Graphics Reference
In-Depth Information
Lacking exact measurement of inks, the usual conversion from RGB to CMY
is that the RGB color
(
r
,
g
,
b
)
is the same as the CMY color
(
1
b
)
.
Because of the interactions between inks, the arrangements of dots in dot-based
printing, and many other factors, this should be regarded as a
gross approximation
.
Indeed, in computer graphics there's almost no situation in which you should rep-
resent an image by CMY colors. Most modern printers have software that accepts
RGB colors and converts them, as well as possible for the particular printer tech-
nology, to amounts of ink to be used at each point.
In practice, the color
(
1, 1, 1
)
is not really very black; the mix of cyan,
magenta, and yellow inks doesn't really manage to absorb all light. So printers
often have a fourth ink, which is black (denoted K). This is used to replace parts
of the darker mixes of C, M, and Y.
−
r
,1
−
g
,1
−
The YIQ color model (which we should call
Y
IQ
to follow the convention about
nonlinear coordinates) is used in U.S. commercial television broadcast. It's a nice
example of a color model designed with engineering constraints in mind; these
constraints were (a) the need to broadcast a signal that could be used to drive both
black-and-white and color television receivers, and (b) the desire to use bandwidth
most efficiently.
To satisfy the first goal, the YIQ color model's
Y
value is, as described above,
the
luma,
which is
Y
=
0.299
r
0.42
+
0.587
g
0.42
+
0.114
b
0.42
,
(28.45)
and is therefore distinct from the IE XYZ model's
Y
value. (We've used a prime
both to emphasize this distinction and to indicate that it does not vary linearly as a
function of
R
,
G
, and
B
.) The
I
and
Q
values then remain to encode chrominance
information. They are essentially rotated and scaled versions of the
u
∗
and
v
∗
values. We omit the details, because with the rapid growth in the use of component
video, the YIQ standard is less and less relevant. Perhaps the most significant
aspect of it is that the
Y
of
Y
IQ
is
not
the same as the
Y
coordinate in
XYZ
-
coordinates, but instead is roughly similar to the 0.42 power of
Y
.
The allocation of bandwidth to the transmission of the three channels (which
corresponds to the number of bits of precision with which each is communicated)
is carefully chosen: 4 MHz is assigned to
Y
,1.5MHzto
I
, and 0.6 MHz to
Q
;this
corresponds to our strong sensitivity to luminance and to sharp discontinuities
in luminance (the result of using too few bits of precision), and to the relative
sensitivities of the visual system to color variation along the
I
and the
Q
axes.
Modern component video is encoded in various ways that are similar to
Y
IQ
,in
the sense that one component carries intensity information while two others carry
chromaticity information. Following Poynton [Poya], let's examine one encoding
a decoding process, starting from the unambiguous
XYZ
description of a color (see
Figure 28.25).
The entire process is described by the HDTV standard [Uni90], informally
known as Rec. 709. The transformation from
XYZ
to
RGB
(as specified in
Rec. 709, so we append the subscript 709) is (to three decimal places)
