Gray Balance Adjusting in Electrophotography by Means of Discrete Geodesics of Gradation Surfaces

Gray balance is one of the key issues of color balance and color appearance adjustment during printing. It takes into account the overlap of two or more colorants to achieve a visually neutral tone. It works in parallel with the adjustment of the main color channels. In electrophotography, the setting of color channels separately is usually carried out using tone reproduction curves. However, this traditional approach does not take into account the effect of changes in shades caused by their overlapping, We previously suggested using gradation trajectories (an analogue of tone reproduction curves in CIE Lab space) as an alternative paradigm for color channel adjustment. Further, we expanded the idea to the gradation surfaces as an expression of binary overlays. We proposed both analytic and discrete approaches to the computation of gradation trajectories and surfaces. The computations use the mathematical apparatus of differential geometry of spatial curves and surfaces. Discretization uses color quantization in digital printing devices and means that color coordinates are considered as continuous functions of filling a discrete raster cell with dyes. The color space metric is determined by the value of the CIE dE color difference. As gradation trajectories, we apply the discrete type of geodesic lines on the gradation surfaces of the corresponding binaries. In this work, we suggest using gradation surfaces in discrete form as a mathematical model of double dye overlays to adjust the gray balance in electrophotography.