1.3.4 Systematization of colour

Figure 1.6: A Maxwell triangle representing the colour space of red,
green and blue primaries. The secondary colours (cyan, magenta
and yellow) are on the edges of the triangle, half way between the
primaries (at points C, M and J respectively); white (‘equalenergy
white’) is at point E. The dashed line is a mixture line, and indicates
the positions of the colours in this diagram producable by mixing red
and cyan light together; P is a pink mixture of red and cyan.
Given three specific additive primary stimuli, we can represent the
colour or chromaticity of an additive mixture as a point inside a
triangle with the primaries at the corners, known as a Maxwell
triangle; the gamut of colours expressible by all possible mixtures of
these primaries lies within or on the edge of the triangle (see figure
1.6). The chromaticity that is represented in Maxwell’s triangle is
the qualitative aspect of psychophysical colour; the quantity of that
colour – corresponding to brightness or luminance – is not
represented.
To work out the position of a mixture of primaries in the Maxwell
triangle, let r, g and b be the amounts of red, green and blue in the
mixture. Then the position is at xcoordinate
r
r+g+b and ycoordinate
g
r+g+b ; for example, if r = 60, g = 80 and b = 60 (a greenish gray),
the chromaticity coordinates are (0.3,0.4) and the total luminance is
200.
Using this coordinate system, we can now specify precisely colours
as an additive mixture of specified primaries, produced perhaps in
some wellde
fined physical situation. However, as mentioned in
section 1.2.2 above, it is not possible to find any three stimuli which
can produce all visible colours by addition; the gamut of all colours
does not form a triangle – instead, to match some colours, it is
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CC227 Creative Computing II Perception and Information Retrieval
necessary to add primaries to that colour in order to produce
something that can be matched with the other primaries.
The Commission internationale de l’´eclairage or CIE is an
international authority on light, colour and illumination; it was
established in 1913, and has produced standards for describing
colours unambiguously. The colour space in question resembles
figure 1.6, with three primary stimuli, but the primaries themselves
do not correspond to visible colours – the gamut of the primaries is
larger than that of all colours.
700
600
560
520
500
490
480
380
y
x 0 0.5
0
0.5
Figure 1.7: The CIE 1931 standard observer on the xy plane. The
gamut of visible colours lies within the thick line; all other points
in the plane contain impossible negative components of some real
colour. The dotted line is the limit of the (imaginary) CIE 1931
gamut; colours from pure wavelengths lie along the the thick solid
curve (the numbers correspond to the wavelength in nanometres),
and the thick dashed curve is the ‘purple line’, nonspectral
colours
which are perceptually a mixture of red and blue.
The CIE 1931 colour space selected three imaginary primaries,
known to as the CIE 1931 standard observer. The quantity of the
imaginary primaries (or tristimulus values) X, Y and Z, then define
a specific colour; exactly as with red, green and blue, we can
construct a Maxwell triangle for the chromaticity in that colour
space, defining x = X
X+Y +Z and y = Y
X+Y +Z . The resulting
chromaticity diagram for the CIE 1931 colour space is shown in
figure 1.7; any visible colour can be specified by its position in that
chromaticity diagram, along with a luminance value. To convert
back from chromaticity and luminance (xyY values) to tristimulus
(XYZ) values, we use X = x
y Y and Z = 1−x−y
y Y .
The CIE 1931 colour space is adequate for its intended purpose,
which is to specify all possible visible colours unambiguously; as an
example of its use, we can now present the colours that people with
particular forms of anomalous vision will be unable to distinguish,
as in figure 1.8. It does not, however, represent a perceptually
uniform space; there is much more resolution in the green area
(around 500nm) than the red and blue, even allowing for the
greater sensitivity of the eye to greens. This means that the CIE
1931 space does not represent colour differences in a uniform way;