Three-Dimensional Control of Color Management Systems - Control of Color Imaging Systems: Analysis and Design - page 368

K-function curve is more rounded at small L*. The parameter determines the shape

of the K-function in the middle range of L*. To set the parameters of Equations 7.90
and 7.91, the information at the boundary of the color gamut can be used since there
is unique correspondence between L*a*b*toCMYK at that location.
Because there are four parameters (

b

, L 0 ) to be optimized and the search
space is huge, the simultaneous perturbation stochastic approximation (SPSA)
method [107] can be used to determine a local region where the parameters could
be trained using boundary values.
Complete procedure that is used to create the K-restricted (GCR constrained)
L*a*b*toCMYK LUT is shown below. The following steps are described for one
in-gamut node color:

a , b , h

nonuniformly sampled high density CMYK to L*a*b*
LUT. This data can be obtained from the printer model (e.g., a 16 4 CMYK to
L*a*b* LUT). These data can also be obtained by printing a set of patches
and measuring L*a*b* values with a sensor.
b. Calculate the K value for the node color (L*a*b* data) using the K-function
(Equations 7.90 and 7.91).
c. Find all

a. Create a uniformly =

D E 2000 values between node L*a*b* value and the L*a*b* values
from the characterization LUT of step (a). Rank order the colors with
respect 6 (or any

reasonable threshold which is set depending on the desired accuracy).
There could be multiple CMYK values for any given node color. Record
their corresponding CMYK values.
d. Compare K values between steps (b) and (c) for each of the colors picked in
step (c). Pick few colors that are closest to K value in the K-function.
e. Compute the Jacobian and gain matrices for each of the colors picked in
step (d). Run a 4-to-3 iterative control algorithm of Figure 7.41 on a printer
model. If experimental characterization input

to D E 2000 values and pick all colors with D E 2000 <

output data is available, then
use numerical interpolation techniques described in Chapter 6 in place of
the printer model.
f. Compare the

-

D E 2000 numbers and select CMYK values with the smallest
D E 2000 numbers. This gives the K-restricted GCR constrained CMYK value
for the node color.
g. Repeat steps (b) through (f) until the CMYK values are found for all the
in-gamut node colors.
h. Use the CMYK values from step (g) to complete the ICC pro le. If the

ICC pro le has undesirable kinks in CMYK response between neigh-

boring nodes, then another preconditioning step is required, which
would involve applying multidimensional

filtering techniques [108]
(Chapter 6) to soften the kinks. Filtering may make the in-gamut CMYK
values inaccurate, but these inaccuracies can be minimized by running the
steps described in Section 7.5.5 using the

filtered K-restricted pro le as

the source.

Example 7.9 uses these steps to create a K-constrained ICC pro le.