Abstract
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.
Similar content being viewed by others
References
Abramowitz, M. and Stegun, I. 1968. Handbook of Mathematical Functions.National Bureau of Standards, Washington.
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.
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.
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.
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.
Breene, R.G. 1961. The Shift and Shape of Spectral Lines.Pergamon Press: Oxford.
Brill, M. H. and West, G. 1986. Chromatic adaptation and color constancy: A possible dichotomy. Color Research and Application, 11:196-204.
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.
CIE, 1974. Method of Measuring and Specifying Colour Rendering Properties of Light Sources. Bureau Central de la CIE: Paris.
De Bruijn, N.G. 1961. Asymptotic Methods in Analysis. North-Holland Publishing Co.: Amsterdam.
Fairchild, M.D. and Lennie, P. 1992. Chromatic adaptation to natural and incandescent illuminants. Vision Research. 32:2077-2085
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.
Forsyth, D.A. 1990. A novel algorithm for color constancy. International Journal of Computer Vision, 5:5-36.
Goldberg, R.R. 1970. Fourier Transforms.Cambridge University Press: Cambridge.
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.
Lythgoe, J.N. 1979. The Ecology of Vision. Clarendon Press: Oxford
Polya, G. and Szegö, G. 1964. Aufgaben und Lehrsätze aus der Analysis, I, p. 5 (34).
Schrödinger, E. 1920. Theorie der Pigmente von grösster Leuchtkraft. Ann. Physik, 62:603-622.
Smith, V.C. and Pokorny, J. 1975. Spectral sensitivities of the foveal cone photopigments between 400 and 500 nm. Vision Research, 15:161-171.
Sproson, W.N. 1983. Color Science in Television and Display Systems. Adam Hilger Ltd.: Bristol.
Szegö, G. 1967. Orthogonal Polynomials. American Mathematical Society Colloquium Publications, Providence: Rhode Island.
Titchmarsh, E.C. 1960. The Theory of Functions. Oxford University Press: Oxford.
Thornton, W.A. 1986. Evidence for the three spectral responses of the normal human visual system. Color Research and Application, 11:160-163.
Van Trigt, C. 1990a. Smoothest reflectance functions I, definition and main results. Journal of the Optical Soc. of Am. A, 7:1891-1904.
Van Trigt, C. 1990b. Smoothest reflectance functions II, Complete results. Journal of the Optical Soc. of Am. A, 7:2208-2222.
Van Trigt, C. 1994. Metameric blacks and estimating reflectance. Journal of the Optical Society of Am. A, 11:1003-1024.
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.
Van Trigt, C. 1997. Visual system-response functions and estimating reflectance. Journal of the Optical Soc. of Am. A, 14:741-755.
Van Trigt, C. 1999. Color rendering, a reassessment, Appendix A. Color Research and Appl, 24:197-206.
Vos, J.J. and Walraven, P.L. 1971. On the derivation of the foveal receptor primaries. Vision Research, 11:799-818.
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.
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.
Whittaker, E.T. and Watson, G.N. 1962. A Course of Modern Analysis. Cambridge University Press: Cambridge.
Worthey, J.A. 1985. Limitations of color constancy. Journal of the Optical Society of America, 2:1014-1025.
Wyszecki, G. and Stiles, W.S. 1982. Color Science: Concepts and Methods, Quantitative Data and Formulae. John Wiley & Sons: New York.
Yule, J.A.C. 1967. Principles of Color Reproduction.John Wiley and Sons: New York.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
van Trigt, C. Illuminant-Dependence of Von Kries Type Quotients. International Journal of Computer Vision 61, 5–30 (2005). https://doi.org/10.1023/B:VISI.0000042932.05887.4e
Issue Date:
DOI: https://doi.org/10.1023/B:VISI.0000042932.05887.4e