Abstract
Lambert's model for diffuse reflection is extensively used in computational vision. It is used explicitly by methods such as shape from shading and photometric stereo, and implicitly by methods such as binocular stereo and motion detection. For several real-world objects, the Lambertian model can prove to be a very inaccurate approximation to the diffuse component. While the brightness of a Lambertian surface is independent of viewing direction, the brightness of a rough diffuse surface increases as the viewer approaches the source direction. A comprehensive model is developed that predicts reflectance from rough diffuse surfaces. The model accounts for complex geometric and radiometric phenomena such as masking, shadowing, and interreflections between points on the surface. Experiments have been conducted on real samples, such as, plaster, clay, sand, and cloth. All these surfaces demonstrate significant deviation from Lambertian behavior. The reflectance measurements obtained are in strong agreement with the reflectance predicted by the proposed model. The paper is concluded with a discussion on the implications of these results for machine vision.
Similar content being viewed by others
References
Beckmann, P. and Spizzichino, A.The Scattering of Electromagnetic Waves from Rough Surfaces, Pergamon, New York, 1963.
Beckmann, P. “Shadowing of random rough surfaces,”IEEE Transactions on Antennas and Propagation, AP-13:384–388, 1965.
Blinn, J.F. “Models of light reflection for computer synthesized pictures,”ACM Computer Graphics (SIGGRAPH 77), 19(10):542–547, 1977.
Buhl, D., Welch, W.J. and Rea, D.G. “Reradiation and thermal emission from illuminated craters on the lunar surface,”Journal of Geophysical Research, 73(16):5281–5295, August 1968.
Cabral, B., Max, N. and Springmeyer, R. “Bidirectional reflection functions from surface bump maps,”ACM Computer Graphics (SIGGRAPH 87), 21(4):273–281, 1987.
Chandrasekhar, S.Radiative Transfer, Dover Publications, 1960.
Forsyth, D. and Zisserman, A. “Mutual illumination,”Proc. Conf. Computer Vision and Pattern Recognition, pp. 466–473, 1989.
Hapke, B.W. and Huge van Horn, “Photometric studies of complex surfaces, with applications to the moon,” Journal of Geophysical Research, 68(15):4545–4570, August 1963.
Hapke, B.W., Nelson, R.M. and Smythe, W.D. “The opposition effect of the moon: The contribution of coherent backscatter,”Science, 260(23):509–511, April 1993.
Hering, R.G. and Smith, T.E. “Apparent radiation properties of a rough surface,”AIAA Progress in Astronautics and Aeronautics, 23:337–361, 1970.
Horn, B.K.E. and Brooks, M.J. editors,Shape from Shading, The MIT Press, 1989.
Horn, B.K.E.Robot Vision, The MIT Press, 1986.
Jakob, M.Heat Transfer, Wiley, 1957.
Kajiya, J.T. “Anisotropic reflection model,”ACM Computer Graphics (SIGGRAPH 91), 25(4): 175–186, 1991.
Koenderink, J.J. and van Doom, A.J. “Geometrical modes as a general method to treat diffuse interreflections in radiometry,”Journal of the Optical Society of America, 73(6):843–850, 1983.
Kuga, Y. and Ishimaru, A. “Retroreflectance from a dense distribution of spherical particles,”Journal of the Optical Society of America A, 1(8):831–835, August 1984.
Lambert, J.H. “Photometria sive de mensure de gratibus luminis, colorum umbrae,”Eberhard Klett, 1760.
Minnaert, M. “The reciprocity principle in lunar photometry,”AstrophysicalJournal, 93:403–410, 1941.
Nayar, S.K., Ikeuchi, K. and Kanade, T. “Shape from interreflections,”International Journal of Computer Vision, 6:(3):173–195, 1991.
Nayar, S.K., Ikeuchi, K. and Kanade, T. “Surface reflection: Physical and geometrical perspectives,”IEEE Transactions on Pattern Analysis and Machine Intelligence, 13(7):611–634, July 1991.
Nicodemus, F.E., Richmond, J.C. and Hsia, J.J.Geometrical Considerations and Nomenclature for Reflectance, National Bureau of Standards, October 1977, Monograph No. 160.
Oetking, P. “Photometric studies of diffusely reflecting surfaces with application to the brightness of the moon,”Journal of Geophysical Research, 71(10):2505–2513, May 1966.
Opik, E. “Photometric measures of the moon and the earth-shine,”Publications de L'Observatorie Astronomical de L'Universite de Tartu, 26(1):1–68, 1924.
Oren, M. and Nayar, S.K. “Diffuse reflectance from rough surfaces,”IEEE Conference on Computer Vision and Pattern Recognition, June 1993.
Orlova, N.S. “Photometric relief of the lunar surface,”Astron. Z, 33(100):93–100, 1956.
Poulin, P. and Fournier, A. “A model for anisotropic reflection,” ACMComputer Graphics (SIGGRAPH 90), 24(4):273–282, 1990.
Press, W.H., Flannery, B.P., Teukolsky, S.A. and Vetterling, W.T.Numerical Recipes in C, Cambridge University Press, 1989.
Siegel, R. and Howell, J.R.Thermal Radiation Heat Transfer, Hemisphere Publishing Corporation, third edition, 1972.
Smith, B.G. “Lunar surface roughness: Shadowing and thermal emission,”Journal of Geophysical Research, 72(16):4059–4067, August 1967.
Tagare, H.D. and deFigueiredo, R.J.P. “A theory of photometric stereo for a class of diffuse non-Lambertian surfaces,”IEEE Transactions on Pattern Analysis and Machine Intelligence, 13(2):133–152, February 1991.
Torrance, K. and Sparrow, E. “Theory for off-specular reflection from rough surfaces,”Journal of the Optical Society of America, 57:1105–1114, September 1967.
Tsang, L. and Ishimaru, A. “Backscattering enhancement of random discrete scatterers,”Journal of the Optical Society of America A, 1(8):836–839, August 1984.
Wagner, R.J. “Shadowing of randomly rough surfaces,”Journal of the Acoustical Society of America,41(1:138–147, June 1966.
Woodham, R.J. “Photometric method for determining surface orientation from multiple images,”Optical Engineering, 19(1):139–144, January-February 1980.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Oren, M., Nayar, S.K. Generalization of the Lambertian model and implications for machine vision. Int J Comput Vision 14, 227–251 (1995). https://doi.org/10.1007/BF01679684
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01679684