225, issue.1, pp.891-909, 2007.
DOI : 10.1016/j.jcp.2007.01.003

A. Jazwinski, Stochastic Processes and Filtering Theory, 1970.

E. Jimenez, M. Hussaini, and S. Goodrick, Quantifying parametric uncertainty in the Rothermel model, International Journal of Wildland Fire, vol.17, issue.5, pp.638-649, 2008.
DOI : 10.1071/WF07070

L. , L. Gratiet, S. Marelli, and B. Sudret, Metamodel-Based Sensitivity Analysis: Polynomial Chaos Expansions and Gaussian Processes, Handbook of Uncertainty Quantification, pp.1-37, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01428947

J. Li and D. Xiu, A generalized polynomial chaos based ensemble Kalman filter with high accuracy, Journal of Computational Physics, vol.228, issue.15, pp.5454-5469, 2009.
DOI : 10.1016/j.jcp.2009.04.029

L. Li, F. Dimet, J. Ma, and A. Vidard, A Level-Set-Based Image Assimilation Method: Potential Applications for Predicting the Movement of Oil Spills, IEEE Transactions on Geoscience and Remote Sensing, vol.55, issue.11, 2016.
DOI : 10.1109/TGRS.2017.2726013

V. Mallet, D. Keyes, and F. Fendell, Modeling wildland fire propagation with level set methods, Computers & Mathematics with Applications, vol.57, issue.7, pp.1089-1101, 2009.
DOI : 10.1016/j.camwa.2008.10.089
URL : https://hal.archives-ouvertes.fr/inria-00566147

M. Martins, S. Ferreira-jr, and M. Vilela, Multiscale models for the growth of avascular tumors, Physics of Life Reviews, vol.4, issue.2, pp.128-156, 2007.
DOI : 10.1016/j.plrev.2007.04.002

P. Moireau and D. Chapelle, Reduced-order unscented Kalman filtering with application to parameter identification in largedimensional systems. Control, Optimisation and Calculus of Variations, pp.380-405, 2011.
URL : https://hal.archives-ouvertes.fr/inria-00550104

P. Moireau, D. Chapelle, and P. L. Tallec, Joint state and parameter estimation for distributed mechanical systems, Computer Methods in Applied Mechanics and Engineering, vol.197, issue.6-8, pp.6-8659, 2008.
DOI : 10.1016/j.cma.2007.08.021
URL : https://hal.archives-ouvertes.fr/hal-00175623

H. Moradkhani, S. Sorooshian, H. Gupta, and P. Houser, Dual state???parameter estimation of hydrological models using ensemble Kalman filter, Advances in Water Resources, vol.28, issue.2, pp.135-147, 2005.
DOI : 10.1016/j.advwatres.2004.09.002

D. Mumford and J. Shah, Optimal approximations by piecewise smooth functions and associated variational problems, Communications on Pure and Applied Mathematics, vol.3, issue.5, pp.577-685, 1989.
DOI : 10.1109/TPAMI.1984.4767596

S. Osher and R. Fedkiw, Level set methods and dynamic implicit surfaces, Applied Mathematical Sciences, vol.153, 2003.
DOI : 10.1115/1.1760520

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, pp.81-103, 2008.
DOI : 10.1007/978-3-662-03620-4
URL : https://hal.archives-ouvertes.fr/hal-00596154

R. Paugam, M. Wooster, and G. Roberts, Use of Handheld Thermal Imager Data for Airborne Mapping of Fire Radiative Power and Energy and Flame Front Rate of Spread, IEEE Transactions on Geoscience and Remote Sensing, vol.51, issue.6, pp.3385-3399, 2013.
DOI : 10.1109/TGRS.2012.2220368

H. Pitsch, A consistent level set formulation for large-eddy simulation of premixed turbulent combustion, Combustion and Flame, vol.143, issue.4, pp.587-598, 2005.
DOI : 10.1016/j.combustflame.2005.08.031

G. Poëtte, B. Després, and D. Lucor, Treatment of uncertain material interfaces in compressible flows, Computer Methods in Applied Mechanics and Engineering, vol.200, issue.1-4, pp.284-308, 2011.
DOI : 10.1016/j.cma.2010.08.011

S. Ravela, Amplitude-Position Formulation of Data Assimilation, Proceedings of the 6th International Conference on Computational Science -Volume Part III, ICCS'06, pp.497-505, 2006.
DOI : 10.1007/11758532_66

R. Rehm and R. Mcdermott, Fire front propagation using the level set method, 2009.
DOI : 10.6028/NIST.TN.1611

R. Reichle, Data assimilation methods in the Earth sciences, Advances in Water Resources, vol.31, issue.11, pp.1411-1418, 2008.
DOI : 10.1016/j.advwatres.2008.01.001

G. D. Richards, An elliptical growth model of forest fire fronts and its numerical solution, International Journal for Numerical Methods in Engineering, vol.13, issue.6, pp.1163-1179, 1990.
DOI : 10.1080/00049158.1967.10675433

P. Riggan and G. Robert, Chapter 6 Airborne Remote Sensing of Wildland Fires, Wildland Fires and Air Pollution, pp.139-168, 2009.
DOI : 10.1016/S1474-8177(08)00006-5

M. C. Rochoux, Vers une meilleure prévision de la propagation d'incendies de forêt : ´ evaluation de modèles et assimilation de données, 2014.

M. C. Rochoux, B. Delmotte, B. Cuenot, S. Ricci, and A. Trouvé, Regional-scale simulations of wildland fire spread informed by real-time flame front observations, Proceedings of the Combustion Institute, pp.2641-2647, 2013.
DOI : 10.1016/j.proci.2012.06.090

M. C. Rochoux, C. Emery, S. Ricci, B. Cuenot, and A. Trouvé, Towards predictive data-driven simulations of wildfire spread ??? Part II: Ensemble Kalman Filter for the state estimation of a front-tracking simulator of wildfire spread, Natural Hazards and Earth System Science, vol.15, issue.8, pp.151721-1739, 2015.
DOI : 10.5194/nhess-15-1721-2015
URL : https://hal.archives-ouvertes.fr/hal-01346735

M. C. Rochoux, S. Ricci, D. Lucor, B. Cuenot, and A. Trouvé, Towards predictive data-driven simulations of wildfire spread ??? Part I: Reduced-cost Ensemble Kalman Filter based on a Polynomial Chaos surrogate model for parameter estimation, Natural Hazards and Earth System Science, vol.14, issue.11, pp.142951-2973, 2014.
DOI : 10.5194/nhess-14-2951-2014
URL : https://hal.archives-ouvertes.fr/hal-01332351

B. Rosic, A. Kucerov, J. Sykora, O. Pajonk, A. Litvinenko et al., Parameter identification in a probabilistic setting, Engineering Structures, vol.50, pp.179-196, 2013.
DOI : 10.1016/j.engstruct.2012.12.029

J. J. Ruiz, M. Pulido, and T. Miyoshi, Estimating Model Parameters with Ensemble-Based Data Assimilation: A Review, Journal of the Meteorological Society of Japan. Ser. II, vol.91, issue.2, pp.79-99, 2013.
DOI : 10.2151/jmsj.2013-201

J. Sethian, Level set methods and fast marching methods, 1999.

J. A. Sethian, Theory, algorithms, and applications of level set methods for propagating interfaces, Acta Numerica, vol.11, issue.1, pp.309-395, 1996.
DOI : 10.1007/BF00133570

B. Sudret, Global sensitivity analysis using polynomial chaos expansions, Reliability Engineering & System Safety, vol.93, issue.7, pp.964-979, 2008.
DOI : 10.1016/j.ress.2007.04.002
URL : https://hal.archives-ouvertes.fr/hal-01432217

A. Sullivan, Wildland surface fire spread modelling, 1990???2007. 2: Empirical and quasi-empirical models, International Journal of Wildland Fire, vol.18, issue.4, pp.369-386, 2009.
DOI : 10.1071/WF06142
URL : http://arxiv.org/pdf/0706.3074

M. Trani, R. Arts, and O. Leeuwenburgh, Seismic History Matching of Fluid Fronts Using the Ensemble Kalman Filter, SPE Journal, vol.18, issue.01, pp.159-171, 2012.
DOI : 10.2118/163043-PA

D. Xiu, Numerical methods for stochastic computations. A spectral method approach, 2010.

R. Yildizoglu, J. Aujol, and N. Papadakis, Active contours without level sets, 2012 19th IEEE International Conference on Image Processing, pp.2549-2552, 2012.
DOI : 10.1109/ICIP.2012.6467418
URL : https://hal.archives-ouvertes.fr/hal-00696065

C. Zhang, M. C. Rochoux, W. Tang, M. Gollner, J. B. Filippi et al., Evaluation of a data-driven wildland fire spread forecast model with spatially-distributed parameter estimation in simulations of the FireFlux I field-scale experiment, Fire Safety Journal, vol.91
DOI : 10.1016/j.firesaf.2017.03.057