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Surface Reflection: Physical and Geometrical Perspectives
July 1991 (vol. 13 no. 7)
pp. 611-634

Reflectance models based on physical optics and geometrical optics are studied. Specifically, the authors consider the Beckmann-Spizzichino (physical optics) model and the Torrance-Sparrow (geometrical optics) model. These two models were chosen because they have been reported to fit experimental data well. Each model is described in detail, and the conditions that determine the validity of the model are clearly stated. By studying reflectance curves predicted by the two models, the authors propose a reflectance framework comprising three components: the diffuse lobe, the specular lobe, and the specular spike. The effects of surface roughness on the three primary components are analyzed in detail.

[1] P. Beckmann and A. Spizzochino,The Scattering of Electromagnetic Waves from Rough Surfaces, New York: Pergamon, 1963.
[2] J. M. Bennett and L. Mattsson,Introduction to Surface Roughness and Scattering, Washington, DC: Optical Soc. Amer., 1989.
[3] R. C. Birkebak and E. R. G. Eckert, "Effects of roughness of metal surfaces on angular distribution of monochromatic reflected radiation,"J. Heat Transfer, 87, pp 85-94, Feb. 1965.
[4] E. V. Bohn,Introduction to Electromagnetic Fields and Waves, Reading, MA:Addison-Wesley, 1967.
[5] S. Chandrashekar,Radiative Transfer, New York: Dover, 1960.
[6] E. N. Coleman and R. Jain, "Obtaining 3-dimensional shape of textured and specular surface using four-source photometry,"Comput. Graphics Image Processing, vol. 18, no. 4, pp. 309-328, Apr. 1982.
[7] R. L. Cook and K. E. Torrance, "A reflectance model for computer graphics,"ACM Comput. Graphics, vol. 15, no. 3, pp. 307-316, 1981.
[8] H. Davies, "The reflection of electromagnetic waves from rough surfaces,"Proc. IEEE, Pt III, vol. 101, pp. 209-214, 1954.
[9] W. G. Egan, T. Hilgeman, and J. Reichman, "Determination of absorption and scattering coefficients for nonhomogeneous media. 1: Experiment,"Appl. Opt., vol. 12, no. 8, pp. 1816-1823, Aug. 1973.
[10] G. Healey and T. O. Binford, "Local shape for specularity," inProc. Image Understanding Workshop, vol. 2, Feb. 1987, pp. 874-887.
[11] 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.
[12] B. K. P. Horn and R. W. Sjoberg, "Calculating the reflectance map,"Appl. Opt., vol. 18, no. 11, pp. 1770-1779, June 1979.
[13] B. K. P. Horn, "Hill shading and the reflectance map,"Proc. IEEE, vol. 69, no. 1, pp. 14-47, Jan. 1981.
[14] B. K. P. Horn,Robot Vision. New York: McGraw-Hill, 1986.
[15] B. K. P. Horn and M. J. Brooks (Eds.),Shape from Shading. Cambridge, MA: MIT Press, 1989.
[16] A. F. Houchens and R. G. Hering, "Bidirectional reflectance of rough metal surfaces," inThermophysics of spacecraft and planetary bodies, New York: G. B. Heller, Eds. Academic, 1967.
[17] K. Ikeuchi, "Determining surface orientations of specular surfaces by using the photometric stereo method,"IEEE Trans. Pattern Anal. Machine Intell., vol. 3, no. 6, pp. 661-669, Nov. 1981.
[18] P. Kubelka and F. Munk, "Ein Beitrag sur Optik der Farbanstriche,"Z. Phys., vol. 12, 593, 1931.
[19] J. H. Lambert,Photometria sive de mensura de gratibus luminis, colorum et umbrae., Augsberg, Germany: Eberhard Klett, 1760.
[20] S. K. Nayar, A. C. Sanderson, L.E. Weiss, and D. D. Simon, "Specular surface inspection using structured highlight and Gaussian images,"IEEE Trans. Robotics Automat., vol. 6, no. 2, pp. 208-218, Apr. 1990.
[21] S. K. Nayar, K. Ikeuchi, and T. Kanade, "Determining shape and reflectance of hybrid surfaces by photometric sampling,"IEEE Trans. Robotics Automat., vol. 6, no. 4, pp. 418-431, Aug. 1990.
[22] S. K. Nayar, K. Ikeuchi, and T. Kanade, "Surface reflection: Physical and geometrical perspectives,"Proc. Image Understanding Workshop, pp. 185-212, Sept. 1990.
[23] F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, "Geometrical considerations and nomenclature for reflectance," NBS Monograph 160, National Bureau of Standards, Oct. 1977.
[24] A. P. Pentland, "Local shading analysis,"IEEE Trans. on Pattern Anal. Machine Intell. vol. 6, no. 2, pp. 170-187, Mar. 1984.
[25] B. T. Phong, "Illumination for computer generated pictures,"Commun. Ass. Comput. Mach., vol. 18, no. 6, June 1975.
[26] American institute of Physics Handbook., New York: McGraw-Hill, 1972.
[27] J. Reichman, "Determination of absorption and scattering coefficients for nonhomogeneous media, 1: Theory,"Appl. Opt., vol 12, no. 8, pp. 1811-1815, Aug. 1973.
[28] W. A. Rense, "Polarization studies of light diffusely reflected from ground and etched glass surfaces,"J. Opt. Soc. Amer.vol. 40, no. 1, pp. 55-59, Jan. 1950.
[29] A. C. Sanderson, L. E. Weiss, and S. K. Nayar, "Structured highlight inspection of specular surfaces,"IEEE Trans. Pattern Anal. Machine Intell. New York: vol. 10, no. 1, pp. 44-55, Jan. 1988.
[30] R. Siegel and J.R. Howell,Thermal Radiation Heat Transfer, New York: McGraw-Hill, 1972.
[31] W. M. Silver, "Determining shape and reflectance using multiple images," S. M. thesis, Dept. of Elec. Eng. and Comput. Sci., MIT, Cambridge, MA, June 1980.
[32] B. G. Smith, "Geometrical shadowing of a random rough surface,"IEEE Trans. Antennas Propag., vol. AP-15, no. 5, pp. 668-671, Sept. 1967.
[33] E. Sparrow and R. Cess,Radiation Heat Transfer, New York: McGraw-Hill, 1978.
[34] J. M. Stone,Radiation and Optics, New York: McGraw-Hill, 1963.
[35] H. D. Tagare and Rui J. P. deFigueriedo, "A framework for the construction of general reflectance maps for machine vision," Tech. Rep. Dept. of Elect. and Comput. Eng., Rice University, Houston, TX, 1988.
[36] H. D. Tagare, "Simultaneous estimation of reflectance map and surface normal using photometric stereo," inProc. Int. Conf. Computer Vision, 1990.
[37] K. Torrance and E. Sparrow, "Off-specular peaks in the directional distribution of reflected thermal radiation,"J. Heat Transfer, pp. 223-230, May 1966.
[38] K. Torrance and E. Sparrow, "Theory for off-specular reflection from roughened surfaces,"J. Opt. Soc. Amer., no. 57, pp. 1105-1114, 1967.
[39] L. B. Wolff, "Spectal and polarization stereo methods using a single light source," inProc. Image Understanding Workshop, vol. 2, Feb. 1987, pp. 81-820.
[40] R. J. Woodham, "Photometric stereo: A reflectance map technique for determining surface orientation from image intensity,"Proc. SPIE, vol. 155, pp. 136-143, 1978.

Index Terms:
surface reflection; Beckmann-Spizzichino model; Torrance-Sparrow model; machine vision; physical optics; geometrical optics; reflectance; diffuse lobe; specular lobe; specular spike; surface roughness; geometrical optics; light reflection; optical information processing; reflectivity
Citation:
S.K. Nayar, K. Ikeuchi, T. Kanade, "Surface Reflection: Physical and Geometrical Perspectives," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 13, no. 7, pp. 611-634, July 1991, doi:10.1109/34.85654
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