Image Processing Reference
In-Depth Information
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Iteration No.
Iteration No.
FIGURE 7.31
Convergence plot for 5192 in-gamut nodes using nominal values calculated
from MM algorithm.
TABLE 7.9
Accuracy Statistics for In-Gamut Nodes before
the Start and End of Iterations
D
E
2000
D
E
a
*
Mean
95% Max
Mean
95% Max
Start of iteration
1.86
6.37
60.18
2.67
9.18
62.41
End of iteration
0.00
0.00
0.58
0.01
0.00
0.77
have to be carefully tuned to avoid oscillations during iteration (or instability) and
potential actuator saturation for near-boundary colors.
Figure 7.31 shows the convergence plot for all the in-gamut nodes when the
nominal CMY values are calculated using the MM algorithm mentioned in Section
6.3.2. Nominal CMY values can also be calculated using other algorithms (e.g., ICI
from Section 6.4.3). This plot clearly indicates that the convergence error (shown in
Table 7.9 for both
D
E
a
*
and
D
E
2000
) is near zero for all the nodes at the end of the
iterations, which is a signi
cant improvement when compared with other inversion
algorithms used in the industry.
During iterations, the
D
E errors shown in Figure 7.31 for node colors at the
gamut boundary, may go higher in a more recent iteration than the previous one,
which can result in the choice of wrong inverse (i.e., CMY). That is, node colors near
the boundary may reach saturation (i.e., their CMY values may go to 0 or 255). This
can lead to limit cycles during control iterations, meaning
D
E descent with respect to
iterations can oscillate. Since iterations contain the history of oscillations, a unique
best actuator algorithm shown in the diagrams of Figure 7.32 can be used to select
proper CMY values that give the best inverse for the node colors at the gamut
boundary. Assume that there are N
0
colors that will be adjusted by the algorithm,
which will iterate N
t
times and all iteration history is stored. The best CMY selection
algorithm starts from the second block in Figure 7.32a where the algorithm picks the
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