Numerical solution of the perspective shape-from-shading problem

Proceedings of Science

Volumn 18, Issue , 2005, Pages

  Cristiani, Emiliano ^a   Falcone, Maurizio ^a   Seghini, Alessandra ^a  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

CONTROL SYSTEMS;

FIRST ORDER; HAMILTON - JACOBI EQUATIONS; NUMERICAL SOLUTION; PERSPECTIVE SHAPE-FROM-SHADING; REGULAR SOLUTION; SEMI-LAGRANGIAN; SIMPLE ALGORITHM; WEAK SOLUTION;

BOUNDARY CONDITIONS;

EID: 85055834413     PISSN: None     EISSN: 18248039     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (21)

1. G. Barles, Viscosity solutions of Hamilton-Jacobi equations, Springer Verlag, 1994.
2. F. Camilli and M. Falcone, An approximation scheme for the maximal solution of the shape-from-shading model, Proceedings ICIP 96 International Conference on Image Processing vol. I, IEEE Inc., 1996, 49-52.
3. F. Camilli and M. Falcone, Approximation of optimal control problems with state constraints: estimates and applications, B.S. Mordukhovic, H.J. Sussman eds., “Nonsmooth analysis and geometric methods in deterministic optimal control”, IMA Volumes in Applied Mathematics 78, Springer Verlag, 1996, 23-57.
4. F. Camilli and L. Grune, Numerical approximation of the maximal solution for a class of degenerate Hamilton-Jacobi equations, SIAM J Num. Anal. 38 (2000), 1540-1560.
5. F. Camilli and A. Siconolfi, Maximal subsolutions for a class of degenerate Hamilton-Jacobi problems, Indiana Univ. Math. J. 48 (1999), 1111-1131.
6. F. Courteille, A. Crouzil, J.D. Durou, P. Gurdjos, Towards shape from shading under realistic photographic conditions, Proceedings of the 17th International Conference on Pattern Recognition - ICPR 2004, vol.2, Cambridge, 277-280.
7. M. G. Crandall, H. Ishii and P. L. Lions, User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc., 27 (1992), 1-67.
8. J.D. Durou, M. Falcone, M. Sagona, A survey of numerical methods for Shape-from-Shading, Rapport de Recherche IRIT n. 2004-2-R, 2004.
9. J.D. Durou, D. Piau, Ambiguous Shape from Shading with critical points, Journal of Mathematical Imaging and Vision, 12 (2000), 99-108.
10. M. Falcone, Ch. Makridakis, Numerical methods for viscosity solutions and applications, World Scientific, Singapore, 2001.
11. M. Falcone, M. Sagona. An algorithm for the global solution of the shape-from-shading model, LNCS 1310 International Conference on Image Analysis and Processing, 1997, 1596Ð603.
12. M. Falcone, M. Sagona e A. Seghini, A global alghorithm for the Shape-from-Shading problem with black shadows, in F. Brezzi, A. Buffa, S. Corsaro, A. Murli (eds) "Numerical Mathematics and Advanced Applications" - ENUMATH 2001, Springer Verlag, 503-512.
13. B.K.P. Horn and M.J. Brooks, Shape from Shading, The MITPress, 1989.
14. P.L. Lions, E. Rouy and A. Tourin, Shape from shading,viscosity solution and edges, Numerische Mathematik, 64 (1993), 323-353.
15. E. Prados, Application of the theory of viscosity solutions to the Shape-from-Shading problem, PhD Thesis, University of Nice - Sophia Antipolis, 2004.
16. E. Prados, O. Faugeras, Perspective Shape-from-Shading and viscosity solutions, IEEE, Proceedings of ICCV'03, 2003, 826-831.
17. E. Prados, O. Faugeras, F. Camilli Shape-from-Shading: a well posed-problem ?, Rapport de Recherche n. 5297. INRIA, 2004.
18. E. Prados, O. Faugeras, et E. Rouy, Shape from shading and viscosity solutions, Rapport de Recherche RR-4638, INRIA, November 2002.
19. E. Rouy and A. Tourin, A viscosity solutions approach to Shape from Shading, SIAM J. Numer. Anal., 29 (1992), 867-884.
20. M. Sagona, Numerical methods for degenerate eikonal type equations and applications, PhD Thesis, Università di Napoli "Federico II", 2001.
21. M. Sagona e A. Seghini, An adaptive scheme on unstructured grids for the shape-from shading problem, in [10], 197-219.