Three-Dimensional Control of Color Management Systems - Control of Color Imaging Systems: Analysis and Design - page 364

three regions in the L*a*b* color space for color reproduction: (1) the out-of-gamut
region, (2) the CMY gamut, and (3) the region outside the CMY gamut but within the
CMYK gamut. When the available gamut is limited by the CMY gamut, the out-of-
gamut colors have to be mapped to the boundary of the CMY gamut as opposed to
the CMYK gamut. This makes the interactions between gamut mapping and the
GCRs even more complex. Hence a preferred approach would be to completely
eliminate the loss of gamut due to GCRs, that is, to use the same gamut volume for
minimum or maximum black. A 4-to-3 control-based, constrained inversion gener-
ated by (a) iterating on the printer model or (b) by directly iterating on the printer can
offer full CMYK gamut for any GCR curve and high accuracy inversion to node
colors inside the gamut.

7.5.4.1 A 4-to-3 Control-Based Inversion

The 4-to-3 control-based inversion is applicable to a four-color printer. As in
previous method (Figure 7.29) the node colors in the device-independent color
space, L*a*b* are generated by applying suitable transformations on a uniformly

=
nonuniformly sampled RGB color grid (e.g., genRGB). Figure 7.41 shows the block
diagram of the 4-to-3 control-based inversion, which is clearly very similar to Figure
7.29. The key differences between 3-to-3 and 4-to-3 inversion are

a. contain the GCR strategy for in-gamut

node colors, whereas, in the 3-to-3 inversion, a GCR strategy is de

Initial (or nominal) CMYK values

'' ''

ned in

the CMY to CMYK transformation.
b. No augmented printer or printer model is used. This allows the use of full
CMYK gamut when creating the inverse.
c. Printer

printer model Jacobian (Equation 7.89) and gain matrices contain the
sensitivity of output color to black separation. In addition vectors {x, u, V}
and matrices {A, B, C} in the state variable model and the feedback contain
terms associated with black separation.

=

Initial CMYK
values

Feedback
controller

(Reference r )
L * a * b *

+

Printer model x ( k )

K Integrator

+

V

u

e

-

Measured
L * a * b *

x ( k+ 1) =Ax ( k ) +Bu ( k )

FIGURE 7.41 Closed-loop control algorithm with a gain matrix and the integrator as
controller for a 4-to-3 control-based inversion.