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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 15, Iss. 11 — Nov. 1, 1998
  • pp: 2903–2912

Phenomenological description of bidirectional surface reflection

Jan J. Koenderink and Andrea J. van Doorn  »View Author Affiliations

JOSA A, Vol. 15, Issue 11, pp. 2903-2912 (1998)

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General surface scattering is characterized through the bidirectional reflection distribution function (BRDF). The BRDF is a function of the directions of the incident and remitted beams and thus depends on four parameters. Under very general assumptions one shows that the BRDF is invariant under interchange of the incident and remitted beams, the so-called Helmholtz reciprocity. For isotropic surfaces the BRDF depends only on the absolute value of the difference between the azimuths of the incident and remitted beams. Since these exhaust the symmetries, the BRDF is a very complicated function. For many applications it would be advantageous to be able to summarize empirical data or to smooth and/or interpolate (often even extrapolate) BRDF data. We present a principled way to do this, exactly respecting the symmetry properties.

© 1998 Optical Society of America

OCIS Codes
(120.5630) Instrumentation, measurement, and metrology : Radiometry
(120.5700) Instrumentation, measurement, and metrology : Reflection
(240.6700) Optics at surfaces : Surfaces
(290.0290) Scattering : Scattering

Original Manuscript: January 26, 1998
Revised Manuscript: May 27, 1998
Manuscript Accepted: July 29, 1998
Published: November 1, 1998

Jan J. Koenderink and Andrea J. van Doorn, "Phenomenological description of bidirectional surface reflection," J. Opt. Soc. Am. A 15, 2903-2912 (1998)

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  1. K. J. Dana, B. van Ginneken, S. K. Nayar, J. J. Koenderink, “Reflectance and texture of real-world surfaces,” (Columbia University, New York, 1996).
  2. L. da Vinci, Treatise on Painting, A. P. McMahon, transl. (Princeton U. Press, Princeton, N.J., 1959).
  3. G. Kortüm, Reflectance Spectroscopy, J. E. Lohr, transl. (Springer-Verlag, Berlin, 1969).
  4. S. K. Nayar, K. Ikeuchi, T. Kanade, “Surface reflection: physical and geometrical perspectives,” IEEE Trans. Pattern. Anal. Mach. Intell. 13, 611–634 (1991). [CrossRef]
  5. S. K. Nayar, M. Oren, “Visual appearance of matte surfaces,” Science 267, 1153–1156 (1995). [CrossRef] [PubMed]
  6. F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, T. Limperis, “Geometrical considerations and nomenclature for reflectance,” (National Bureau of Standards, Washington, D.C., 1977).
  7. H. L. F. von Helmholtz, Treatise on Physiological Optics (Dover, New York, 1962), Vol. I, p. 231.
  8. M. Minnaert, “The reciprocity principle in lunar photometry,” Astrophys. J. 93, 403–410 (1941). [CrossRef]
  9. M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1959).
  10. P. Beckmann, A. Spizzochino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963).
  11. B. K. P. Horn, M. J. Brooks, Shape from Shading (MIT Press, Cambridge, Mass., 1989).
  12. B. K. P. Horn, R. W. Sjoberg, “Calculating the reflectance map,” Appl. Opt. 18, 1770–1779 (1979). [CrossRef] [PubMed]
  13. M. Oren, S. K. Nayar, “Generalization of the Lambertian model and implications for machine vision,” Int. J. Comput. Vis. 14, 227–251 (1995). [CrossRef]
  14. M. Oren, S. K. Nayar, “Generalization of Lambert’s reflectance model,” , 239–246 (1994).
  15. H. D. Tagare, R. J. P. deFegueiredo, “A theory of photometric stereo for a class of diffuse non-Lambertian surfaces,” IEEE Trans. Pattern Anal. Mach. Intell. 13, 133–152 (1991). [CrossRef]
  16. K. E. Torrance, E. M. Sparrow, “Theory of off-specular reflection from roughened surfaces,” J. Opt. Soc. Am. 57, 1105–1114 (1967). [CrossRef]
  17. J. H. Lambert, Photometria sive de mensura de gradibus luminis, colorum et umbræ (Eberhard Klett, Augsburg, Germany, 1760).
  18. B. G. Smith, “Geometrical shadowing of a random rough surface,” IEEE Trans. Antennas Propag. AP-15, 668–671 (1967). [CrossRef]
  19. E. Öpik, “Photometric measures of the moon and the earth-shine” [Publications de L’Observatorie Astronomical de L’Université de Tartu (Estonia), 1924], Vol. 26, pp. 1–68.
  20. J. F. Blinn, “Models of light reflection for computer synthesized pictures,” , 542–547 (1977).
  21. R. L. Cook, K. E. Torrance, “A reflectance model for computer graphics,” ACM Comput. Graphics 15, 309–328 (1982).

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