Three-Dimensional Control of Color Management Systems - Control of Color Imaging Systems: Analysis and Design - page 350

(or darkness) as compared to printers without K separation. It helps to reproduce
shadows, gray areas, and muted tones in images. Other bene ts of introducing K are

toner savings and improved stability. A potential disadvantage in using high K levels
throughout the gamut is the dirty esh tones, sky

tones, and other important colors. Smoothness and gamut coverage must also be taken
into account while rendering pixels with black. GCR is a critical element in the
inversion process since it introduces redundant solutions. Thus, GCR optimization
requires a delicate trade-off among these competing requirements, and depends
strongly on the physics of the printer. Generally, print vendors

= grainy appearance that can arise in

fine-tune the addition
of black intelligently either by using complex algorithms or by using carefully
designed experiments. Experiments are often done with many iterations to get the
right amount of K. Once the tuning is done, the GCR will be included as a part of the
multidimensional LUT. We will further elaborate on this topic later.
Printer characterization gives an approximation to the forward map (from device-
speci c CMYK space into the device-independent CIELab or spectral space).

An accurate multidimensional pro

le LUT is intended to provide the inverse of the
printer (or inverse of the characterized printer map) for every input color node described
as L*a*b* which is a transformation of the node fromCIELab into a CMYK color space.
Numerous techniques are available in the literature [71 80] that use variety of methods

to characterize the printer and then compute inverse. For pixels not on the nodes, during
real-time image processing, numerous interpolation schemes are used. Among these,
tetrahedral interpolation is the most commonly used method inside the ICC pro

-

le. For
any given node, in control terminology, the four-color forward printer map can be
considered as a four-input three-output plant with four input variables (CMYK)usedto
control three outputs (L*a*b*). Since the forward map is the representation of a printer
with an over-actuated system, there exist many possible combinations of CMYK values
that produce a given L*a*b*. To avoid this kind of degeneracy and determine a unique
combination for four separations, GCR constraints are required. These constraints are
included in the inverse map (L*a*b*toCMYK LUT).
The inverse map can be thought of as cascade of two LUTs: (1) a three-to-three
mapping LUT, CIELab to CMY and then (2) a three-to-four mapping LUT, CMY to
CMYK. In such a LUT architecture, conceptually an RGB node will be transformed

finally
followed by a transformation to four-color space, CMYK, prior to rendering. This is
described next.

first to three-color space, CIELab, then to another three-color space, CMY,

7.5.1 A S IMPLE GCR F UNCTION
A simple GCR function, CMY to CMYK transformation, is shown in Figure 7.25
[71]. The GCR function is described in terms of two components: (1) black
addition and (2) under color removal (UCR). As the figure indicates, we first
subtract 0.5x 2 from all three-component values of CMY and add black colorant
per Equation 7.86.

K ¼ x 2

( : )

7 86

where x ¼ min(C, M, Y).