This Article 
 Bibliographic References 
 Add to: 
Where and Why Local Shading Analysis Works
February 1989 (vol. 11 no. 2)
pp. 198-206

An apparent contradiction in the shape-from-shading literature is examined. Although practical experience suggests that shape can be inferred from the local analysis of shading, mathematical analyses support the opposite. A criterion for exact surface recovery is derived, and it is shown that, as a result of surface geometry, elliptic, hyperbolic, and doubly curved surfaces could be recovered to reasonable accuracy provided that surface curvature and/or foreshortening were limited. In other words, by relaxing the requirement that surfaces be recovered exactly, it is found that local analysis of shading can provide useful descriptions of shape as evidenced by the results presented.

[1] A. Bruss, "The image irradiance equation: Its solution and application," M. I. T. AI Memo 623, Cambridge, MA, June 1981.
[2] F. P. Ferrie, "Reconstructing and interpreting the 3D shape of moving objects," Ph.D. dissertation, Dep. Elec. Eng., McGill Univ. Montréal, P. Q., Canada, Mar. 1986.
[3] F. P. Ferrie and M. D. Levine, "Deriving coarse 3D models of objects," inProc. IEEE Comput. Vision Patt. Recogn.(Ann Arbor, MI), June 5-9, 1988, pp. 345-353.
[4] B. K. P. Horn, "Shape from shading: A method for obtaining the shape of a smooth opaque object from one view," MIT Project MAC Int. Rep. TR-79 and MIT AI Lab, Tech. Rep. 232, Nov. 1970.
[5] B. K. P. Horn, "Obtaining shape from shading information," inThe Psychology of Computer Vision(P. H. Winston, Ed.). New York: McGraw-Hill, 1975, pp. 115-155, ch. 4; also inShape from Shading. Cambridge, MA: MIT Press, 1989.
[6] B. K. P. Horn, "Understanding image intensities,"Art. Intell., no. 8, pp. 201- 231, 1977.
[7] K. Ikeuchi, "Constructing a depth map from images," M. I. T. AI Memo 744, Cambridge, MA, 1983.
[8] K. Ikeuchi and B. K. P. Horn, "Numerical shape for shading and occluding boundaries,"Art. Intell., vol. 17, no. 1-3, pp. 141-184, Aug. 1981.
[9] Y. G. Leclerc, "Capturing the local structure of image discontinuities in two dimensions," inProc. IEEE Conf. Comput. Vision Pattern Recognition, San Francisco, CA, June 1985, pp. 34-39.
[10] Y. Leclerc and S. W. Zucker, "The local structure of image discontinuities in one dimension,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-9, pp. 341-355, 1987.
[11] C. Lee and A. Rosenfeld, "Improved methods of estimating shape from shading using the light source coordinate system," Univ. Maryland, College Park, Tech. Rep. TR-1277, 1983.
[12] A. P. Pentland, "Finding the illuminant direction,"J. Opt. Soc. Amer., vol. 72, pp. 448-455, Apr. 1982.
[13] A. P. Pentland, "Local shading analysis,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-6, pp. 170-187, Mar. 1984.
[14] A. P. Pentland, "Shading into texture,"Artificial Intell., vol. 29, pp. 147-170, 1986.
[15] G. B. Smith, "Shape from shading: An assessment," SRI Tech. Note 287, Menlo Park, CA, 1983.
[16] K. A. Stevens, "Surface perception from local analysis of texture and contour," Ph.D. dissertation, Dep. Elec. Eng. Comput. Sci., M.I.T., Cambridge, 1979.
[17] A. P. Witkin, "Recovering surface shape and orientation from texture,"Art. Intell., vol. 17, no. 1-3, pp. 17-45, Aug. 1981.
[18] S. W. Zucker, "Early vision," in S. Shapiro, Ed.,The Encyclopedia of Artificial Intelligence. New York: Wiley, 1987.

Index Terms:
picture processing; local shading analysis; surface recovery; surface curvature; picture processing
F.P. Ferrie, M.D. Levine, "Where and Why Local Shading Analysis Works," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 11, no. 2, pp. 198-206, Feb. 1989, doi:10.1109/34.16715
Usage of this product signifies your acceptance of the Terms of Use.