FAST MARCHING METHOD FOR SHAPE FROM SHADING UNDER PERSPECTIVE PROJECTION

The fast marching method has recently been applied to the shape from shading problem for orthographic projection [4]. Unlike many previous researches, the method is stable and monotone, and offer a well posed solution to the shape from shading problem. In this paper, the method is extended to perspective projection using a model that accounts for the foreshortening effect of perspective projection. Experimental results on synthetic images are also reported. A simple and practical method is also presented which generates realistic synthetic testing images under perspective projection.

[1]  Berthold K. P. Horn.  Obtaining shape from shading information , 1989 .

[2]  Ron Kimmel,et al.  Optimal Algorithm for Shape from Shading and Path Planning , 2001, Journal of Mathematical Imaging and Vision.

[3]  Virginie Daru,et al.  Level Set Methods and Fast Marching Methods – Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science by J.A. Sethian (Cambridge University Press, Cambridge, UK, 1999, 2nd edition, 378 pp.) £18.95 paperback ISBN 0 521 64557 3 , 2000 .

[4]  J A Sethian,et al.  A fast marching level set method for monotonically advancing fronts. , 1996, Proceedings of the National Academy of Sciences of the United States of America.

[5]  Kyoung Mu Lee,et al.  Shape from Shading with Perspective Projection , 1994 .

[6]  P. Dupuis,et al.  Direct method for reconstructing shape from shading , 1991, Proceedings 1992 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[7]  Clésio Luiz Tozzi,et al.  Shape from shading with perspective projection and camera calibration , 1996, Comput. Graph..

[8]  Michael A. Penna,et al.  Local and semi-local shape from shading for a single perspective image of a smooth object , 1989, Comput. Vis. Graph. Image Process..

[9]  U. Ascher,et al.  A multigrid method for shape from shading , 1993 .

[10]  Michael A. Penna,et al.  A Shape From Shading Analysis for a Single Perspective Image of a Polyhedron , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[11]  C.-C. Jay Kuo,et al.  Shape from Shading with a Generalized Reflectance Map Model , 1997, Comput. Vis. Image Underst..

[12]  E. Rouy,et al.  A viscosity solutions approach to shape-from-shading , 1992 .

[13]  Aly A. Farag,et al.  A 3-D reconstruction system for the human jaw using a sequence of optical images , 2000, IEEE Transactions on Medical Imaging.