FIGURE 1. (a) CIE Lab color space body, (b) gradation
trajectory with projections, (c) gradation surface with experimental
dots.
The GT’s arc length is defined as an integral of the dE units.
The arc is split into n segments of equal length in order to
match them with the same tone increment. We have suggested an empirical
description of the GT by polynomials of the 4thdegree, as well as the discrete approach to the GT computation on the
basis of intrinsic color quantization in the digital printing systems.
Further, we expanded the approach onto the binary overlapping of the
initial colorants. Thus, the method of gradation surfaces (GS) has been
developed [13]. On the basis of the proposed approaches, methods
were developed for determining the linearization of various printing
systems and determining the gray balance [14]. In the case of
printing colorants, their paired double overlays (binaries) correspond
to additive primary colors (RGB). Since the RGB and CMYK spaces are both
device-dependent, there has not been any simple or general
transformation formula that converts them. Using the gradation surface
as a gradation trajectory of two colorants, we have suggested the way to
develop such a conversion.
If we consider an ideal colorant’s GT as a particular geodesic line on
the GS of some basic colorants, then we could calculate it using both an
analytical and discrete approaches. This work aims to establish a
discrete approach for searching the ideal colorants’ gradation
trajectories based on a color quantization in digital printing systems.