Page 22 - Computational Colour Science Using MATLAB

A BRIEF REVIEW OF THE CIE SYSTEM OF COLORIMETRY 9
large changes in illumination. Secondly, the system is perceptually non-uniform.
For a given Euclidean distance between two points in XYZ space the magnitude
of the perceptual colour difference between the two stimuli represented by those
points can vary by an order of magnitude or more. This second limitation in
particular has presented industrial practitioners of colorimetry with serious
problems, and even today not all of those problems have been resolved.
Although it is useful to be able to state that two stimuli are a visual match (under
the strict conditions under which the colour-matching functions were derived) if
they have the same tristimulus values, it is also useful to be able to predict the
visual difference between two stimuli whose tristimulus values are not identical.
Ideally, we would like a uniform colour space in which equal distances in that
space correspond to equal perceptual differences.
A major advance was made by the CIE in 1976 with the introduction of the
CIELAB system of colour specification. This non-linear transform of the XYZ
values provided partial solutions to both the problems of colour appearance and
colour difference. The transformation from tristimulus values to L*a*b*
coordinates is given by

1=3
L* ¼ 116ðY=Y n Þ 16,
1=3 1=3
a* ¼ 500½ðX=X n Þ ðY=Y n Þ Š, ð1:5Þ
1=3 1=3
Š,
b* ¼ 200½ðY=Y n Þ ðZ=Z n Þ
where X , Y and Z are the tristimulus values of a specified white achromatic
n
n
n
stimulus (see Chapter 5 for the complete equations).
CIELAB provides a three-dimensional colour space where the a* and b* axes
form one plane and the lightness L* axis is orthogonal to this plane. The
CIELAB transform was intended to be used for surface colours (a separate
transform, CIELUV, was provided for use with self-luminous colour stimuli
such as those generated using additive colour-reproduction devices) and includes
several interesting features.
Firstly, the inclusion of difference signals crudely models processes that are
believed to take place in the human visual system. Thus, whereas the retina
initially captures responses derived from the cone spectral sensitivities, these
responses are combined at an early (retinal) stage of visual processing to provide
a luminance signal and two opponent signals that can be described as being
yellow-blue and red-green. Similarly, CIELAB represents colour stimuli as an
achromatic signal (L*) and two chromatic channels representing yellow-blue (b*)
and red-green (a*).
Secondly, the normalization by the illuminant achieves a colour space that
makes better predictions of colour appearance than the tristimulus space from
which it is derived. Thus, whereas the x and y chromaticities of a perfect white
surface vary with the illuminant, the CIELAB coordinates remain constant at
L* ¼ 100 and a* ¼ b* ¼ 0. CIELAB also allows the representation of a colour