Page 97 - Computational Colour Science Using MATLAB

84 CHROMATIC-ADAPTATION TRANSFORMS AND COLOUR APPEARANCE
at least loosely based on the von Kries model of adaptation. The likely
mechanism underlying this process is that under a reddish light, for example, the
long-wavelength-sensitive cones in particular will adapt and so become less
sensitive. Under a bluish light, however, the sensitivity of the long-wavelength-
sensitive cones will increase. In this way, the idea is that the cone responses for a
given surface will stay almost the same even when the illumination is changed,
and that the visual system will be able to use the cone excitations to provide a
constant appearance for a surface when the illumination changes even though
the spectral distribution of light entering the eye is changed.
The changes in sensitivity can be modelled for a static visual system by
assuming that the cone responses for a surface under one illuminant can be
predicted from those under another illuminant by simple scaling factors. Thus,
the long-wavelength response for a surface viewed under one light source can be
obtained by multiplying the long-wavelength response for the surface viewed
under a different light source by a scalar. The scalar values may be different for
each cone class but critically do not depend upon the reflectance or chromaticity
of the sample. In terms of linear algebra we can state that the cone responses for
(a sample viewed under) one illuminant can be related to those for another
illuminant by a linear transform. Since the linear transform’s system matrix has
non-zero entries only along the major diagonal, it is referred to as a diagonal
transform. Thus, for example, the cone responses under one illuminant
(represented by the 361 column matrix e ) are related to the cone responses
1
under a second illuminant (represented by the 361 column matrix e ) by the
2
diagonal matrix D, thus
e 2 ¼ De 1 , ð6:1Þ

where the coefficients of the diagonal matrix are given by the ratios of the long-,
medium-, and short-wavelength-sensitive cone responses for a white object
viewed under each of the two illuminants,
2 3
0 0
L 2 /L 1
0 0 .
4 5
D ¼ M 2 /M 1
0 0 S 2 /S 1
The von Kries law is sometimes called the coefficient law or the scaling law since
it assumes that the effect of an illumination change can be modelled simply by
scaling the tristimulus values or cone responses by scalars or coefficients (the
diagonal elements of D). When the von Kries adaptation transform is performed
using cone space, Terstiege (1972) has termed this a genuine von Kries
transformation, whereas in practice it is often carried out in CIE XYZ space or in
an RGB space when it is referred to as a wrong von Kries transformation.
Analyses of experimental data suggest that although Equation (6.1) cannot
perfectly predict the performance of observers in psychophysical experiments,
psychophysical data can be modelled by such a system at least to a first-order