International Journal of Computer Vision

, Volume 61, Issue 1, pp 5–30 | Cite as

Illuminant-Dependence of Von Kries Type Quotients

  • C. van Trigt


A von Kries quotient is defined as the cone signal of a reflectance under some illuminant divided by the same cone signal of the illuminant. A von Kries type quotient is a similar ratio, the cone sensitivity being replaced with some linear combination of the F color matching functions P(λ). We study the illuminant-(in)dependent behavior of von Kries type quotients by means of an expansion consisting of one illuminant-independent term and a series of illuminant-dependent ones. It is proved that the series rapidly decreases and that the dominating first term is small if P(λ) is a narrow function of wavelength and the reflectance and spectral distribution functions are sufficiently broad-band, defined in the text. Von Kries type quotients have a favorable illuminant-independent behavior if and only if the reflectance and spectral distribution functions are smooth functions of wavelength with chromaticity coordinates in a restricted neighborhood of the achromatic point belonging to the equal-energy spectrum, dependent on the narrowness of P(λ), comprising the object color solid only if P(λ) were a delta-function.

von Kries hypothesis colour constancy discounting the illuminant chromatic adaptation narrow sensor reflectance spectral distribution function 


  1. Abramowitz, M. and Stegun, I. 1968. Handbook of Mathematical Functions.National Bureau of Standards, Washington.Google Scholar
  2. Bäuml, K.-H. 1999. Color constancy: The role of image surfaces in illuminant adjustment. Journal of the Optical Soc. of Am. A, 16:1521-1529.Google Scholar
  3. Bäuml, K.-H. 1995. Illuminant changes under different surface collections: Examining some principles of colour appearance. Journal of the Optical Soc. of Am. A, 12:261-271.Google Scholar
  4. Brainard, D.H. and Wandell, B.A. 1992. Asymmetric color matching: How appearance depends on the illuminant. Journal of the Optical Soc. of Am. A, 9:1433-1448.Google Scholar
  5. Brainard, D.H., Brunt, W.A., and Speigle, J.M. 1997. Color constancy in the nearly natural image. I. Asymetric matches. Journal of the Optical Soc. of Am. A, 14:2091-2110.Google Scholar
  6. Breene, R.G. 1961. The Shift and Shape of Spectral Lines.Pergamon Press: Oxford.Google Scholar
  7. Brill, M. H. and West, G. 1986. Chromatic adaptation and color constancy: A possible dichotomy. Color Research and Application, 11:196-204.Google Scholar
  8. Chichilnisky, E.J. and Wandell, B.A. 1995. Photoreceptor sensitivity changes explain color appearance shift induced by large uniform backgrounds in dichoptic matching. Vision Research, 35:239-254.Google Scholar
  9. CIE, 1974. Method of Measuring and Specifying Colour Rendering Properties of Light Sources. Bureau Central de la CIE: Paris.Google Scholar
  10. De Bruijn, N.G. 1961. Asymptotic Methods in Analysis. North-Holland Publishing Co.: Amsterdam.Google Scholar
  11. Fairchild, M.D. and Lennie, P. 1992. Chromatic adaptation to natural and incandescent illuminants. Vision Research. 32:2077-2085Google Scholar
  12. Finlayson, G.D., Drew, M.S., and Funt, B.V. 1994 Spectral sharpening: Sensor transformations for improved color constancy. Journal of the Optical Soc. of America A, 11:1553-1563.Google Scholar
  13. Forsyth, D.A. 1990. A novel algorithm for color constancy. International Journal of Computer Vision, 5:5-36.Google Scholar
  14. Goldberg, R.R. 1970. Fourier Transforms.Cambridge University Press: Cambridge.Google Scholar
  15. Judd, D.B., MacAdam, D.L., and Wyszecki, G.W. 1964. Spectral distribution of typical daylight as a function of correlated color temperature. Journal of the Optical Society of Am, 54:1031-1040.Google Scholar
  16. Lythgoe, J.N. 1979. The Ecology of Vision. Clarendon Press: OxfordGoogle Scholar
  17. Polya, G. and Szegö, G. 1964. Aufgaben und Lehrsätze aus der Analysis, I, p. 5 (34).Google Scholar
  18. Schrödinger, E. 1920. Theorie der Pigmente von grösster Leuchtkraft. Ann. Physik, 62:603-622.Google Scholar
  19. Smith, V.C. and Pokorny, J. 1975. Spectral sensitivities of the foveal cone photopigments between 400 and 500 nm. Vision Research, 15:161-171.Google Scholar
  20. Sproson, W.N. 1983. Color Science in Television and Display Systems. Adam Hilger Ltd.: Bristol.Google Scholar
  21. Szegö, G. 1967. Orthogonal Polynomials. American Mathematical Society Colloquium Publications, Providence: Rhode Island.Google Scholar
  22. Titchmarsh, E.C. 1960. The Theory of Functions. Oxford University Press: Oxford.Google Scholar
  23. Thornton, W.A. 1986. Evidence for the three spectral responses of the normal human visual system. Color Research and Application, 11:160-163.Google Scholar
  24. Van Trigt, C. 1990a. Smoothest reflectance functions I, definition and main results. Journal of the Optical Soc. of Am. A, 7:1891-1904.Google Scholar
  25. Van Trigt, C. 1990b. Smoothest reflectance functions II, Complete results. Journal of the Optical Soc. of Am. A, 7:2208-2222.Google Scholar
  26. Van Trigt, C. 1994. Metameric blacks and estimating reflectance. Journal of the Optical Society of Am. A, 11:1003-1024.Google Scholar
  27. Van Trigt, C. 1994. Color Video system with illuminant-independent properties. International patent application PCT/NL 94/00049, United States Patent 5,905,543, granted May 18, 1999.Google Scholar
  28. Van Trigt, C. 1997. Visual system-response functions and estimating reflectance. Journal of the Optical Soc. of Am. A, 14:741-755.Google Scholar
  29. Van Trigt, C. 1999. Color rendering, a reassessment, Appendix A. Color Research and Appl, 24:197-206.Google Scholar
  30. Vos, J.J. and Walraven, P.L. 1971. On the derivation of the foveal receptor primaries. Vision Research, 11:799-818.Google Scholar
  31. Werner, J. and Walraven, J. 1982. Effect of chromatic adaptation on the achromatic locus: The role of contrast, luminance and background color. Vision Research, 22:929-943.Google Scholar
  32. West, G. and Brill, M.H. 1982. Necessary and sufficient conditions for von Kries chromatic adaptation to give colour constancy. Journal Mathematical Biology, 15:249-258.Google Scholar
  33. Whittaker, E.T. and Watson, G.N. 1962. A Course of Modern Analysis. Cambridge University Press: Cambridge.Google Scholar
  34. Worthey, J.A. 1985. Limitations of color constancy. Journal of the Optical Society of America, 2:1014-1025.Google Scholar
  35. Wyszecki, G. and Stiles, W.S. 1982. Color Science: Concepts and Methods, Quantitative Data and Formulae. John Wiley & Sons: New York.Google Scholar
  36. Yule, J.A.C. 1967. Principles of Color Reproduction.John Wiley and Sons: New York.Google Scholar

Copyright information

© Kluwer Academic Publishers 2005

Authors and Affiliations

  • C. van Trigt
    • 1
  1. 1.Saturnus 8HeezeThe Netherlands

Personalised recommendations