Unifying approaches and removing unrealistic assumptions in shape from shading: Mathematics can help

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 3024, Issue , 2004, Pages 141-154

  Prados, Emmanuel ^a   Faugeras, Olivier ^a  

^a INRIA   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; APPROXIMATION ALGORITHMS; COMPUTER VISION; VISCOSITY;

BOUNDARY DATA; CONVERGENT ALGORITHMS; MATHEMATICAL FRAMEWORKS; NUMERICAL APPROXIMATIONS; NUMERICAL SOLUTION; SHAPE FROM SHADING; VISCOSITY SOLUTIONS; WEAK SOLUTION;

ALUMINUM;

EID: 35048885102     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-24673-2_12     Document Type: Article

References (30)

1. M. Bardi and I. Capuzzo-Dolcetta. Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations. Birkhauser, 1997.
2. G. Barles and P. Souganidis. Convergence of approximation schemes for fully nonlinear second order equations. Asymptotic Analysis, 4:271-283, 1991.
3. F. Camilli and A. Siconolfi. Maximal subsolutions for a class of degenerate hamilton-jacobi problems. Indiana Univ. Math. J., 48(3):1111-1132, 1999.
4. F. Camilli and A. Siconolfi. Nonconvex degenerate Hamilton-Jacobi equations. Mathematische Zeitschrift, 242:1-21, 2002.
5. F. Courteille, A. Crouzil, J.-D. Durou, and P. Gurdjos. Shape from Shading en conditions réalistes d'acquisition photographique. In Proceedings of RFIA'04, 2004.
6. P. Dupuis and J. Oliensis. An optimal control formulation and related numerical methods for a problem in shape reconstruction. The Annals of Applied Probability, 4(2):287-346, 1994.
7. J.-D. Durou and H. Maitre. On convergence in the methods of Strat and Smith for shape from shading. IJCV, 17(3):273-289, 1996.
8. M. Falcone, M. Sagona, and A. Seghini. A scheme for the shape-from-shading model with "black shadows". In Proceedings of ENUMATH 2001, 2001.
9. J. Hasegawa and C. Tozzi. Shape from shading with perspective projection and camera calibration. Computers and Graphics, 20(3):351-364, May 1996.
10. B. Horn and M. Brooks, editors. Shape from Shading. The MIT Press, 1989.
11. H. Ishii and M. Ramaswamy. Uniqueness results for a class of Hamilton-Jacobi equations with singular coefficients. Comm. Par. Diff. Eq., 20:2187-2213, 1995.
12. J. Kain and D. Ostrov. Numerical shape-from-shading for discontinuous photographic images. IJCV, 44(3):163-173, 2001.
13. K. Lee and C. Kuo. Shape from shading with perspective projection. CVGIP: Image Understanding, 59(2):202-212, 1994.
14. P.-L. Lions. Generalized Solutions of Hamilton-Jacobi Equations. Number 69 in Research Notes in Mathematics. Pitman Advanced Publishing Program, 1982.
15. P.-L. Lions, E. Rouy, and A. Tourin. Shape-from-shading, viscosity solutions and edges. Numer. Math., 64:323-353, 1993.
16. J. Oliensis. Uniqueness in shape from shading. IJCV, 2(6):75-104, 1991.
17. M. Penna. Local and semi-local shape from shading for a simple perspective image of a smooth object. CVGIP, 46:346-366, 1989.
18. E. Prados and O. Faugeras. Une approche du "Shape from Shading" par solutions de viscosité. Master's thesis, Université de Nice Sophia-Antipolis, France, 2001.
19. E. Prados and O. Faugeras. A mathematical and algorithmic study of the lambertian SFS problem for orthographic and pinhole cameras. Technical Report RR-5005, INRIA, Nov. 2003.
20. E. Prados and O. Faugeras. "Perspective Shape from Shading" and viscosity solutions. In Proceedings of ICCV'03, volume 2, pages 826-831, 2003.
21. E. Prados and O. Faugeras. A viscosity method for Shape from Shading without boudary data and some of its applications. Technical report, INRIA, To appear.
22. E. Prados, O. Faugeras, and E. Rouy. Shape from Shading and viscosity solutions. In Proceedings of ECCV'02, volume 2351, pages 790-804, May 2002.
23. E. Rouy and A. Tourin. A Viscosity Solutions Approach to Shape-from-Shading. SIAM Journal of Numerical Analysis, 29(3):867-884, June 1992.
24. H.M. Soner. Optimal control with state space constraints. SIAM J. Contr. Optim, 24:Part I: 552-562,
25. SIAM J. Contr. Optim, Part II: 1110-1122, 1986.
26. P. Soravia. Optimal control with discontinuous running cost: eikonal equation and shape from shading. In 39th IEEE CDC, pages 79-84, 2000.
27. A. Tankus, N. Sochen, and Y. Yeshurun. A new perspective [on] Shape-from-Shading. In Proceedings of ICCV'03, volume 2, pages 862-869, 2003.
28. I. Weiss. A perspective 3D formalism for shape from shading. In Proceedings of DARPA Image. Understanding Workshop, volume 2, pages 1393-1402, May 1997.
29. S. Yuen, Y. Tsui, Y. Leung, and R. Chen. Fast marching method for sfs under perspective projection. In Proceeding of VIIP'02, pages 584-589, 2002.
30. R. Zhang, P.-S. Tsai, J.-E. Cryer, and M. Shah. Shape from Shading: A survey. IEEE Trans. PAMI, 21(8):690-706, Aug. 1999.