M. Bardi and I. Capuzzo-dolcetta, Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations, 1997.
DOI : 10.1007/978-0-8176-4755-1

G. Barles, An approach of deterministic control problems with unbounded data, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.7, issue.4, pp.235-258, 1990.
DOI : 10.1016/S0294-1449(16)30290-6

G. Barles, Solutions de Viscosité des Equations de Hamilton?Jacobi, 1994.

G. Barles and B. Perthame, Comparison principle for dirichlet-type Hamilton-Jacobi equations and singular perturbations of degenerated elliptic equations, Applied Mathematics & Optimization, vol.25, issue.1, pp.21-44, 1990.
DOI : 10.1007/BF01445155

I. Barnes and K. Zhang, Instability of the eikonal equation and shape from shading, ESAIM: Mathematical Modelling and Numerical Analysis, vol.34, issue.1, pp.127-138, 2000.
DOI : 10.1051/m2an:2000134

F. Camilli and A. Siconolfi, Maximal subsolutions for a class of degenerate Hamilton-Jacobi problems, Indiana University Mathematics Journal, vol.48, issue.3, pp.1111-1132, 1999.
DOI : 10.1512/iumj.1999.48.1678

F. Camilli and A. Siconolfi, Nonconvex degenerate Hamilton-Jacobi equations, Mathematische Zeitschrift, vol.242, issue.1, pp.1-21, 2002.
DOI : 10.1007/s002090100302

I. Capuzzo-dolcetta and P. Lions, Hamilton-Jacobi equations with state constraints, Transactions of the American Mathematical Society, vol.318, issue.2, pp.643-68, 1990.
DOI : 10.1090/S0002-9947-1990-0951880-0

F. H. Clarke, Optimization and Nonsmooth Analysis, SIAM, Classics in Applied Mathematics, vol.5, 1990.
DOI : 10.1137/1.9781611971309

M. G. Crandall and P. , Viscosity solutions of Hamilton-Jacobi equations, Transactions of the American Mathematical Society, vol.277, issue.1, pp.1-42, 1983.
DOI : 10.1090/S0002-9947-1983-0690039-8

P. Dupuis and J. Oliensis, An Optimal Control Formulation and Related Numerical Methods for a Problem in Shape Reconstruction, The Annals of Applied Probability, vol.4, issue.2, pp.287-346, 1994.
DOI : 10.1214/aoap/1177005063

M. Falcone and M. Sagona, An algorithm for the global solution of the shape-from-shading model, Proceedings of the International Conference on Image Analysis and Processing, pp.596-603, 1310.
DOI : 10.1007/3-540-63507-6_250

H. Ishii and M. Ramaswamy, Uniqueness results for a class of hamilton-jacobi equations with singular coefficients, Communications in Partial Differential Equations, vol.20, issue.11-12, pp.2187-2213, 1995.
DOI : 10.1080/03605309508821168

H. Ishii, A boundary value problem of the Dirichlet type for Hamilton-Jacobi equations, Ann. Scuola Norm. Sup. Pisa Cl. Sci, vol.16, pp.105-135, 1989.

R. Kimmel, K. Siddiqi, B. B. Kimia, and A. Bruckstein, Shape from shading: Level set propagation and viscosity solutions, International Journal of Computer Vision, vol.98, issue.3, pp.107-133, 1995.
DOI : 10.1007/BF01539551

P. Lions, Generalized Solutions of Hamilton?Jacobi Equations. Number 69 in Research Notes in Mathematics, 1982.

P. Lions, E. Rouy, and A. Tourin, Shape-from-shading, viscosity solutions and edges, Numerische Mathematik, vol.24, issue.No. 2, pp.323-353, 1993.
DOI : 10.1007/BF01388692

M. Malisoff, Bounded-from-below solutions of the Hamilton-Jacobi equation for optimal control problems with exit times: vanishing lagrangians, eikonal equations, and shape-from-shading, NoDEA : Nonlinear Differential Equations and Applications, vol.11, issue.1, pp.95-122, 2004.
DOI : 10.1007/s00030-003-1051-8

J. Oliensis and P. Dupuis, Direct method for reconstructing shape from shading, Geometric Methods in Computer Vision, pp.116-128, 1991.
DOI : 10.1117/12.48418

E. Prados and O. Faugeras, "Perspective shape from shading" and viscosity solutions, Proceedings Ninth IEEE International Conference on Computer Vision, pp.826-831, 2003.
DOI : 10.1109/ICCV.2003.1238433

URL : https://hal.archives-ouvertes.fr/inria-00394240

E. Prados and O. Faugeras, A Generic and Provably Convergent Shape-from-Shading Method for Orthographic and Pinhole Cameras, International Journal of Computer Vision, vol.65, issue.1-2, pp.97-125, 2005.
DOI : 10.1007/s11263-005-3844-1

URL : https://hal.archives-ouvertes.fr/inria-00378704

E. Prados, F. Camilli, and O. Faugeras, A Unifying and Rigorous Shape from Shading Method Adapted to Realistic Data and Applications, Journal of Mathematical Imaging and Vision, vol.2, issue.6, 2006.
DOI : 10.1007/s10851-006-6899-x

URL : https://hal.archives-ouvertes.fr/inria-00377391

E. Prados, O. Faugeras, and E. Rouy, Shape from Shading and Viscosity Solutions, Proceedings of the 7th European Conference on Computer Vision, pp.790-804, 2002.
DOI : 10.1007/3-540-47967-8_53

URL : https://hal.archives-ouvertes.fr/inria-00394240

E. Rouy and A. Tourin, A Viscosity Solutions Approach to Shape-From-Shading, SIAM Journal on Numerical Analysis, vol.29, issue.3, pp.867-884, 1992.
DOI : 10.1137/0729053

H. M. Soner, Optimal Control with State-Space Constraint I, SIAM Journal on Control and Optimization, vol.24, issue.3, pp.1110-1122, 1986.
DOI : 10.1137/0324032

H. J. Sussmann, Uniqueness results for the value function via direct trajectory-construction methods, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475), pp.3293-3298, 2003.
DOI : 10.1109/CDC.2003.1271651

A. Tankus, N. Sochen, and Y. Yeshurun, A new perspective [on] shape-from-shading, Proceedings Ninth IEEE International Conference on Computer Vision, pp.862-869, 2003.
DOI : 10.1109/ICCV.2003.1238439

D. Tschumperlé, PDE's Based Regularization of Multivalued Images and Applications, 2002.

R. Zhang, P. Tsai, J. Cryer, and M. Shah, Shape-from-shading: a survey, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.21, issue.8, pp.690-706, 1999.
DOI : 10.1109/34.784284