This Article 
 Bibliographic References 
 Add to: 
Reflections on Shading
July 1991 (vol. 13 no. 7)
pp. 671-679

It is demonstrated that mutual illumination can produce significant effects in real scenes. An example is presented to illustrate the difficulties that mutual illumination presents to shape recovery schemes. These effects are qualitatively modeled by the radiosity equation. Using the radiosity equation, the authors predict the occurrence of spectral events in the radiance, namely, discontinuities in the radiance and its derivatives. Experimental evidence establishes the validity of this approach. Mutual illumination can generate discontinuities in the derivatives of radiance unrelated to local geometry. It is argued that it is not possible to obtain veridical dense depth or normal maps from a shading analysis. However, discontinuities in radiance are tractably related to scene geometry and, moreover, can be detected.

[1] A. Blake, A. Zisserrman, and G. Knowles, "Surface descriptions from stereo and shading,"Image Vision Comput., vol. 3, pp. 183-191, 1985 (also included in-[20]).
[2] J. M. Brady and J. Ponce, "Toward a surface primal sketch," MIT Al-Memo 824, MIT AI Lab, Cambridge, MA, 1985.
[3] D. R. Baum, H. E. Rushmeier, and J. M. Winget, "Improving radiosity solutions through the use of analytically determined form-factors," inProc. SIGGRAPH '89, 1989, pp. 325-334.
[4] J. F. Canny, "A computational approach to edge detection,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-8, pp. 679-697, 1986.
[5] B. Carrihill and R. Hummel, "Experiments with the intensity depth ratio sensor,"CVGIP, vol. 32, pp. 337-358, 1985.
[6] M.F. Cohen and D.P. Greenberg, "The hemi-cube: A radiosity solution for complex environments," inProc. SIGGRAPH '85, 1985, pp. 31-40.
[7] M.F. Cohen D.P. Greenberg, D.S. Immel, and P.J. Brock, "An efficient radiosity approach for realistic image synthesis,"IEEE Comput. Graphics Applicat., pp. 27-35, Mar. 1986.
[8] M.F. Cohen, S.E. Chen, J.R. Wallace, and D.P. Greenberg, "A progressive refinement approach to fast radiosity image generation," inProc. SIGGRAPH '88, 1988, pp. 75-84.
[9] D.A. Forsyth and A. Zisserman, "Mutual illumination," inProc. CVPR, 1989.
[10] D.A. Forsyth and A. Zisserman, "Shape from shading in the light of mutual illumination,"Image Vision Comput., vol. 8, pp. 42-49, 1990.
[11] A. L. Gilchrist, "The perception of surface blacks and whites,"Sci. Amer., vol. 240, pp. 112-124, 1979.
[12] A. L. Gilchrist and A. Jacobsen, "Perception of lightness and illumination in a world on one reflectance,"Perception, vol. 13, pp. 5-19, 1984.
[13] C. M. Goral, K. E. Torrance, D. P. Greenberg, and B. Battaile, "Modeling the interaction of light between diffuse surfaces," inProc. SIGGRAPH '84, 1984, pp. 213-222.
[14] M.G. Hatzitheodorou and J. Kender, "An optimal algorithm for the derivation of shape from darkness," inProc. CVPR, 1988.
[15] M. G. Hatzitheodorou, "The derivation of 3D surface shape from shadows," inProc. DARPA Image Understanding, 1989.
[16] G. Healy, "Local shape from specularity," inProc. 1st ICCV, 1987, pp. 151-160.
[17] B. K. P. Horn, "Obtaining shape from shading information," P. H. Winston, Ed., inThe Psychology of Computer Vision, New York: McGraw-Hill, 1975.
[18] B. K. P. Horn, "Understanding image intensities,"Artificial Intell., vol. 8, pp. 201-231, 1977.
[19] B. K. P. Horn,Robot Vision. New York: McGraw-Hill, 1986.
[20] B. K. P. Horn, Ed.,Shape from Shading. Cambridge, MA: MIT Press, 1989.
[21] K. Ikeuchi, H. K. Nishihara, B. K. P. Horn, P. Sobalvarro, and S. Nagata, "Determining grasp configurations using photometric stereo and the PRISM binocular stereo system,"Int. J. Robot. Res., vol. 5, no. 1, 1986.
[22] K. Ikeuchi, "Determining a depth map using a dual photometric stereo,"Int. J. Robot. Res., vol. 6, no. 1, 1987.
[23] J. Kender and E. M. Smith, "Shape from darkness; deriving surface information from dynamic shadows,"Proc. AAAI, 1986.
[24] J. J. Koenderink and A. J. Van Doorn, "Photometric invariants related to solid shape,"Opt. Acta., vol. 27, pp. 981-996, 1980.
[25] J. J. Koenderink and A. J. Van Doorn, "Geometrical modes as a general method to treat diffuse interreflections in radiometry,"J. Opt. Soc. Amer., vol. 73, pp. 843-850, 1983.
[26] G. W. Meyer, H. E. Rushmeier, M. F. Cohen, D. P. Greenberg, and K. E. Torrance, "An experimental evaluation of computer graphics imagery,"ACM Trans. Graphics, vol. 5, no. 1, pp. 30-50, 1986.
[27] M. C. Morrone and R. A. Owens, "Feature detection from local energy,Patt. Recog. Lett., vol. 6, pp. 303-313, 1987.
[28] S. K. Nayar, K. Ikeuchi, and T. Kanade, "Shape from interreflections," Int. Rep. CMU-RI-TR-90-14, Carnegie-Mellon Univ., Pittsburgh, PA, 1990.
[29] B. O'Neill,Elementary Differential Geometry, New York: Academic, 1966.
[30] D.E. Pearson and J.A. Robinson, "Visual communication at very low data rates,"Proc. IEEE, vol. 74, no. 4, pp. 795-812, 1985.
[31] P. Perona and J. Malik, "Detecting and localizing edges composed of steps, peaks and roofs," inProc. 3rd Int. Conf. Comput. Vision(Osaka, Japan), 1990.
[32] H. D. Tagare and R. J. P. deFigueiredo, "A theory of photometric stereo for a general class of reflectance maps," inProc. IEEE Conf. Comput. Vision Patt. Recognition (CVPR)(San Diego, CA), June 1989, pp. 38-45.
[33] F. G. Tricomi,Integral Equations, New York: Dover, 1985.
[34] J. R. Wallace, M. F. Cohen, and D. P. Greenberg, "A two-pass solution to the rendering equation: A synthesis of ray tracing and radiosity methods," inProc. SIGGRAPH '87, 1987, pp. 311-320.
[35] J. R. Wallace, K. A. Elmquist, and E. A. Haines, "A ray tracing algorithm for progressive radiosity," inProc. SIGGRAPH '89, 1989, pp. 315-324.

Index Terms:
picture processing; mutual illumination; shape recovery; radiosity equation; veridical dense depth; normal maps; shading analysis; scene geometry; geometrical optics; light reflection; lighting; optical information processing
D. Forsyth, A. Zisserman, "Reflections on Shading," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 13, no. 7, pp. 671-679, July 1991, doi:10.1109/34.85657
Usage of this product signifies your acceptance of the Terms of Use.