ABSTRACT
Lambert's model for body reflection is widely used in computer graphics. It is used extensively by rendering techniques such as radiosity and ray tracing. For several real-world objects, however, Lambert's model can prove to be a very inaccurate approximation to the body reflectance. While the brightness of a Lambertian surface is independent of viewing direction, that of a rough surface increases as the viewing direction approaches the light source direction. In this paper, a comprehensive model is developed that predicts body reflectance from rough surfaces. The surface is modeled as a collection of Lambertian facets. It is shown that such a surface is inherently non-Lambertian due to the foreshortening of the surface facets. Further, the model accounts for complex geometric and radiometric phenomena such as masking, shadowing, and interreflections between facets. Several experiments have been conducted on samples of rough diffuse surfaces, such as, plaster, sand, clay, and cloth. All these surface demonstrate significant deviation from Lambertian behavior. The reflectance measurements obtained are in strong agreement with the reflectance predicted by the model.
Supplemental Material
Available for Download
- 1.P. Beckmann. Shadowing of random rough surfaces. IEEE Transactions on Antennas and Propagation, AP-13:384-388, 1965.Google ScholarCross Ref
- 2.P. Beckmann and A. Spizzichino. The Scattering of Electro-magnetic Waves from Rough Surfaces. Pergamon, New York, 1963.Google Scholar
- 3.J. F. Blinn. Models of light reflection for computer synthe-sized pictures. ACM Computer Graphics (SIGGRAPH 77), 19(10):542-547, 1977. Google ScholarDigital Library
- 4.D. Buhl, W. J. Welch, and D. G. Rea. Reradiation and thermal emission from illuminated craters on the lunar surface. Journal of Geophysical Research, 73(16):5281-5295, August 1968.Google ScholarCross Ref
- 5.B. Cabral, N. Max, and R. Springmeyer. Bidirectional re-flection functions from surface bump maps. ACM Computer Graphics (SIGGRAPH 87), 21(4):273-281, 1987. Google ScholarDigital Library
- 6.S. Chandrasekhar. Radiative Transfer. Dover Publications, 1960.Google Scholar
- 7.M. F. Cohen and D. P. Greenberg. The hemi-cube, a radiosity solution for complex environments. ACM Computer Graphics (SIGGRAPH 85), 19(3):31-40, 1985. Google ScholarDigital Library
- 8.R. L. Cook and K. E. Torrance. A reflection model for com-puter graphics. ACM Transactions on Graphics, 1(1):7-24, 1982. Google ScholarDigital Library
- 9.D. Forsyth and A. Zisserman. Mutual illumination. Proc. Conf. Computer Vision and Pattern Recognition, pages 466- 473, 1989.Google ScholarCross Ref
- 10.R. Hall. Illumination and Color in Computer Generated Im-agery. Springer-Verlag, 1989. Google ScholarDigital Library
- 11.P. Hanrahan and W. Krueger. Reflection from layered surfaces due to subsurface scattering. Computer Graphics Proceedings (SIGGRAPH 93), pages 165-174, 1993. Google ScholarDigital Library
- 12.B. W. Hapke, R. M. Nelson, and W. D. Smythe. The opposition effect of the moon: The contribution of coherent backscatter. Science, 260(23):509-511, April 1993.Google ScholarCross Ref
- 13.B. W. Hapke and Huge van Horn. Photometric studies of complex surfaces, with applications to the moon. Journal of Geophysical Research, 68(15):4545-4570, August 1963.Google ScholarCross Ref
- 14.X. D. He, K. E. Torrance, F. X. Sillion, and D. P. Greenberg. A comprehensive physical model for light reflection. ACM Computer Graphics (SIGGRAPH 91), 25(4):175-186, 1991. Google ScholarDigital Library
- 15.R. G. Hering and T. F. Smith. Apparent radiation proper-ties of a rough surface. AIAA Progress in Astronautics and Aeronautics, 23:337-361, 1970.Google Scholar
- 16.M. Jakob. Heat Transfer. Wiley, 1957.Google Scholar
- 17.J. T. Kajiya. Anisotropic reflection model. ACM Computer Graphics (SIGGRAPH 91), 25(4):175-186, 1991. Google ScholarDigital Library
- 18.J. J. Koenderink and A. J. van Doorn. Geometrical modes as a general method to treat diffuse interreflections in radiometry. Journal of the Optical Society of America, 73(6):843-850, 1983.Google ScholarCross Ref
- 19.Y. Kuga and A. Ishimaru. Retroreflectance from a dense dis-tribution of spherical particles. Journal of the Optical Society of America A, 1(8):831-835, August 1984.Google ScholarCross Ref
- 20.J. H. Lambert. Photometria sive de mensure de gratibus lumi-nis, colorum umbrae. Eberhard Klett, 1760.Google Scholar
- 21.M. Minnaert. The reciprocity principle in lunar photometry. Astrophysical Journal, 93:403-410, 1941.Google ScholarCross Ref
- 22.S. K. Nayar, K. Ikeuchi, and T. Kanade. Shape from in-terreflections. International Journal of Computer Vision, 6:3:173-195, 1991. Google ScholarDigital Library
- 23.F. E. Nicodemus, J. C. Richmond, and J. J. Hsia. Geometrical Considerations and Nomenclature for Reflectance. National Bureau of Standards, October 1977. Monograph No. 160.Google ScholarCross Ref
- 24.P. Oetking. Photometric studies of diffusely reflecting surfaces with application to the brightness of the moon. Journal of Geophysical Research, 71(10):2505-2513, May 1966.Google ScholarCross Ref
- 25.E. Opik. Photometric measures of the moon and the moon the earth-shine. Publications de L'Observatorie Astronomical de L'Universite de Tartu, 26(1):1-68, 1924.Google Scholar
- 26.N. S. Orlova. Photometric relief of the lunar surface. Astron. Z, 33(1):93-100, 1956.Google Scholar
- 27.P. Poulin and A. Fournier. A model for anisotropic reflection. ACM Computer Graphics (SIGGRAPH 90), 24(4):273-282, 1990. Google ScholarDigital Library
- 28.T. Shibata, W. Frei, and M. Sutton. Digital correction of solar illumination and viewing angle artifacts in remotely sensed images. Machine Processing of Remotely Sensed Data Sym-posium, pages 169-177, 1981.Google Scholar
- 29.R. Siegel and J. R. Howell. Thermal Radiation Heat Transfer. Hemisphere Publishing Corporation, third edition, 1972.Google Scholar
- 30.B. G. Smith. Lunar surface roughness: Shadowing and thermal emission. Journal of Geophysical Research, 72(16):4059-4067, August 1967.Google ScholarCross Ref
- 31.K. Torrance and E. Sparrow. Theory for off-specular reflec-tion from rough surfaces. Journal of the Optical Society of America, 57:1105-1114, September 1967.Google ScholarCross Ref
- 32.L. Tsang and A. Ishimaru. Backscattering enhancement of random discrete scatterers. Journal of the Optical Society of America A, 1(8):836-839, August 1984.Google ScholarCross Ref
- 33.S. Upstill. The RenderMan Companion. Addison Wesley, 1989.Google Scholar
- 34.R. J. Wagner. Shadowing of randomly rough surfaces. Journal of the Acoustical Society of America, 41(1):138-147, June 1966.Google ScholarCross Ref
- 35.H.W. Westin, J.R. Arvo, and K.E. Torrance. Predicting re-flectance functions from complex surfaces. ACM Computer Graphics (SIGGRAPH 92), 26(2):255-264, 1992. Google ScholarDigital Library
- 36.T. Whitted. An improved illumination model for shaded dis-play. Communications of the ACM, 23(6):343-349, 1980. Google ScholarDigital Library
Index Terms
- Generalization of Lambert's reflectance model
Recommendations
Measuring bidirectional texture reflectance with a kaleidoscope
SIGGRAPH '03: ACM SIGGRAPH 2003 PapersWe describe a new technique for measuring the bidirectional texture function (BTF) of a surface that requires no mechanical movement, can measure surfaces in situ under arbitrary lighting conditions, and can be made small, portable and inexpensive. The ...
Printing reflectance functions
The reflectance function of a scene point captures the appearance of that point as a function of lighting direction. We present an approach to printing the reflectance functions of an object or scene so that its appearance is modified correctly as a ...
Measuring bidirectional texture reflectance with a kaleidoscope
We describe a new technique for measuring the bidirectional texture function (BTF) of a surface that requires no mechanical movement, can measure surfaces in situ under arbitrary lighting conditions, and can be made small, portable and inexpensive. The ...
Comments