# A Study on DNN-Based Practical Model for Predicting Spot Color
## 1 Introduction
### Related Works  
In the field of color prediction, the Kubelka-Munk (K-M) model has been a representative study and remains a fundamental tool for understanding and predicting color behavior in various materials [5]. By modeling light absorption and scattering into coefficients, this theory has advanced the ability to predict and reproduce color, especially in diffusely reflecting materials such as paint coatings. The theory's ability to mathematically relate the optical properties of materials to their perceived color makes it valuable for predicting how different colorants and substrates will interact under different lighting conditions. In addition, its simplicity and ease of use made it easy for non-experts to understand and use. Its widespread application in many fields related to color reproduction, even to this day, emphasizes the fundamental role of this theory in the field of color science. However, the K-M model, first proposed in the 1930s, had several limitations, such as the assumption of a homogeneous surface, which made it difficult to account for the diverse and complex conditions of actual industrial sites. As a result, later studies attempted to predict color more comprehensively. To measure the color of glossy materials, [PERSON] [6] adjusted the reflectance value by applying a correction factor that accounts for the specular reflectance of the material's surface. [PERSON] [7] extended the K-M model to a two-constant theory that could better handle materials with high scattering and absorption by introducing additional scattering coefficients to account for the scattering of light at different wavelengths. While the K-M theory emerged from the need to understand the optical properties of opaque or translucent materials, other theories emerged in response to the challenges of color reproduction in printing. [PERSON] [8] presented an equation that predicts the optical density of a print given the reflectance of the unprinted substrate and the known percent area covered by halftone dots. This simple equation later became the standard for calibrating printers for consistent color. [PERSON] [9] developed the Neugebauer equations, which predict the color produced by a combination of halftones printed in cyan, magenta, and yellow inks, based on the assumption that the color of a printed area can be predicted by the area coverage of each primary color. Building on these foundational works, several studies have attempted to predict the color printed by ink. [PERSON] and [PERSON] [10] used a generalized K-M model to predict the reflectance spectrum of transparent fluorescent inks printed on paper. They then incorporated the Neugebauer model to create a new prediction model that explains light scattering in printing and ink diffusion [11]. [PERSON] and [PERSON] [12] revised the K-M model to describe systems composed of absorption-dominant and scattering-dominant materials, such as a mixture of ink and paper, and [PERSON] et al. (2013) used the K-M model to predict the reflectance of paper printed with a combination of two primary inks. Conversely, other studies have focused on predicting primary ink composition using reflectance information ([PERSON] and [PERSON], 2016; [PERSON] et al., 2017). [PERSON] and [PERSON] (2016) predicted reflectance and transmittance in the presence of a transparent film over paper using the Yule-Nielsen Modified Spectral Neugebauer model, which accounts for the scattering of light within the paper. Because predicting spot color inks requires complex calculations, [PERSON] and [PERSON] (2017) proposed a simplified model that uses the XYZ color space to compute CMYK and two spot color combinations. [PERSON] et al. (2018) also simplified the Clapper-Yule model ([PERSON] et al., 2018), which considers the reflection of light from multiple overlapping inks, by treating spot color inks as multiple inks in parallel or in a superimposed configuration.