Page 21 - Computational Colour Science Using MATLAB

8 INTRODUCTION
consequence of this normalization is that it is only necessary to know the relative
energy of the illuminant at each wavelength.
The CIE (1931) colour-matching functions were derived from RGB colour-
matching experiments that used a bipartite field that subtended 28 (in terms of
visual angle) at the retina. A second set of colour-matching functions was
measured in 1964 using a larger (108) field size. The 1931 and 1964 colour-
matching functions are based on the same XYZ primaries but exhibit some
marked differences. One reason for this is that the distribution of cones (the light-
sensitive cells in the eye) is not uniform across the retina. For example, it is
known that there are no cones that contain short-wavelength-sensitive pigment
in the central region of the retina known as the fovea. The present situation
whereby there are two sets of colour-matching functions known as the 2-degree
(1931) and the 10-degree (1964) standard observers has served the colour
industry well over the last 70 years but is ultimately unsatisfactory. Users need to
make a choice based upon which set of colour-matching functions best represents
any given viewing situation. This presents problems from time to time when the
size of the stimulus is not exactly 28 or 108. The CIE is currently working towards
the development of a set of colour-matching functions that vary continuously for
a wide range of stimulus sizes.
The CIE XYZ tristimulus values specify a colour stimulus in terms of the
visual system. It is often useful, however, to compute the chromaticity
coordinates x and y from the tristimulus values:

x ¼ X=ðX þ Y þ ZÞ, y ¼ Y=ðX þ Y þ ZÞ: ð1:4Þ

The chromaticity diagram is derived by plotting y against x and this provides a
useful map of colour space. However, it should be noted that stimuli of identical
chromaticity but different luminance are collapsed onto the same point in the
two-dimensional plane of the chromaticity diagram. One of the benefits of the
chromaticity diagram is that, according to Grassman’s law, additive mixtures of
two primaries fall on a straight line joining the two points that represent the two
primaries in the chromaticity diagram. If three primaries are used, then the
gamut of the additive system is given by a triangle, with the vertices defined by
the chromaticities of the three primaries. The gamut of all physically realizable
colours is contained by the convex shape of the spectral locus and a straight line
that can be considered to be drawn between the two ends of the locus. It can
readily be seen that this is so if one considers any real colour stimulus to consist
of the additive sum of energy at individual wavelengths.
The CIE system of colorimetry is a system of colour specification. However, it
has two limitations which are important to understand. First, the system was
designed for colour specification rather than for colour appearance. The
chromaticities of a perfect reflecting diffuser will change as the illumination
changes. However, it has already been mentioned that the colour appearance of
such a surface would be expected to remain approximately constant under quite