One-Dimensional, Two-Dimensional, and Spot-Color Management and Control Methods - Control of Color Imaging Systems: Analysis and Design - page 457

Let us assume that there are no replicas required to average out the noise. Using the
predictive algorithm, we will print only half the number of patches per each
iterations. We now describe the algorithm for predictive gray balance below.

(a) Switching Strategy : Assume that there are 10 target patches t 1 , t 2 ,..., t 10
and thus 10 different control loops are running in parallel. We divide these
10 loops into two sets: the odd set containing t 1 , t 3 ,..., t 9 and the even set
containing t 2 , t 4 ,..., t 10 . In the

first iteration, we print and measure the
patches corresponding to the odd set and use a predictive method to
compute the CMY values (control actuation) corresponding to the patches
in the even set. In the second iteration, we do the reverse that is print and
measure for the even set and estimate the CMY values (control actuation)
for the odd set. This kind of switching process is repeated till we converge
to the true CMY value. That is, we alternate between a set of loops with
actual state measurement by printing those control patches and assess which
ones do not need printing, and can work well with predictive algorithm.
This way, we can save printing of redundant patches. Other switching
strategies include (a) dividing the N loops into M disjoint sets, and selecting
one set at each iteration different from the others in a round-robin fashion
(e.g., iteration 1

¼ set 1, iteration 2 ¼ set 2, . . . , iteration M ¼ set M, iter-

ation M þ 1 ¼ set 1, . . . ). The case described earlier is for M ¼ 2 and each

set containing M loops. Yet, other strategy include first printing control

patches for all N loops say for two iterations. After that print only those that
show the largest errors.
(b) Predictive Technique : Ultimately, for each iterations and for each one of
the N loops, we need to compute the CMY values. If for a given loop,
we print and measure a patch, we use the normal iterative approach to
update the CMY values as obtained by the control algorithm. If we do not
print a patch for a control loop, then we use a prediction method to estimate
their CMY values. From the new values of CMY already computed for
other loops using the control algorithm, we estimate the new CMY values
for the loops where we do not print a patch. Linear and nonlinear inter-
polation fitting algorithms

can be used for estimating the required CMY values. As an example, let the
cyan components of the

= extrapolation or polynomial least-square curve

five measured and controlled patches plus the two
corner points be, as shown in Table 8.8, in one of the iteration cycles. Let
the five unmeasured patches have the L* target values of 20, 45, 55, 70, and

85. Since our gray-balance aim is the pure neutral axis, we assume
a*

¼ b* ¼

0.

A plot of the data in Table 8.8 with cubic interpolation is shown in Figure 8.25.
From this interpolation, the predicted (or estimated) values of the cyan components
of the

five unmeasured patches corresponding to L* values of 20, 45, 55, 70, and
85 are estimated respectively as 83.5, 52.1, 37.32, 25.85, and 15.28. In Table 8.9,
we show an example of the D E a * vs. iterations) for the

case when we print all patches and for the case when we print half of them.

D E a * convergence response (