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.

灰平衡是打印过程中颜色平衡和颜色外观调整的关键问题之一。它考虑了两种或多种着色剂的重叠以获得视觉中性色调。它与主要色彩通道的调整并行工作。在电子照相术中，通常使用色调重现曲线分别进行颜色通道的设置。但是，这种传统方法没有考虑到阴影重叠所引起的阴影变化的影响。我们以前建议使用渐变轨迹（CIE Lab中音调再现曲线的类似物空间）作为颜色通道调整的替代范例。此外，我们将该概念扩展为渐变表面，以表示二进制叠加层。我们提出了解析方法和离散方法来计算渐变轨迹和曲面。该计算使用空间曲线和曲面的微分几何的数学仪器。离散化在数字打印设备中使用颜色量化，这意味着颜色坐标被认为是用染料填充离散栅格像元的连续函数。色彩空间指标由CIE dE的值确定颜色差异。作为渐变轨迹，我们将离散类型的测地线应用于相应二进制文件的渐变表面上。在这项工作中，我们建议使用离散形式的灰度表面作为双染料覆盖的数学模型来调整电子照相中的灰度平衡。