Page 20 - Computational Colour Science Using MATLAB

A BRIEF REVIEW OF THE CIE SYSTEM OF COLORIMETRY 7
it today is based upon a transformation of the original colour-matching
functions averaged from Guild and Wright to a set of primaries known as X, Y
and Z. The colour-matching functions are known for each wavelength and are
therefore represented by x(l), y(l) and z(l).
The CIE also defined standard illuminants – tables of spectral power
distributions – that can be used to compute the colour signal for a surface
given the spectral reflectance factors of the surface. The introduction of tables of
illuminants allowed the computation of tristimulus values for surface colours as
well as for self-luminous colours. A practical formula for computing the CIE
1931 tristimulus values for a surface with spectral reflectance P(l) under an
illuminant of relative spectral power E(l)is

X ¼ kSEðlÞPðlÞxðlÞ,
Y ¼ kSEðlÞPðlÞyðlÞ, ð1:3Þ
Z ¼ kSEðlÞPðlÞzðlÞ,
where k is 100/[S yðlÞEðlފ.
At each wavelength interval the product E(l)P(l) gives the amount of energy
in the stimulus at wavelength l and the amount of the primary required to match
this is given by multiplying this product by the colour-matching function at that
wavelength. In order to arrive at the amount of the primary required to match
the stimulus it is only necessary to sum across all wavelengths [Equation (1.3)].
Note that the implication of the normalizing factor k is that the absolute spectral
power distribution for the illuminant is not required so that, for surface colours
at least, Y ¼ 100 for a perfect white surface [for which P(l) ¼ 1 for all l].
Furthermore, note that a perfect white surface will give Y ¼ 100 for any
illuminant E. This normalisation is reasonable given the processes of adaptation
that take place in our everyday vision. In order to appreciate these processes,
imagine a piece of white paper with reflectance of 1 at all wavelengths and a piece
of black coal with reflectance 0.01 at all wavelengths. Now consider viewing these
two surfaces indoors (under an equal-energy light source with 100 units of light
at each wavelength) and outdoors (under an equal-energy light source with
10 000 units of light at each wavelength). When viewed indoors the paper reflects
100 units of light at each wavelength whereas the coal reflects only 1 unit of light
at each wavelength, but the amount of light reflected outdoors is 10 000 and 100
for the paper and coal, respectively. Even though the paper reflects 100 times as
much light outdoors as it does indoors, the colour appearance of the paper
remains approximately constant under the two light sources. More surprisingly,
the coal reflects as much light outdoors as the paper does indoors and yet the
coal is veridically seen as black. This remarkable property of colour constancy is
central to our whole visual experience. The normalizing factor k in the CIE
system ensures that for a perfectly white surface the Y tristimulus value will
always be 100 irrespective of the quantity and quality of the illuminant. One