Three-Dimensional Control of Color Management Systems - Control of Color Imaging Systems: Analysis and Design - page 358

7.5.2.3 Inverse by Iterating Directly on the Printer

If we can directly iterate on the printer for any node color using control algorithms,
the historical methodology of building a printer model and then inverting that model
for developing multidimensional LUTs may not be necessary. The iteration process
contains the following steps.

a. Find nominal CMY values for the node colors of interest using ICI or other
inversion algorithms on a coarse printer model. A coarse printer model is a
less accurate representation of the printer. The corresponding CMYK values
are calculated for these nominal CMY values, using the CMY to CMYK
GCR function.
b. Create a test image containing the color patches of the determined CMYK
values and print. The L*a*b* values of the color patches on the printed test
image are measured.
c. Using the controller shown in Figure 7.29 (e.g., gain matrix and the integra-
tor), process the error between the measured L*a*b* values and the target
L*a*b* values. The gain matrix can be found using pole-placement or LQR
methods a priori at the nominal CMY values or using any of the control
approaches shown in Refs. [96 100].

d. Continue with steps a through c for a few iteration cycles.

-

The best actuator selection method described in the previous subsectionmay be required
for node colors near the gamut boundary. Improvement of accuracy in performance for
boundary colors can also be achieved by scheduling multiplicity of gain matrices for
every node color using MIMO model-predictive-control methods [100].

Example 7.8

Generate a GCR constrained ICC destination pro le with a 3-to-3 control-based

inversion using the GCR function of Figure 7.25 for a test printer. Evaluate
the quantitative round trip accuracy and gamut volume. Compare the effective
volume with respect to the gamut volume obtained from the characterization data.
Use a suitable gamut-mapping strategy described in Section 7.6. Evaluate the
visual response of the ICC pro le for a test image.

S OLUTION
We constructed a 33 3 le using the steps shown in Section 7.8 and the

GCR of Figure 7.25. The steps involved in evaluating the ICC pro

ICC pro

les are covered

in detail in Section 7.7.
The CMYK response of the ICC pro le for RGB neutral sweep is shown in Figure

7.33. Clearly, most of the neutrals are produced using CMY separations and no
black. This is good for high quality rendering. The rapid rise of magenta and yellow
separations between R¼G¼B¼ 0 to about 50 digital counts is caused by mapping

out-of-gamut colors to the printer gamut. This could cause image quality defects,
such as contours for dark colors if left unattended. Also a sharp transition in the cyan
separation for dark colors can cause problems. In Figure 7.34, an L* linearity plot is
shown. Clearly, we see problems with dark colors (once again) that is a problem at