pigmented colorants: dependence on media and time - Cornell ...

is repeated many times for different subjects and averaged, resulting in a set of
standard observer color matching curves for the particular set of color primaries
(Figure 3.17). Given standard matching functions ¯r(λ), ¯g(λ), ¯ b(λ), which describe
how much light is required to match a particular reference stimulus P (λ), we can
compute R, G, andB:
R =
G =
B =
∞
0
∞
0
∞
0
P (λ)¯r(λ)dλ
P (λ)¯g(λ)dλ
67
P (λ) ¯ b(λ)dλ (3.1)
Unfortunately, when using combinations of only three light sources there are
always colors that cannot be reproduced exactly. This situation might occur, for
instance, when trying to match an intense yellow light using red, green and blue
primaries. Remember in additive color, full intensities of green and red will yield
yellow. However, if the yellow test lamp is too vivid, full intensity green and
red will not be able to match it exactly. In this case, if enough blue is added
to the yellow test lamp to desaturate it, the red and green lights can match it.
Mathematically speaking, we used a negative amount of blue light to match the
vivid yellow test lamp: Y − B ˆ b = Rˆr + Gˆg. While this limits the system, digital
displays are not necessarily compromised in this situation, as there are a number
of ways to gracefully display a plausible suitable color instead. However, these out
of gamut colors do create inconveniences in performing color calculations.
To eliminate the inconveniences associated with negative values in tristimulus
color spaces, the CIE (Comission Internationale de l’ Éclairage) in 1931 defined a
set of tristimulus color primaries X, Y ,andZ which encompass all of the visible