Color - Computer Graphics: Principles and Practice - page 774

⎡ ⎤ ⎡ ⎤

r
g
b

r
g
b

⎣ ⎦ )=( M − 2 M 1 ) ⎣ ⎦

M − 1
2

( M 1 (28.42)

for display 2, so the matrix M − 2 M 1 will take RGB color descriptions for display
1 to those for display 2.
It will often happen that some RGB color triple for display 1, after multipli-
cation by the transition matrix, will produce a color triple for display 2 some of
whose entries are greater than one, or less than zero. This indicates that there's a
color in display 1's gamut that is outside the gamut of display 2. What can we do
in such a case? There are several solutions, ranging from the simple to the com-
plex. We can simply ignore the transition matrix, replacing it with the identity; this
fails to match colors, but avoids the gamut-overshoot issue entirely (indeed, this is
mostly what's done in practice with images transferred over the Internet). We can
clamp the resultant color values between 0 and 1; this produces unpleasant arti-
facts in the darkest and brightest areas of the image, but it's simple. Or we can take
a more sophisticated approach like the ones described by Hall [Hal12], or those
described in the ICC profile model's rendering intents [Con12], which include a
strategy that maps the white point of the source image to the white point of the
medium on which it is to be displayed, and then warps other colors accordingly, a
strategy that attempts to map the most saturated colors to the most saturated col-
ors, and then warps others to be consistent with this, and a strategy that attempts to
capture the perceptual relations among colors in an image as faithfully as possible.
(Of course, this depends on our knowing the white point for the medium.)
The sRGB standard proposed certain “standard” colors for R , G , and B , based
on the observation that many displays were closely matched to these standards;
their relationships to CIE XYZ coordinates are given by a linear mapping:
⎡ ⎤ ⎡ ⎤ ⎡ ⎤

R
G
B

3.2410 − 1.5374 − 0.4986 X

Y
Z

⎣ ⎦ = ⎣ ⎦ ⎣ ⎦ .

− 0.9692 .18760 0.0416 (28.43)

0.0556 − 0.2040 1.0570

Of course, for two displays that both have RGB primaries described by this
relation, the transition matrix will be the identity.

28.14 CMY and CMYK Color

Cyan-Magenta-Yellow (CMY) color descriptions are used for printers, where the
inks are materials that reflect some portion of incoming light, absorbing other
portions. Cyan ink absorbs red light, but reflects blue and green (i.e., its reflectance
of long-wavelength visible light is low, but of short- and medium-wavelength light
is high); magenta absorbs green, and yellow absorbs blue. Once again, the exact
details of which wavelengths are absorbed must be based on measurement.
Colors are described as a mix of cyan, magenta, and yellow. When two inks
are mixed, the light that's reflected is that which is not absorbed by either ink. So
a mix of cyan and magenta absorbs both red and green, resulting in something that
reflects blue light. Thus, for CMY colors, we write

U = cC + mM + yY (28.44)

and then denote the color by the number triple ( c , m , y ) . In this form, the CMY
color ( 0, 0, 0 ) is white, and ( 1, 1, 1 ) is black.