A Practical Approach
J A STEPHEN VIGGIANO
RIT RESEARCH CORPORATION
ROCHESTER, NY 14623
The transformation of a digital image from a three-dimensional color space, such as RGB, XYZ,
L*u*v*, etc., to four-dimensional colorant space (typically cyan, magenta, yellow, and black) is in
general underdetermined. (The reasons for the addition of a blackcolorant are detailed in Yule.
) We therefore have a degree of freedom for colors within the three-colorant gamut; without
loss of generality we may use this degree of freedom to fix the level of black.
Perhaps the most desirable method for calculating the black level is under Gray Component
Replacement (GCR). GCR is a relatively new phrase, though the idea has been with us for many
years (atleast in theory).  The goal of successful color separation scanners has been, until
recently, to emulate the function performed by film-based systems, which were not able to readily
achieve a significant amount of GCR because of the logic (decision) involved in the process.
We view GCR as a twofold process; to be applied in practice the level of black must be calculated,
and the levels ofthe other colorants must be adjusted for the presence of the black ink. Some of
the earlier literature refers to this second task as Under Color Addition;  because we consider
GCR in a colorimetric context we feel it is better to consider this second task a part of the GCR
The concept of GCR is simple: If a pixel’s color is not too dark or too saturated, it may be producedwith two of the process colors (e.g., magenta and yellow) and black. Typically, a greatly simplified
model is used in the vendor literature  which assumes equal amounts of cyan, magenta, and
yellow inks should produce a neutral.
Unfortunately, this greatly simplified model, based upon the assumptions of “perfect” inks, is
inadequate. In order to derive a rigorous GCR algorithm it ishelpful to use a different colorant
A More Rigorous Solution
Pobboravsky  provided an approach that is adaptable to digital color systems. His method
involved first computing a three-color solution, using the chromatic inks, to obtain cyan, magenta,
and yellow halftone dot areas. Corresponding to any cyan, magenta, or yellow dot area is an
Equivalent Neutral Density (END), which is thedensity of the unique neutral composed of that ink
and the correct amounts of the other two. The gray component of the target color was defined to
be the smallest of the END values corresponding to the calculated cyan, magenta, and yellow dot
areas. The density of the gray component is the smallest END.
(Our current approach bypasses the preliminary three-color solution, and uses a directtransformation
from reproduction color to ENDs. This has the advantage of a faster solution, because the
direct transformation required considerably less computational effort than a solution for the threecolor
Consider Figure 1. In it are represented two different inking combinations which can produce
colorimetrically identical colors, under a specific set of calibrationconditions. The solution on the
left, referred to as “Minimum GCR,” is composed of the three chromatic inks and no black. For
darker colors, the Minimum GCR solution may contain some black ink; we should not infer that
the Minimum GCR solution never contains black. At the right is the “Maximum GCR” solution.
Minimum and Maximum GCR Solutions.
Note that in the Maximum GCR solution, the densities of the chromatic inks have all been
diminished by 0.55. We would expect the density of the black to be increased by this amount; in
fact we see that it has been increased by a figure somewhat higher...