Discrete Gradation Trajectories Computation in Electrophotography

In printing art, color management is largely based on the adjustment and analysis of the behavior of gradation curves calculated for the initial color channels. However, this approach does not take into account the mutual influence of colors and the change in hue, for example, when inks overlap. The approach proposed by the authors earlier offers to replace the two-dimensional tone reproduction curves with three-dimensional gradation trajectories in the CIE Lab metric space. In this paper, we develop this approach. It is shown that calculations using the mathematical apparatus of the differential geometry of spatial curves describing gradation trajectories might be simplified using the discrete approach. Discretization is associated with the peculiarities of color formation in modern digital printing systems. These features are used in the approximation of gradation trajectories using polynomials. In this case, color coordinates are considered as continuous functions of filling a discrete raster cell with dye. The proposed method allows one to calculate trajectories faster and without the use of cumbersome computations. An experimental verification of this approach was carried out using the example of a digital electrophotographic printing system.