This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
A Shape-from-Shading Method of Polyhedral Objects Using Prior Information
April 2006 (vol. 28 no. 4)
pp. 612-624
Hisashi Shimodaira, IEEE Computer Society
We propose a new method for recovering the 3D shape of a polyhedral object from its single 2D image using the shading information contained in the image and the prior information on the object. In a strict sense, we cannot recover the shape of a polyhedron from an incorrect line drawing, even if it is practically almost correct. In order to overcome this problem, we propose a flexible face positioning method that can permit inconsistencies in the recovered shape that arise from vertex-position errors contained in incorrect line drawings. Also, we propose to use prior information about the horizontality and verticality of special faces and the convex and concave properties of the edges in order to attain good solutions and present a method of formulating such prior information as physical constraints. The shape-from-shading method is formulated as a minimization problem of a nonlinear cost function with the nonlinear constraints and its solution is searched by a global optimization algorithm. In the experiments with a synthetic image and three kinds of real images, shapes that are similar to those of the actual objects were recovered in all cases. As a result, the proposed method has proven to be effective in the shape recovery of simple-shape polyhedral objects.

[1] R. Zhang, P.S. Tsai, J.E. Cryer, and M. Shah, “Shape from Sshading: A Survey,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 21, no. 8, pp. 690-706, Aug. 1999.
[2] P.K.P. Horn, “Understanding Image Intensity,” Artificial Intelligence, vol. 8, pp. 201-231, 1977.
[3] K. Sugihara, “An Algebraic Approach to Shape-from-Image Problems,” Artificial Intelligence, vol. 23, pp. 59-95, 1984.
[4] M.A. Penna, “A Shape from Shading Analysis for a Single Perspective Image of a Polyhedron,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 11, no. 6, pp. 545-554, June 1989.
[5] X. Huang and J. Gu, “A Constraint Network Based Approach to a Shape from Shading Analysis of a Polyhedron,” Proc. Int'l Joint Conf. Neural Networks, vol. 1, pp. 441-446, 1992.
[6] Y. Okamoto, N. Ohnishi, and N. Sugie, “Shape from Shading Including Interreflections Using Interpretation of Line Drawings,” Report of Information Processing Soc. of Japan, vol. 76, no. 12, pp. 87-92, 1992.
[7] J. Yang, D. Zhang, N. Ohnishi, and N. Sugie, “Uniqueness of Shape Recovery of a Polyhedron from a Single Shading Image,” Proc. Int'l Soc. for Optical Eng. Conf., vol. 2899, pp. 66-74, 1996.
[8] I. Shimshoni and J. Ponce, “Recovering the Shape of Polyhedra Using Line-Drawing Analysis and Complex Reflectance Models,” Computer Vision and Image Understanding, vol. 65, no. 2, pp. 296-310, 1997.
[9] D.R. Jones, C.D. Perttunen, and B.E. Stuckman, “Lipschitzian Optimization Without the Lipschitz Constant,” J. Optimization Theory and Application, vol. 79, no. 1, pp. 157-181, 1993.
[10] M. Oren and S.K. Nayar, “Generalization of the Lambertian Model and Implication for Machine Vision,” Int'l J. Computer Vision, vol. 14, pp. 227-251, 1995.
[11] D.A. Huffman, “Impossible Objects as Nonsense Sentences,” Machine Intelligence, vol. 6, pp. 295-324, 1971.
[12] M.B. Clowes, “On Seeing Things,” Artificial Intelligence, vol. 2, pp. 79-116, 1971.
[13] A.K. Mackworth, “Interpreting Pictures of Polyhedral Scenes,” Artificial Intelligence, vol. 4, pp. 121-137, 1973.
[14] D.A. Huffman, “Realizable Configurations of Lines in Pictures of Polyhedra,” Machine Intelligence, vol. 8, pp. 493-509, 1977.
[15] L. Ros and F. Thomas, “Overcoming Superstrictness in Line Drawing Interpretation,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 24, no. 4, pp. 456-466, Apr. 2002.
[16] K. Sugihara, “Resolvable Representation of Polyhedra,” Discrete and Computational Geometry, vol. 21, pp. 243-255, 1999.
[17] T. Poggio, V. Torre, and C. Koch, “Computational Vision and Regularization Theory,” Nature, vol. 317, no. 26, pp. 314-319, 1985.
[18] J. Canny, “A Computational Approach to Edge Detection,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 8, no. 6, pp. 679-698, June 1986.
[19] D. Waltz, “Understanding Line Drawings of Scenes with Shadows,” The Psychology of Computer Vision, pp. 19-91, 1975.
[20] W.J. Shomar and G. Seetharaman, “An Expert System for Recovering 3D Shape and Orientation from a Single View,” Computer Vision and Image Processing, pp. 459-515, 1992.

Index Terms:
Vision and scene understanding, scene analysis, 3D/stereo scene analysis, modeling and recovery of physical attributes, shape, shading.
Citation:
Hisashi Shimodaira, "A Shape-from-Shading Method of Polyhedral Objects Using Prior Information," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 28, no. 4, pp. 612-624, April 2006, doi:10.1109/TPAMI.2006.67
Usage of this product signifies your acceptance of the Terms of Use.