# Random Forest-Based Prediction of the Optimal Solid Ink Density in Offset Lithography
## 1 Introduction  
With the rapid development of the current economy, the increasing prevalence of printing products, and the overall dynamic growth of the printing industry, the demand for printing products has surged. The prosperity of the e-commerce and retail industries has led to an increasing demand for printing products, which has, in turn, driven many printing companies to compete for market share. Consequently, the focus of these enterprises has gradually shifted from \"quantity\" to \"quality\". To improve the quality of printed products, many enterprises and industry organizations have proposed relevant control processes and technological approaches during the development of printing technology. In the current printing industry, the primary print quality control processes--the GATF and G7 processes--both rely on the use of cyan (C), magenta (M), yellow (Y), and black (K) color patches (100% ink coverage), with color accuracy controlled by adjusting the intermediate tones through step changes and curves. In actual production operations, regardless of the process used, the first step is to determine the optimal solid ink density of the print [1], which is critical to the production process. Next, the calibration of the machine's color management is performed, as determining the density affects subsequent tonal performance and gamut expansion. Therefore, ensuring the accuracy of the optimal solid ink density is essential. The current method for controlling the solid ink density of printed materials primarily involves the printing press controlling the amount of ink required to achieve optimal print color. However, this traditional method, which relies on visual experience, is prone to error. Additionally, the repeated calibration process results in significant paper waste, increased commissioning costs, and reduced production efficiency. To date, many manufacturers use FORGA, based on the relative contrast formula, for density calculation. However, this method only considers printing contrast and neglects the visual match of the human eye. In fact, the international standard ISO 12647-2:2013 [2] specifies the optimal solid ink density values under different substrate conditions, corresponding to colorimetric values. This standard provides a reference for adjusting the ink volume in actual production. Moreover, how to efficiently use the standard data for ink volume adjustments requires further exploration. In recent years, numerous studies have been conducted on methods for determining the optimal solid ink density in the pre-press color management process. [PERSON] et al. [3] determined the optimal solid ink density range for secondary fiber newsprint through experimental design, combining both the relative contrast and color contrast values. Although this method, proposed by the German Printing Research Association, has been widely adopted for determining optimal solid ink density in the printing industry, it calculates only rough density values. However, since the relative contrast (K value) only correlates with the dot expansion and density values, without accounting for the human eye's visual perception of the printed materials, the adjusted samples are not visually optimal. Based on the minimum color difference method, [PERSON] et al. [4] analyzed the relationship between the L* (Lightness) a* (Red-Green Chromaticity) b* (Yellow-Blue Chromaticity) values and solid ink density (Dc) to develop a method for determining the optimal solid ink density. The established mathematical model clarifies the direction for adjusting the printing ink in production, using the measured density value as a reference to quickly reduce color differences. This method also demonstrates a correlation between the color difference of printed samples and solid ink density. [PERSON] et al. [5] developed a mathematical model using the best relative contrast K value and regression algorithms to relate relative contrast and dot gain values.