Image Processing Reference
In-Depth Information
Solving Equation 7.59 for the unknown ci,
i
, we obtain
n
o
n
o
P
k
¼
1
P
C
lðÞ
1
=
m
1
=
m
1
=
m
1
=
m
½
P
W
lðÞ
½
½
R
C
i
lðÞ
P
W
lðÞ
½
c
i
¼
n
o
2
P
k
¼
1
P
C
lðÞ
(
7
:
60
a)
1
=
m
1
=
m
½
P
W
lðÞ
½
i
¼
0, 1, 2,
...
, 255
The above process is repeated for other three colorants m, y, and k. A dot growth
function (curve) can be easily obtained by using single separation step wedges at
discrete digital counts (see Example 7.7) and then plotting CMYK values against
respective digital counts CMYK. For case w(l)
l
)
6¼
1 Equation 7.60a is modi
ed by
ectance spectra by w
m
(
multiplying each re
l
). The modi
ed equation is given by
n
o
n
o
P
k
¼
1
w
m
1
=
m
1
=
m
1
=
m
1
=
m
½
lð
P
C
lðÞ
w
m
½
lð
P
W
lðÞ
½
w
m
lð
R
C
i
lðÞ
w
m
½
lð
P
W
lðÞ
c
i
¼
n
o
2
P
k
¼
1
w
m
1
=
m
1
=
m
w
m
½
lð
P
C
lðÞ
½
lð
P
W
lðÞ
(
7
:
60
b)
7.4.3.3.2 Optimization in L*a*b* Color Space
In this approach, the error minimization is carried out in the L*a*b* space to assign
visuallymeaningful weights. Unlike in the previous approach, since the transformation
from spectral domain to color space L*a*b* is nonlinear; a closed-form least square
solution is intractable and thus a simple numerical iterative solution is preferred.
Assuming that the dot growth functions are separation independent, as in the
previous section, a set of N cyan, magenta, yellow, black, and neutral patches
are printed and their L*a*b* values are measured. Let
D
E
k
and
D
E
g
be the CIELAB error between the measured L*a*b* values and their corre-
sponding predicted values for cyan, magenta, yellow, and neutral patches from the
Neugebauer model with the appropriate mixing equation. The overall error metric,
D
E,isde
D
E
C
,
D
E
M
,
D
E
Y
,
ned as the weighted sum of the above CIELab errors. Thus,
D
E
(
i
) ¼ a
c
D
E
c
(
i
) þ a
m
D
E
m
(
i
) þ a
y
D
E
y
(
i
) þ a
k
D
E
k
(
i
) þ a
g
D
E
g
(
i
)
(
7
:
61
)
where the weights
a
g
are chosen based on region of the color
space where more accurate reproduction is desirable (e.g.,
a
c
,
a
m
,
a
y
,
a
k
, and
a
c
¼a
m
¼a
y
¼a
k
¼
0.15,
a
g
¼
and
0.4 for more accurate prediction along the neutral axis rather than along
individual colorant axes). The above metric is minimized with respect to the dot
areas c(i), m(i), y(i), and k(i).
Example 7.7
A four-color CMYK printer has 16 usage basis colors for combinations of two states
(0% and 100% area coverages) whose measured spectral curves are shown
in Table 7.6 at 10 nm interval between 400 and 700 nm. The relationship between
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