Three-Dimensional Control of Color Management Systems - Control of Color Imaging Systems: Analysis and Design - page 352

by a four-color CMYK printer (e.g., a calibrated CMYK to L*a*b* printer map), the
other gamut produced by a three-color CMY printer (e.g., a CMY to L*a*b* printer
map including the GCR) using the GCR function of Figure 7.25.
Once the GCR function is selected using the CMYK to L*a*b* printer model, an
augmented CMY to L*a*b* printer map can be generated by including the GCR function
in the system, to produce a new forward map, CMY to L*a*b*. Since this is a determin-
istic forward map; it gives unique colors for a unique combination of CMY and does not
require any constraints during inversion. Inversion of this kind of unconstrained three-
input to three-output forward map is reasonably easy and will be described next.

7.5.2 I NVERSION OF A T HREE - TO -T HREE F ORWARD M AP
The inversion mapping process introduced in the previous section is illustrated in
Figure 7.27 starting from the intermediate RGB space. The CMY values are con-
verted to CMYK using the GCR

= UCR algorithms (e.g., Equation 7.86). In this

=

section let us consider that UCR functions are embedded inside the

augmented forward printer map, Q. The inverse of this map, Q shown symbolically
as Q 1 : L*a*b* ! CMY, where input L*a*b* points are on a three-dimensional
(3-D) grid of size N N N. This grid has a dynamic range 0

the GCR

L* 100, 127

a* 128.

To generate the ICC work

128, and 127 b*

ow, we start with a uniformly or nonuniformly
sampled RGB color LUT in the range 0 - 255. This is an intermediate color space

in the le LUT (see Figures 7.1 and 7.2). Next, we apply a

suitable transformation in the forward direction from RGB to L*a*b* and map the
out-of-gamut colors in L*a*b* to a suitable node on the device boundary (or inside)
of the printer model. Now, to express these RGB nodes (in the reverse direction) in
the PCS, a conversion from RGB to L*a*b*orXYZ is required which is purely an
inverse transformation starting from each of the RGB color nodes of the uniformly or
nonuniformly sampled RGB grid. Since RGB space is not device independent, any of
the standard RGBs (e.g., genRGB, ROMMRGB, etc.) are potential candidates for use
in the multidimensional pro

final ICC destination pro

le LUTs. Figure 7.28 shows a 3-D view of the nodes
when constructed with sRGB, ROMMRGB, and genRGB color spaces. Figure 7.2

GCR/UCR is included with
map Q

Mapped
Lab i

RGB

Lab i CMY i Lab out

Gamut
mapping

Q -1

Q

Transformation

Error (Accuracy)

Uniformly
sampled RGB
nodes
(e.g., for 17 3 )

Gamut mapped nodes for
out-of-gamut colors as in
in-gamut colors are not
mapped

Lab nodes
(e.g., for 17 3 )

FIGURE 7.27 Block diagram illustrating a forward and inverse printer process with GCR in
the augmented printer map, Q.