A unifying and rigorous shape from shading method adapted to realistic data and applications

Journal of Mathematical Imaging and Vision

Volumn 25, Issue 3, 2006, Pages 307-328

  Prados, Emmanuel ^a   Camilli, Fabio ^b   Faugeras, Olivier ^c  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF L'AQUILA   (Italy)

^c INRIA   (France)

Author keywords

Finite differences; Hamilton Jacobi equations; Shape From Shading; States constraints; Viscosity solutions

Indexed keywords

ALGORITHMS; CONSTRAINT THEORY; NUMERICAL METHODS; PROBLEM SOLVING; VISCOSITY;

HAMILTON JACOBI EQUATIONS; SHAPE FROM SHADING; STATES CONSTRAINTS; VISCOSITY SOLUTIONS;

IMAGE ANALYSIS;

EID: 33745306258     PISSN: 09249907     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10851-006-6899-x     Document Type: Conference Paper

References (62)

1. M. Bardi and I. Capuzzo-Dolcetta, "Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations," Birkhauser, 1997.
2. G. Barles. "Solutions de viscosité des equations de hamilton-jacobi," Springer-Verlag, 1994.
3. G. Barles and P.E. Souganidis. "Convergence of approximation schemes for fully nonlinear second order equations," Asymptotic Analysis, Vol. 4, pp. 271-283, 1991.
4. M. Bell and W.T. Freeman, "Learning local evidence for shading and reflectance," In Proceedings of the International Conference on Computer Vision (ICCV'01), Vol. 1, pp. 670-677, July 2001.
5. M. S. Brown and W. B. Seales, "Document restoration using 3D shape," In ICCV'01, 2001.
6. A. M. Bruckstein. "On shape fron shading." Computer Vision Graphics Image Process, Vol. 44, pp. 139-154, 1988.
7. F. Camilli and M. Falcone. "An approximation scheme for the maximal solution of the shape-from-shading model," In ICIP'96, 1996. pp. 49-52.
8. F. Camilli and A. Siconolfi, "Maximal subsolutions for a class of degenerate hamilton-jacobi problems," Indiana Univ. Math. J., Vol. 48 no. 3, pp. 1111-1132, 1999.
9. F. Camilli and A. Siconolfi, "Nonconvex degenerate Hamilton-Jacobi equations," Mathematische Zeitschrift, Vol. 242, pp. 1-21, 2002.
10. I. Capuzzo-Dolcetta and P.-L. Lions. "Hamilton-jacobi equations with state constraints," Trans. Amer. Math. Soc., Vol. 318 no. 2, pp. 643-68, 1990.
11. S.I. Cho and H. Saito. "A Divide-and-conquer strategy in shape from shading problem," In CVRP'97, IEEE Computer Society, 1997.
12. K.M. Choi, P. Wotthington, and E.R. Hancock. "Facial pose using shape-from-shading," In BMVC'99, 1999. pp. 402-411.
13. F. Courteille, A. Crouzil, J-D. Durou, and P. Gurdjos. "Towards shape from shading under realistic photographic conditions," In ICPR'04, 2004. Vol. 2, pp. 277-280 IAPR.
14. B.L. Craine, E.R. Craine, C.J. O'Toole, and Q. Ji, "Digital imaging colposcopy: Corrected area measurements using shape-from-shading," IEEE Transactions on Medical Imaging, Vol. 17, no. 6, pp. 1003-1010, 1998.
15. P.-E. Danielsson. "Euclidean distance mapping," Computer Graphics and Image Processing, Vol. 14, no. 3, pp. 227-248, 1980.
16. P. Dupuis and J. Oliensis. "Direct method for reconstructing shape from shading," SPIE, Vol. 1570, pp. 116-128, 1991.
17. 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, no. 2, pp. 287-346, 1994.
18. P. Dupuis and J. Oliensis, "Shape from shading: Provably convergent algorithms and uniqueness results," In ECCV'94, Vol. 2, pp. 256-268, 1994.
19. J-D. Durou, M. Falcone, and M. Sagona, "A survey of numerical methods for shape from shading," Research report 2004-2-R, IRIT, January 2004.
20. J.-D. Durou and H. Maître, "On convergence in the methods of strat and smith for shape from shading," IJCV, Vol. 17, no. 3, pp. 273-289, 1996.
21. M. Falcone and M. Sagona. "An algorithm for the global solution of the shape-from-shading model," ICIAP, Vol. 1, pp. 596-603, 1997. LNCS 1310.
22. M. Falcone, M. Sagona, and A. Seghini. "A scheme for the shape-from-shading model with "black shadows"," In Proceedings of ENUMATH 2001, 2001.
23. C.H.Q. Forster and C.L. Tozzi. "Towards 3d reconstruction of endoscope images using shape from shading," In 13th Brazilian Symposium on Computer Graphics and Image Processing (SIBGRAPI). IEEE Computer Society, October 2000.
24. G. Hermosillo and O. Faugeras, "Dense image matching with global and local statistical criteria: A variational approach," In Proceedings of CVPR (1). ieee computer society, 2001.
25. B.K. Horn and M.J. Brooks, (Eds.). Shape from Shading, The MIT Press, 1989.
26. B.K.P. Horn, "Obtaining shape from shading information," In P.H. Winston, (Eds.), The Psychology of Computer Vision, McGraw-Hill, New York, 1975.
27. H. Ishii and M. Ramaswamy, "Uniqueness results for a class of Hamilton-Jacobi equations with singular coefficients," Comm. Par. Diff. Eq., Vol. 20, pp. 2187-2213, 1995.
28. R. Kimmel and A.M. Bruckstein. "Global shape-from-shading," CVGIP: Image Understanding, pp. 360-369, 1995.
29. R. Kimmel and A.M. Bruckstein, "Tracking level sets by level sets: A method for solving the shape from shading problem," Computer Vision and Image Understanding, Vol. 62, no. 2, pp. 47-58, 1995.
30. R. Kimmel and J. A. Sethian, "Optimal algorithm for shape from shading and path planning," JMIV, Vol. 14, no. 2, pp. 237-244, 2001.
31. R. Klette, R. Kozera, and K. Schlüns. "Shape from shading and photometric stereo methods," Technical Report CTTR-TR-20, University of Auckland, New Zealand, 1998.
32. C.K. Kwoh, G.N. Khan, and D.F. Gillies, "Automated endoscope navigation and advisory system from medical imaging," In Proceedings of SPIE'99, Vol. 3660, 1999.
33. P.-L. Lions. "Generalized Solutions of Hamilton-Jacobi Equations." Number 69 in Research Notes in Mathematics. Pitman Advanced Publishing Program, 1982.
34. P.-L. Lions, E. Rouy, and A. Tourin. "Shape-from-shading, viscosity solutions and edges,"Numer. Math., Vol. 64, pp. 323-353, 1993.
35. C.S. McCamy, H. Marcus, and J.G. Davidson. A colorrendition chart. J. App. Photog. Eng., Vol. 2, pp. 95-99, 1976.
36. G.W. Meyer, "Wavelength selection for synthetic image generation," CVGIP, Vol. 41, pp. 57-79, 1988.
37. T. Okatani and K. Deguchi, "Shape reconstruction from an endoscope image by shape from shading technique for a point light source at the projection center," CVIU, Vol. 66, no. 2, pp. 119-131, May 1997.
38. J. Oliensis, "Shape from shading as a partially well-constrained problem," CVGIP: Image Understanding, Vol. 54, no. 2, pp. 163-183, 1991.
39. J. Oliensis, "Uniqueness in shape from shading," IJCV, Vol. 2, no. 6, pp. 75-104, 1991.
40. J. Oliensis and P. Dupuis, "A global algorithm for shape from shading," In Proceedings of ICCV'93, 1993, pp. 692-701.
41. E. Prados. "Une approche du "Shape from Shading" par solutions de viscosité," Master's thesis, University of Nice-Sophia Antipolis, France (In French), INRIA, September 2001.
42. E. Prados. "Application of the theory of the viscosity solutions to the Shape From Shading problem". PhD thesis, University of Nice-Sophia Antipolis, October 2004.
43. E. Prados, F. Camilli, and O. Faugeras. "A viscosity method for Shape-From-Shading without boundary data," Technical Report RR-5296, INRIA, 2004.
44. E. Prados, F. Camilli, and O. Faugeras. "A viscosity solution method for shape-from-shading without boundary data," Accepted to ESAIM: Mathematical Modelling and Numerical Analysis, 2006.
45. 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, 2003.
46. E. Prados and O. Faugeras. "Perspective shape from shading and viscosity solutions," In Proceedings of ICCV'03, Vol. 2, pp. 826-831. IEEE Computer Society, 2003.
47. E. Prados and O. Faugeras. "Unifying approaches and removing unrealistic assumptions in shape from shading: Mathematics can help," In Proceedings of ECCV'04 (4), Vol. 3024 of Lecture Notes in Computer Science, pp. 141-154. Springer, 2004.
48. 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, Nos. 1/2, pp. 97-125, 2005.
49. E. Prados, O. Faugeras, and E. Rouy. "Shape from shading and viscosity solutions," In Proceedings of ECCV'02, vol. 2351 of Lecture Notes in Computer Science, pp. 790-804. Springer, 2002.
50. E. Rouy and A. Tourin. "A viscosity solutions approach to shape-from-shading," SIAM J. of Numerical Analysis, 29(3):867-884, 1992.
51. W.A.P. Smith and E.R. Hancock. "Face recognition using shape-from-shading," In Proceedings of British Machine Vision Conference (BMVC)), pp. 597-606, September 2002.
52. Q.Y.L. Smithwick and E.J. Seibel. "Depth enhancement using a scanning fiber optical endoscope," In Proceedings of SPIE BiOS, 2002.
53. H. M. Soner. "Optimal control with state space constraints," SIAM J. Contr. Optim, 24:Part I: 552-562, Part II: 1110-1122, 1986.
54. L. E. Sucar, D. F. Gillies, and H. Rashid. "Integrating shape from shading in a gradient histogram and its application to endoscope navigation," In Proceedings of 5th International Conference on Artificial Intelligence (ICAI-V), 1992.
55. A. Tankus, N. Sochen, and Y. Yeshurun. "A new perspective [on] Shape-from-Shading," in ICCV'03, 2003, Vol. 2, pp. 862-869.
56. A. Tankus, N. Sochen, and Y. Yeshurun. "Reconstruction of medical images by perspective shape-from-shading," in JCPR'04, 2004.
57. D. Tschumperlé and R. Deriche. "Vector-valued image regularization with PDE's: A common framework for different applications," In CVPR'03, 2003.
58. T. Wada, H. Ukida, and T. Matsuyama. "Shape from shading with interreflections under proximal light source-3D shape reconstruction of unfolded book surface from a scanner image," In ICCV'95, 1995.
59. S.M. Yamany and A.A. Farag. "A system for human jaw modeling using intra-oral images," in IEEE-EMBS, 1998, Vol. 20, pp. 563-566.
60. S.Y. Yeung, H.T. Tsui, and A. Yim. "Global shape from shading for an endoscope image," in Proceedings of Medical Image Computing and Computer-Assisted Intervention (MICCAI), volume 1679 of Lecture Notes in Computer Science, Chris Taylor and Alan C. F. Colchester, (Eds.), September 1999. pp. 318-327.
61. R. Zhang, P.-S. Tsai, J.-E. Cryer, and M. Shah. "Shape from shading: A survey," IEEE Transactions on Pattern Analysis and Machine. Intelligence, Vol. 21, no. 8, pp. 690-706, August 1999.
62. W. Zhao and R. Chellappa. "Illumination-insensitive face recognition using symmetric shape-from-shading," in CVPR'00, pp. 1286-1293, 2000.