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.