Discrete Gradation Surfaces Computation in Electrophotography

Fine-tuning the reproduction of the initial colorants pure colors gradations is the basis of color reproduction in modern printing systems. Usually, tone reproduction curves are constructed by successively changing the tone of the basic dyes (CMYK). However, this approach does not take into account the effect of changes in the dyes shade when they overlap. As an alternative basis for color correction, we previously suggested using gradation trajectories, which are analogous to gradation curves in the CIE Lab space. We also proposed a discrete approach to computing them, using natural color discretization in digital printing devices. In this article, we propose to use three-dimensional gradation surfaces in the CIE Lab space as a mathematical model of double color overlays (RGB) and as a further development of the idea of gradation trajectories. The calculations use the mathematical apparatus of the differential geometry of spatial curves and surfaces. The color space metric is determined by the value of the CIE dE color difference. To simplify the application of the model, we also propose to carry out calculations in discrete form. In this case, color coordinates are considered as continuous functions of filling a discrete raster cell with two dyes. As gradation trajectories, we consider geodesic lines on the gradation surfaces of the corresponding double overlaps of dyes. For calculations we also used a discrete approach. Experimental verification was carried out using an electrophotographic printer.