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

spectrum. This insures that the respective color matching functions ¯x(λ), ¯y(λ), and
¯z(λ) are all non-negative. The drawback of having a system in which all visible
colors can be represented is that the primaries are virtual and no longer correspond
to physical colors. The color coordinates of a stimulus P (λ) inXY Z color space
(also known as CIEXY Z)are:
X =
Y =
Z =
∞
0
∞
0
∞
0
P (λ)¯x(λ)d(λ)
P (λ)¯y(λ)d(λ)
68
P (λ)¯z(λ)d(λ) (3.2)
where X, Y ,andZ are the tristimulus values; ¯x, ¯y, and ¯z are the color-matching
functions of the 2 o Observer; and k is a normalizing factor. By convention, the
scalar factor k generally is determined such that Y =100whentheobjectisa
perfect white:
k =
100
∞
0 E(λ)¯y(λ)d(λ)
where E(λ) is the spectrum of the white light illuminating the scene.
If, the stimulus is that of reflected light R(λ), the equation substitutes P (λ) =
E(λ)R(λ). The CIE chose the ¯y color matching function to be identical to the
human luminance efficiency function, which mean that Y encodes the luminance
of a color. The scale factor, k, is defined such that for an ideal diffuse reflector
(the brightest white), Y will have a value of exactly 100. While the range 0-100 is
convenient for humans, computer programs scale XY Z to lie on the range [0,1].