Page 19 - Computational Colour Science Using MATLAB

6 INTRODUCTION
and B, then it is possible to write an equation to denote the matching
condition:
S R½RŠþ G½GŠþ B½BŠ: ð1:1Þ

In this equation the symbol means ‘is matched by’ and the stimulus is denoted
by S. If the tristimulus values are measured separately for each wavelength in the
visible spectrum, then we obtain the tristimulus values as functions of the
wavelength l: R(l), G(l) and B(l). These three functions of wavelength are
called colour-matching functions. The additivity and linearity of colour matches
allow an important property: if a stimulus S is matched by R , G and B and a
1
1
1
1
stimulus S is matched by R , G and B , then it is possible to predict in advance
2
2
2
2
the tristimulus values that define a match to the stimulus defined by the additive
mixture S +S . Thus we can simply write
2
1
S 1 þ S 2 ðR 1 þ R 2 Þ½RŠþðG 1 þ G 2 Þ½GŠþðB 1 þ B 2 Þ½BŠ: ð1:2Þ
Since any real stimulus can be considered to be the sum of energy at many
different wavelengths, it is possible to predict the tristimulus values for any
stimulus in a similar way (without having to resort to physically determining a
visual match for that stimulus using a bipartite colorimeter) given that the
colour-matching functions are known.
In fact, experiments were carried out prior to the publication of the CIE
system by two groups of workers, headed by Wright in 1929 and Guild in 1931,
to determine colour-matching functions. The two groups of workers used
different primaries and consequently the two sets of colour-matching functions
were different. This raises an interesting question: Are the colour-matching
functions arbitrary, given that there is a very wide choice in the selection of the
primaries? Certainly, the actual tristimulus values obtained for a given stimulus
are arbitrary in that they would be different if a different set of primaries was
chosen. However, the matching condition is valid no matter which primaries are
selected subject to some simple criteria (for example, the primaries must be
independent; in other words, it must not be possible to match one of the
primaries using an additive mixture of the other two, etc.). This means that if two
stimuli are a visual match and are specified by the same tristimulus values under
Guild’s system, then they would also be a match under Wright’s system.
Furthermore, the two stimuli would be a match under a system defined by any
other set of three primaries.
It is possible to convert tristimulus values from one system to another by a
simple linear transform (see Chapter 2). It is also possible to compute the colour-
matching functions for a set of known primaries given the colour-matching
functions of another set of primaries. Thus, in 1931 the CIE transformed the two
sets of colour-matching functions obtained from experiments carried out by
Wright and Guild into a single set of colour-matching functions and reassuringly
found good agreement between the two sets of data. The CIE system as we know