Abstract

Shape-from-shading (SFS) is to reconstruct three-dimensional (3D) shape from a single gray image, which is an important problem in computer vision. We propose a novel SFS method based on hybrid reflection model which contains both diffuse reflectance and specular reflectance. The intensity gradient of image is in the direction that the shape of surface changes most, so we use directional derivative of the reflectance map as parts of objective function. When discrete characteristic of digital images is considered, finite difference approximates differential operator. So the reflectance map equation described by a partial differential equation (PDE) turns into an algebra equation about the unknown surface height correspondingly. Using iterative numeric computation, a new SFS method is gained. Experiments on synthesis and real images show that the proposed SFS method is accurate and fast.

© 2007 Chinese Optics Letters

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  1. B. K. P. Horn, in P. H. Winston, (ed.) The Psychology of Computer Vision (McGraw-Hill, New York, 1975) Chap.4, pp.115-155.
  2. B. K. P. Horn, Int. J. Computer Vision 5, 37 (1990).
  3. R. Zhang, P.-S. Tsai, J. E. Cryer, and M. Shah, IEEE Trans. Pattern Analysis and Machine Intelligence 21, 690 (1999).
  4. S.-Y. Cho and T. W. S. Chow, Neural Computation 14, 2751 (2002).
  5. J.-D. Durou, M. Falcone, and H. Sagona, IRIT Research Report 2004-2-R (2004).
  6. Y. Hu, B. Liu, F. Li, and C. Meng, Acta Photon. Sin. (in Chinese) 32, 985 (2003).
  7. C.-T. Lin, W.-C. Cheng, and S.-F. Liang, IEEE Trans. Neural Networks 16, 1601 (2005).
  8. A. Tankus, N. Sochen, and Y. Yeshurun, Int. J. Computer Vision 63, 21 (2005).
  9. R. Kimmel and J. A. Sethian, J. Mathematical Imaging and Vision 14, 237 (2001).
  10. L. Song, X. Qu, K. Xu, and L. Lu, NDT-E International 38, 381 (2005).
  11. A. G. Bors, E. R. Hancock, and R. C. Wilson, IEEE Trans. Pattern Analysis and Machine Intelligence 25, 974 (2003).
  12. H. D. Tagare and R. J. P. deFigueiredo, IEEE Trans. Pattern Analysis and Machine Intelligence 13, 133 (1991).
  13. R. Zhang and M. Shah, IEEE Trans. Systems Man and Cybernetics A 29, 318 (1999).

2005 (3)

C.-T. Lin, W.-C. Cheng, and S.-F. Liang, IEEE Trans. Neural Networks 16, 1601 (2005).

A. Tankus, N. Sochen, and Y. Yeshurun, Int. J. Computer Vision 63, 21 (2005).

L. Song, X. Qu, K. Xu, and L. Lu, NDT-E International 38, 381 (2005).

2003 (2)

A. G. Bors, E. R. Hancock, and R. C. Wilson, IEEE Trans. Pattern Analysis and Machine Intelligence 25, 974 (2003).

Y. Hu, B. Liu, F. Li, and C. Meng, Acta Photon. Sin. (in Chinese) 32, 985 (2003).

2002 (1)

S.-Y. Cho and T. W. S. Chow, Neural Computation 14, 2751 (2002).

2001 (1)

R. Kimmel and J. A. Sethian, J. Mathematical Imaging and Vision 14, 237 (2001).

1999 (2)

R. Zhang, P.-S. Tsai, J. E. Cryer, and M. Shah, IEEE Trans. Pattern Analysis and Machine Intelligence 21, 690 (1999).

R. Zhang and M. Shah, IEEE Trans. Systems Man and Cybernetics A 29, 318 (1999).

1991 (1)

H. D. Tagare and R. J. P. deFigueiredo, IEEE Trans. Pattern Analysis and Machine Intelligence 13, 133 (1991).

1990 (1)

B. K. P. Horn, Int. J. Computer Vision 5, 37 (1990).

Bors, A. G.

A. G. Bors, E. R. Hancock, and R. C. Wilson, IEEE Trans. Pattern Analysis and Machine Intelligence 25, 974 (2003).

Cheng, W.-C.

C.-T. Lin, W.-C. Cheng, and S.-F. Liang, IEEE Trans. Neural Networks 16, 1601 (2005).

Cho, S.-Y.

S.-Y. Cho and T. W. S. Chow, Neural Computation 14, 2751 (2002).

Chow, T. W. S.

S.-Y. Cho and T. W. S. Chow, Neural Computation 14, 2751 (2002).

Cryer, J. E.

R. Zhang, P.-S. Tsai, J. E. Cryer, and M. Shah, IEEE Trans. Pattern Analysis and Machine Intelligence 21, 690 (1999).

deFigueiredo, R. J. P.

H. D. Tagare and R. J. P. deFigueiredo, IEEE Trans. Pattern Analysis and Machine Intelligence 13, 133 (1991).

Hancock, E. R.

A. G. Bors, E. R. Hancock, and R. C. Wilson, IEEE Trans. Pattern Analysis and Machine Intelligence 25, 974 (2003).

Horn, B. K. P.

B. K. P. Horn, Int. J. Computer Vision 5, 37 (1990).

Hu, Y.

Y. Hu, B. Liu, F. Li, and C. Meng, Acta Photon. Sin. (in Chinese) 32, 985 (2003).

Kimmel, R.

R. Kimmel and J. A. Sethian, J. Mathematical Imaging and Vision 14, 237 (2001).

Li, F.

Y. Hu, B. Liu, F. Li, and C. Meng, Acta Photon. Sin. (in Chinese) 32, 985 (2003).

Liang, S.-F.

C.-T. Lin, W.-C. Cheng, and S.-F. Liang, IEEE Trans. Neural Networks 16, 1601 (2005).

Lin, C.-T.

C.-T. Lin, W.-C. Cheng, and S.-F. Liang, IEEE Trans. Neural Networks 16, 1601 (2005).

Liu, B.

Y. Hu, B. Liu, F. Li, and C. Meng, Acta Photon. Sin. (in Chinese) 32, 985 (2003).

Lu, L.

L. Song, X. Qu, K. Xu, and L. Lu, NDT-E International 38, 381 (2005).

Meng, C.

Y. Hu, B. Liu, F. Li, and C. Meng, Acta Photon. Sin. (in Chinese) 32, 985 (2003).

Qu, X.

L. Song, X. Qu, K. Xu, and L. Lu, NDT-E International 38, 381 (2005).

Sethian, J. A.

R. Kimmel and J. A. Sethian, J. Mathematical Imaging and Vision 14, 237 (2001).

Shah, M.

R. Zhang and M. Shah, IEEE Trans. Systems Man and Cybernetics A 29, 318 (1999).

R. Zhang, P.-S. Tsai, J. E. Cryer, and M. Shah, IEEE Trans. Pattern Analysis and Machine Intelligence 21, 690 (1999).

Sochen, N.

A. Tankus, N. Sochen, and Y. Yeshurun, Int. J. Computer Vision 63, 21 (2005).

Song, L.

L. Song, X. Qu, K. Xu, and L. Lu, NDT-E International 38, 381 (2005).

Tagare, H. D.

H. D. Tagare and R. J. P. deFigueiredo, IEEE Trans. Pattern Analysis and Machine Intelligence 13, 133 (1991).

Tankus, A.

A. Tankus, N. Sochen, and Y. Yeshurun, Int. J. Computer Vision 63, 21 (2005).

Tsai, P.-S.

R. Zhang, P.-S. Tsai, J. E. Cryer, and M. Shah, IEEE Trans. Pattern Analysis and Machine Intelligence 21, 690 (1999).

Wilson, R. C.

A. G. Bors, E. R. Hancock, and R. C. Wilson, IEEE Trans. Pattern Analysis and Machine Intelligence 25, 974 (2003).

Xu, K.

L. Song, X. Qu, K. Xu, and L. Lu, NDT-E International 38, 381 (2005).

Yeshurun, Y.

A. Tankus, N. Sochen, and Y. Yeshurun, Int. J. Computer Vision 63, 21 (2005).

Zhang, R.

R. Zhang and M. Shah, IEEE Trans. Systems Man and Cybernetics A 29, 318 (1999).

R. Zhang, P.-S. Tsai, J. E. Cryer, and M. Shah, IEEE Trans. Pattern Analysis and Machine Intelligence 21, 690 (1999).

Acta Photon. Sin. (in Chinese) (1)

Y. Hu, B. Liu, F. Li, and C. Meng, Acta Photon. Sin. (in Chinese) 32, 985 (2003).

IEEE Trans. Neural Networks (1)

C.-T. Lin, W.-C. Cheng, and S.-F. Liang, IEEE Trans. Neural Networks 16, 1601 (2005).

IEEE Trans. Pattern Analysis and Machine Intelligence (3)

R. Zhang, P.-S. Tsai, J. E. Cryer, and M. Shah, IEEE Trans. Pattern Analysis and Machine Intelligence 21, 690 (1999).

A. G. Bors, E. R. Hancock, and R. C. Wilson, IEEE Trans. Pattern Analysis and Machine Intelligence 25, 974 (2003).

H. D. Tagare and R. J. P. deFigueiredo, IEEE Trans. Pattern Analysis and Machine Intelligence 13, 133 (1991).

IEEE Trans. Systems Man and Cybernetics A (1)

R. Zhang and M. Shah, IEEE Trans. Systems Man and Cybernetics A 29, 318 (1999).

Int. J. Computer Vision (2)

B. K. P. Horn, Int. J. Computer Vision 5, 37 (1990).

A. Tankus, N. Sochen, and Y. Yeshurun, Int. J. Computer Vision 63, 21 (2005).

J. Mathematical Imaging and Vision (1)

R. Kimmel and J. A. Sethian, J. Mathematical Imaging and Vision 14, 237 (2001).

NDT-E International (1)

L. Song, X. Qu, K. Xu, and L. Lu, NDT-E International 38, 381 (2005).

Neural Computation (1)

S.-Y. Cho and T. W. S. Chow, Neural Computation 14, 2751 (2002).

Other (2)

J.-D. Durou, M. Falcone, and H. Sagona, IRIT Research Report 2004-2-R (2004).

B. K. P. Horn, in P. H. Winston, (ed.) The Psychology of Computer Vision (McGraw-Hill, New York, 1975) Chap.4, pp.115-155.

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