Tracking level sets by level sets: A method for solving the shape from shading problem

Computer Vision and Image Understanding

Volumn 62, Issue 1, 1995, Pages 47-58

  Kimmel, Ron ^a   Bruckstein, Alfred M ^a  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0029344524     PISSN: 10773142     EISSN: None     Source Type: Journal    
DOI: 10.1006/cviu.1995.1040     Document Type: Article

References (22)

1. A.M. Bruckstein, On shape from shading: Some theoretical considerations, Electrical Engineering Report 524, Technion-Israel Institute of Technology, June 1985.
2. A. M. Bruckstein, On shape from shading, Comput. Vision Graphics Image Process. 44, 1988, 139-154.
3. P. Dupuis and J. Oliensis, An optimal control formulation and related numerical methods for a problem in shape reconstruction, Department of Computer Science COINS TR93-03, University of Massachusetts at Amherst, 1993.
4. C. L. Epstein and M. Gage, The curve shortening flow, in Wave Motion: Theory, Modeling, and Computation (A. Chorin and A. Majda, Eds.), Springer-Verlag, New York, 1987.
5. B. K. P. Horn, Obtaining shape from shading information, In The Psychology of Computer Vision (P. H. Winston, Ed.), pp. 115-155, Mc Graw-Hill, New York, 1987.
6. B. K. P. Horn, Height and gradient from shading, Int. J. Comput. Vision 5, 1990, 37-75.
7. B. K. P. Horn and M. J. Brooks (Eds.), Shape from Shading, MIT Press, Cambridge, MA, 1989.
8. R. Kimmel, Shape from shading via level sets, M.Sc. thesis. Technion-Israel Institute of Technology, June 1992. [In Hebrew].
9. R. Kimmel, A. Amir, and A.M. Bruckstein, Finding shortest paths on graph surfaces, Center for Intelligent Systems Report CIS 9301, Technion-Israel Institute of Technology, Israel, January 1993.
10. R. Kimmel and A. M. Bruckstein, Shape from shading via level sets, Center for Intelligent Systems Report CIS 9209, Technion-Israel Institute of Technology, Israel, June 1992.
11. R. Kimmel, K. Siddiqi, B. B. Kimia, and A. M. Bruckstein, Shape from shading: Level set propagation and viscosity solutions, Int. J. Comput. Vision, in press.
12. C. H. Lee and A. Rosenfeld, Improved methods of estimating shape from shading using the light source coordinate system, Artif. Intell. 26(1), 1985, 125-143.
13. R. J. Le Veque, Numerical Methods for Conservation Laws, Lectures in Mathematics, Birkhauser-Verlag, Basel, 1992.
14. J. Oliensis and P. Dupuis, Direct method for reconstructing shape from shading, in Proceedings SP1E Conference 1570 on Geometric Methods in Computer Vision, 1991, pp. 116-128.
15. S. Osher and L. Rudin, Rapid convergence of approximate solutions to shape-from-shading problem, Technical report, Cognitech Inc., 1993, unpublished.
16. S. Osher and C. W. Shu, High-order essentially nonoscillatory schemes for Hamilton-Jacobi equations, SIAM J. Numer. Anal. 28(4), 1991, 907-922.
17. S. J. Osher, A level set formulation for the solution of the Dirichlet problem for Hamilton-Jacobi equations, SIAMJ. Math. Anal. 24(5), 1993, 1145-1152.
18. S. J. Osher and J. A. Sethian, Fronts propagating with curvature dependent speed: Algorithms based on Hamilton-Jacobi formulations, J. Comput. Phys. 79, 1988, 12-49.
19. A. P, Pentland, Local shading analysis, IEEE Trans. Pattern Anal. Mack. Intell. 6(2), 1984, 170-187. Also in Shape from Shading (B. K. P. Horn and M. J. Brooks), MIT Press, Cambridge, MA, 1989.
20. E. Rouy and A. Tourin, A viscosity solutions approach to shape from-shading, SIAMJ. Numer. Anal. 29(3), 1992, 867-884.
21. J. A. Sethian, A review of recent numerical algorithms for hypersurfaces moving with curvature dependent speed, J. Different. Geom. 33, 1989, 131-161.
22. J. A. Sethian and J. Strain, Crystal growth and dendritic solidification, J. Comput. Phys. 98, 1992, 231-253.