1. Introduction
In the color management, the color reproduction adjustment is closely
related to the fine tuning of the basic colorants gradations. This
approach works in conjunction with various color prediction models
embedded in the color management systems and aims to adjust colors, save
amount of inks used, and to predict the resulting color in print.
Initial colorants in the frame of the standard subtractive color model
are represented by three basic colors (CMY) and one additional Black
(K). The color formation in such a model is a separate complicated task,
although all color prediction models have to rely on those four
colorants and their overlapping.
On the other hand, a few is known about the initial colorants in real
printing systems. Usually, each manufacturer uses its own recipe of the
CMYK inks formation based on the fossil pigments. Hence, each color
reproduction system, in fact, uses a unique initial colorants set,
especially, considering the non-ideality of the printing system itself.
Anyway, each system reproduces quite accurate colors after the procedure
of calibration and color tuning with the help of color prediction models
used in the color management software is carried out.
There are many different color prediction models applied in color
management. The empirical surface models take into account
superposition of ink halftones and do not deal with the light
propagation and fading within the print. The physically inspired
models engage a more detailed analysis of light-print interaction based
on the prediction of how the light paths go within a halftone print and
what the resulting fade is. The ink spreading models characterize
the effective surface of an ink dot after it has been printed at a given
nominal surface coverage compared to the effective surface coverage that
forms the physical dot gain. The spectral reflection color
prediction models deal with spread-based light
propagation-transportation probability. These models study the impact of
different factors influencing the range of printable colors (the inks,
substrate, illumination conditions, and halftones) and create the
printer characterization profiles for the purpose of color management
[1]. These models together with the ink-spreading models take into
account the physical dot gain and are able to predict the reflectance
spectra as a function of ink surface coverage for 2–4 inks (binary and
ternary color systems). The models use the multiple tone reproduction
(ink spreading) curves to characterize the physical dot gain of the ink
halftones on the substrate and under all solid ink-superposition
conditions [2–4].
The color prediction models have been successfully applied to the color
reproduction management [5–9], however, all the proposed approaches
require a significant number of measurements, computations and checks.
However, since most of them are based on empirical relationships, the
accuracy of predicting some shades of the reflection spectrum remains
low.
If one looks at the problem of color reproduction from the other side,
the use of the “ideal” initial colorants might be an excellent
solution providing the basic color stability. An ideal colorant is such
a combination of the initial colorants, which ensures minimal
fluctuations of color tone in the range from a white substrate to a full
dye. In this case, the ideal colorant will be a specific mixture of two
initial colorants.
In previous works, the gradation trajectories (GT) as a
three-dimensional interpretation of tone reproduction curves (TRC) in
CIE Lab space were introduced [10–12] (see also Fig.1 (a,
b)). Thus, any color is uniquely described by a three-component vector
in the 3D Lab space. The metric of the space is the color
difference dE (or ΔE ), which is defined at least by the
root squared sum of color components differences. Presence of any metric
in the sense of the method of measuring distances turns the color space
into a metric one.