Image Processing Reference
In-Depth Information
FIGURE 10.57 Two views of the color gamuts after single separation coefficient optimiza-
tion (solid: real printer and wire mesh: virtual printer model).
which are shown in Tables 10.10 and 10.11. The combination of the transferred
masses that these color mixing coef
cients affect are shown in Equation 10.61. The
first three masses are just primaries and hence the color mixing coef
cients are all
1
s. The fourth element is a combination of C and M channels and there are two
coef
'
cients that affect them, namely C 41 and C 42 . Similarly, the combination of
M and Y channels has coef
cients of C 52 and C 53 , the combination of C and Y
channels has coef
cients of C 61 and C 63 , the combination of C, M, and Y channels
has coef
cients of C 71 , C 72 , and C 73 . To determine C 41 and C 42 , we use 25 uniformly
spaced points with combinations of C and M primaries while keeping Y ¼ K ¼
0. To
determine C 52 and C 53 , we use 25 uniformly spaced points with combinations of
M and Y primaries while keeping C ¼ K ¼
0. To determine C 61 and C 63 , we use 25
uniformly spaced points with combinations of C and Y primaries while keeping
M ¼ K ¼
0. To determine C 71 , C 72 , and C 73 , we use 125 uniformly spaced points
with combinations of C, M, and Y primaries while keeping K ¼
0.
The L*a*b* values for a real printer patch set can be regarded as the reference
values. The cost function shown in Equation 10.82 is minimized to
find the optimal
values of the corresponding color mixing coef
cients:
( L*a*b*
X
N
2
) i ( L*a*b*
) ref
F ( C ji ) ¼
(
10
:
82
)
2
i ¼ 1
All the color mixing coef
cients are unbounded and unconstrained. Therefore, we
use an unconstrained nonlinear least-squares optimization algorithm to minimize
Equation 10.82. The Levenberg
Marquardt algorithm provides a good tool for this
purpose. The complete description of the method can be found in Ref. [36]. The
optimized color mixing coef
-
cients are shown in Table 10.15.
The color gamuts of the real printer and the tuned virtual printer model are
shown in Figure 10.58. One can observe a major issue at the bottom of the gamut
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