Image Processing Reference
In-Depth Information
,
t(
m
i
;
l) ¼ exp
M
i
(l)a
i
1
exp b
i
m
g
i
½
ð
Þ
i
¼
C
=
M
=
Y
(
10
:
79
)
i
(
"
#
)
þ b
K
2
m
K
r
t
m
K
r
t
t(
m
i
;
l) ¼ exp a
K
(
10
:
80
)
This transmittance term is used in Equation 10.69 to obtain the spectral re
ectance
values for any color patches that are then converted to tristimulus values and L*a*b*.
Let us consider the cyan channel for illustration. Consider 10 uniformly spaced
points along the cyan primary while keeping M
¼
Y
¼
K
¼
0. Print these patches on
the real printer. The L*a*b* values are measured from the printed patches using a
spectral measurement device. The measured L*a*b* values represent the reference
values. The cost function shown in Equation 10.81 is then minimized to
nd the
optimal values of
a
,
b
, and
g
:
(
L*a*b*
X
10
2
)
i
(
L*a*b*
)
i
ref
F
a
i
,
ð
b
i
,
g
i
Þ¼
(
10
:
81
)
2
i
¼
1
a
has a lower bound as it cannot go negative
since it is in the exponent. So a bound-constrained nonlinear least-squares optimiza-
tion algorithm is used to minimize Equation 10.81. Such an algorithm was developed
by Coleman and Li [35]. The optimized single separation coef
and
b
do not have any constraints, but
g
cients are shown in
Table 10.14.
The color gamuts of the real printer and the partially tuned virtual printer model
are shown in Figure 10.57. One can observe that the color gamuts are well matched
near the primaries C, M, and Y. Matching at the bottom of the gamut is not good
because of the differences in the physics of the virtual printer model and the real
printer in that region. The other regions are also not well matched because we have
not yet optimized the color mixing coef
cients.
10.7.3 D
ETERMINATION OF
C
OLOR
M
IXING
C
OEFFICIENTS
{C
ji
}
The color mixing coef
cients shown in Equation 10.59 determine the way the
transferred masses on paper are mixed in the color model to generate the mathemat-
ical masses, which in turn affect the re
ectance spectra of each color. There are nine
color mixing coef
cients that are required to determine the mathematical masses,
TABLE 10.14
Single Separation Coef
cients
C
M
Y
K
a
5.1886
4.3987
3.8420
26.5352
b
62.7119
7.4488
6.4264
9.2957
g
1.2416
1.1029
1.1302
—
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