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Article

A Study on DNN-Based Practical Model for Predicting Spot Color

by
Jaekyeong Moon
†,
Geonhee Yang
† and
Hyunchul Tae
*
Department of Digital Healthcare R&D, Korea Institute of Industrial Technology (KITECH), Cheonan-si 31056, Republic of Korea
*
Author to whom correspondence should be addressed.
†
These authors contributed equally to this work.
Appl. Sci. 2023, 13(24), 13100; https://doi.org/10.3390/app132413100
Submission received: 14 October 2023 / Revised: 30 November 2023 / Accepted: 1 December 2023 / Published: 8 December 2023
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Abstract

:
The color of product packaging plays an important role in brand awareness and consistency. Given the importance of consistent color reproduction, the use of standardized spot colors is essential. However, the reproduction of specific spot colors in offset packaging printing involves additional processes and costs. This study presents an efficient approach to predict the color result of spot color inks in the packaging printing industry, using only the amount of ink involved in the mixing process as an input. Using a neural network-based model, our approach uses the CIEDE2000 color difference formula as a loss function to accurately estimate the final color. This method provides a simplified alternative to traditional color mixing techniques, which often involve subjective judgment and can be resource-intensive. Particularly beneficial for smaller companies, our approach reduces the complexity and cost associated with achieving accurate spot colors. The significance of this work lies in its practical application, providing a simpler, more objective and cost-effective solution for consistent color reproduction in packaging printing.

1. Introduction

1.1. Backgrounds

Product packaging does more than just attract the consumer’s attention. It provides essential information about the product, allowing consumers to make quick and informed decisions. But a subtle but critical aspect of packaging is its color. Think of Coca-Cola’s bold red or Starbucks’ signature green, and it becomes clear that packaging color alone can evoke a specific product or brand [1]. As a result, many brands are recognizing color not just as an aesthetic choice, but as a powerful communication tool that is integral to their brand identity. Consistent color presentation is a priority for them, regardless of their global location.
Given the importance of color, the use of spot colors becomes essential. Spot colors refer to predefined, specific colors. A leading example of standardization is the Pantone Matching System (PMS) [2]. Developed by Pantone, it is used worldwide for color communication. Within the system, each spot color is identified by its unique number and name, allowing for consistent reference and reproduction around the world. This allows brands to ensure that their distinctive colors are expressed consistently.
But the reality in the packaging printing industry, where mass production is essential, is relatively complex. The dominant method in this field is the CMYK model, which is based on the use of four primary colors: Cyan (C), Magenta (M), Yellow (Y), and Key (Black) (K). These inks are used in varying proportions to produce a wide range of colors. The CMYK model works on the principle of subtractive color mixing, where colors are created by subtracting different amounts of light. Unlike additive color models, which work by adding light (like screens), subtractive color models work by absorbing some wavelengths of light and reflecting others. By combining these four inks in varying proportions, a wide range of colors can be reproduced on the printed material. This method is particularly economical for high-volume printing, ensuring consistent quality across large batches of printed materials [3]. However, complexity is introduced by the use of spot colors, which are specific pre-mixed inks used to achieve precise shades that are not easily achieved with CMYK mixing. These standard spot colors, such as those from the Pantone Matching System (PMS), require additional processes to accurately reproduce. In particular, the manual mixing and testing of these spot colors by colorists can be error-prone, resulting in discrepancies between intended and final print colors. This issue is particularly challenging for smaller printers, where operator expertise and subjective judgment play an important role. Factors such as lighting conditions can also affect their perception, leading to inconsistencies and inefficiencies in the mixing process. These inconsistencies result in wasted resources and increased costs. From the customer’s perspective, the use of spot colors is to achieve consistent coloration, so the inconsistent print results are undesirable from a quality control standpoint.
In response to these challenges, this study presents a deep learning-based model that predicts ink mixing results without actual ink mixing in packaging printing. The use of these techniques has become more prevalent in the manufacturing domain, increasing productivity in recent years [4]. Based on actual process data, the model is designed to reduce the human color perception bias.

1.2. 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, Saunderson [6] adjusted the reflectance value by applying a correction factor that accounts for the specular reflectance of the material’s surface. Allen [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. Murray [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. Neugebauer [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. Emmel and Hersch [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]. Yang and Kruse [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 Rouselle et al. [13] 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 [14,15]. Machizaud and Hebert [16] 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, Deshpande and Green [17] proposed a simplified model that uses the XYZ color space to compute CMYK and two spot color combinations. Lin et al. [18] also simplified the Clapper-Yule model [19], 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.
Meanwhile, as academic interest in machine learning (especially neural networks) has grown over the past few decades, studies have been conducted in the printing industry to apply these techniques. In a cross-disciplinary effort within the industry, Joost and Salomon [20] proposed a neural network-based image pre-processing method to cope with the quality degradation caused by thicker printing plates, and optimized the parameters of the neural network using evolutionary algorithms. Limchesing et al. [21] used an ANN model to predict the percentage frequency of common spoilage problems in offset printing based on information about the ink used in the print, the machine, the paper, and the design, while Sarkar et al. [22] used machine learning techniques to analyze the relationship between ink thickness and other process variables to predict ink thickness as a function of process variables in an offset press sensitive to environmental conditions. Villalba-Diez et al. [23] used DNN to improve traditional visual inspection methods in the production of gravure cylinders used in printing. It achieved 98.4% classification accuracy on files used to engrave cylinders and on surface scans of produced cylinders. Zhang et al. [24] used DCNN to extract features from print samples with an unbalanced number of samples according to defect types, and then classified the defect types into four categories. Based on data collected from actual printed products at the factory, a classification accuracy of 96.86% was achieved. Brumm et al. [25] evaluated CNN-based models to automate traditional manual labor in gravure pattern classification and found a model with a classification accuracy of 95.2%. Haik et al. [26] presented a real-time deep learning approach for detecting differences between reference and printed images in variable data printing. Chen et al. [27] used ResNet-50 to classify the conditions under which an image was printed based on the moiré pattern present in the print. The results suggest that deep learning technology can be applied to printing to prevent document forgery. More recently, with the advent of printed electronics technology, which uses functional inks to produce electronic circuits, Brishty et al. [28] used machine learning models to analyze the movement of ink droplets and predict the quality of jetting in inkjet printing methods. Gafurov et al. [29] proposed a print quality assessment system for printed electronics using gravure offset printing. The system uses a DCNN with skip connections to classify print quality and a pre-trained object detection model to detect defects in the print.
Regarding color, Bishop and Westland [30] investigated a neural network approach to learning the relationship between colorant and color as an alternative to the K-M model for the recipe prediction problem. Tominaga [31] proposed a color reproduction method for dye sublimation printers using a neural network that learns the mapping from the RGB coordinates of the printed color to the CMY value, the primary color of the print, using a back-propagation technique. Littlewood et al. [32] presented an ANN model as a function for converting device-independent CIELAB values from digital images to CMYK spaces for printing. Hajipour and Shams-Nateri [33] improved the accuracy of predicting CMYK values for reproducing printed sample colors by introducing a cascade-forward neural network on training samples divided into multiple subgroups by a competitive neural network. Due to the non-uniformity of the LAB color space, Zhao and Chen [34] divided the printed color sample into 10 parts based on hue angle and developed a model that uses a separate neural network for each part to learn the complex relationship between printed colors and digital pixel values (RGB).
However, these previous studies are mainly limited to data printed with predetermined CMYK inks, which is not directly applicable to the printing environment of an integrated packaging printer. The diversity of packaging formats has led companies to use a variety of inks to achieve accurate color reproduction on different types of substrates, some with the same CMYK but different properties, and some with no pigments and only additives. Spot color inks, which are blends of these inks, may contain different spot colors in addition to the basic CMYK and additives. There are also slight differences between inks of the same CMYK, depending on the manufacturer, so decisions in the color mixing process need to be able to cover a wide range of inks, but there is a lack of research in this area. In painting, another field where color reproduction is important, Xu et al. [35] proposed a neural network-based model to predict the reflectance and transmittance of a mixture of 18 pigments for water-based painting, and Chen et al. [36] built a deep neural network (DNN)-based smart palette system with 13 pigments for novice painters who find it difficult to create the desired color, but they differ from the color matching process in printing in that only two colors are used in each mixture. Souper et al. [37] modeled a DNN that predicts the color of mixed materials by considering the mixing of multiple glazes and pigments in the ceramic industry and proposed an optimization strategy to improve the prediction performance, but it is difficult to assume the same situation because the mixture is applied to a non-paper substrate.
Therefore, this study aims to present a practical prediction model that uses data collected during the color mixing process for actual printing without making assumptions about specific situations. The prediction is achieved by exclusively using the usage information of the inks involved in the color mixing process. This approach simplifies the prediction process and provides an efficient way to predict the results of color mixing process. Rather than a comprehensive consideration of the different environments of all packaging printers, we present an approach based on the company’s data as a starting point that can be applied in the future by any company with data in a similar field.

2. Materials and Methods

2.1. Data Acquisition

In this study, data collection was conducted to develop a color prediction model based on spot color ink mixing ratios. We obtained a total of 19,032 records of spot color ink production data from a small comprehensive packaging printing company, Deoksu Industries Co., Ltd., Cheongju-si, Republic of Korea, with KBA Rapida 105, a printing press from Koenig & Bauer AG, Würzburg, Germany, from 20 May 2020 to 5 January 2022. Spot color inks are produced by mixing conventional inks to achieve specific colors. The data was collected during the actual printing process, specifically from the ink mixing procedures to produce spot color inks. It is important to note in the printing industry that the reproduction of ink colors on printed substrates is more important than the intrinsic color of the inks themselves. For this reason, a test print is made on a sample of the paper to be printed to assess the color reproducibility of the spot color inks prior to the start of the mass production run. This test printing serves as a measure of quality control for the color-matching process. So, we measured the color information printed on the test print paper for spot color inks created using 62 types of basic inks. Table 1 lists the data collected on the production information of the spot inks.
The color of the printed ink was accurately measured using the eXact Standard spectrophotometer from X-Rite, Inc., Grand Rapids, MI, US. Each data point includes reflectance information for 31 segments within the visible light spectrum, as well as LAB values. Reflectance in the visible spectrum indicates the amount of visible light reflected by an object, which is critical to understanding color intensity and brightness. In the printing industry, it is used to quantify the color characteristics of substrates or inks. In our research, reflectance was measured by dividing the wavelength between 400 nm and 700 nm into 31 sections. On the other hand, LAB values refer to the three numerical components of a particular color in the LAB color space. The LAB color space is an absolute color representation method specified by the International Commission on Illumination(CIE) based on human vision. It encompasses all perceivable colors and consists of L*, a*, and b* values, which indicate lightness, the range from green to red, and the range from blue to yellow, respectively. These values provide consistent color information under different lighting conditions and locations, making color comparisons easier. The mixing amount of each of the 62 basic inks was recorded as a variable necessary for ink manufacture, with the basic ink information represented by codes (e.g., 20120002) used by the supplier company. Since the test prints were not consistently made on identical paper during the color mixing process, the data also included the size and weight of each test printing paper, along with its reflectance for the 31 segments in the visible light range measured by the spectrophotometer.

2.2. Data Preprocessing

The data was obtained from operator-recorded measurements, which posed a challenge in ensuring absolute accuracy due to potential recording errors and measurement discrepancies. To obtain reliable results, entries with reflectance values below 0 or above 100, as well as those with zero total ink usage, were removed, resulting in 8267 valid data points out of a total of 19,032. The reason for excluding reflectance values outside the 0–100 range is that reflectance is measured as a percentage. Values below 0 or above 100 indicate likely errors in measurement or data collection, likely due to the challenges associated with delegating data collection to field workers. Such anomalies are not feasible within the standard parameters of reflectance measurement and are treated as inaccuracies. In addition, the removal of records with zero total ink usage is based on the fundamental principle of spot color ink production. Each row in our data set represents a record of spot color ink created by mixing different material inks. When the total amount of material ink used is recorded as zero, it contradicts the very process of ink creation and suggests a recording error or data entry oversight. Therefore, these records were considered invalid for the purposes of our analysis to ensure the integrity and reliability of the data set.
In some cases, despite the consistent mixing process, the measured color values show variations (as shown in Table 2). While minor color differences may appear as noise, data points with significant color differences were considered potentially detrimental to the performance of the model. Therefore, a simple algorithm was created to recognize and remove such inaccurate data points prior to model training.
The data can be divided into three groups based on the ink used for mixing and its corresponding usage. These groups consist of data sets that share a common mixing method with one data point, two data points, or more than three data points. If there is only one data point for a particular mixing method, the data is considered to be accurately collected. Discrepancies are detected based on color values when the same mixing method appears in multiple data points. However, since print results may vary depending on the test paper used, the anomaly detection process also takes into account the color similarity of the paper. Since the color information of the paper was collected only through the spectral reflectance, the LAB converted value was used.
First, if a subset of data sharing a mixing method consists of two entries with a small difference in paper color but a significant difference in printed color, both are considered anomalous (since it’s difficult to determine which is correct, both are excluded). If more than three entries are created using the same mixing technique, this subset of data is clustered based on paper color similarity. If a cluster is formed that contains two entries with significant differences in printed color, they are identified as anomalies. For clusters with more than three entries, any data point that has a significant average color difference from the others within the cluster is categorized as an outlier. Here, the color difference is measured in National Bureau of Standards(NBS) units (1), a scale that has perceptual thresholds for values. Based on the established criteria (as shown in Table 3), an NBS unit greater than 6 is considered a significant color difference. After this preprocessing, a total of 7146 valid data were available.
NBS unit = 0.92 × [ ( Δ L * ) 2 + ( Δ a * ) 2 + ( Δ b * ) 2 ) ] 1 / 2

2.3. Deep Learning Model

To create a predictive model for spot color inks, we used deep learning techniques. We selected the mixing method of the basic inks and the characteristics of the paper as input features for the model, recognizing their significant influence on the resulting colors. To address problems that may arise from the high dimensionality of the input features, we converted the color and specification information of the paper into LAB values and density, respectively. We also excluded five types of basic inks that were not used in any data. In addition, we simplified the model to directly predict LAB values for better interpretability when analyzing the results. Figure 1 is the result of the correlation analysis on the input features, which shows no obvious spatio-temporal dependencies among the selected input features. Thus, CNN or RNN models proved to be ineffective for learning from this data. Therefore, a Deep Neural Network (DNN) architecture was implemented to effectively process structured data for model design.
The designed DNN model consists of a single input layer, several hidden layers, and a single output layer. The input layer is composed of neurons representing 61 input features, while the output layer is composed of three neurons representing the L*, a*, and b* color values we want to predict (Figure 2).
The expressiveness of such a DNN structure is due to the number of hidden layers and the corresponding number of parameters. As the depth of the network increases, it can learn complex data patterns more accurately. However, simply increasing the depth of the network is prone to problems such as gradient vanishing and overfitting. To improve the performance of the model while remaining robust to these challenges, the following strategies were employed in this study.
  • SELU Activation Function: SELU is a variant of the ELU function. It has self-normalizing property that keeps the output of each layer at a mean of 0 and a standard deviation of 1 during training. This helps to avoid problems such as gradient vanishing or explosion, thereby improving the stability of the learning process [39]. However, these properties are maintained exclusively under certain model structures, namely fully connected layers in feed-forward neural networks. As the DNN structure used in this study adheres to this framework, SELU was chosen as the activation function. Before being fed into the model, the input features are standardized, and all hidden layer weights are initialized using the LeCun initialization technique to employ SELU.
  • AdamW Optimizer & Early Stopping: The model optimization algorithm used the AdamW optimizer, an improved version of Adam that applies weight decay through L2 regularization. AdamW is known to limit model complexity, thus preventing overfitting to the training data and improving generalization capabilities [40]. In addition, we adopted an early stopping strategy, where model weights are only saved when performance declines on the validation data. This approach aims to mitigate overfitting.
  • 1-Cycle Scheduling [41]: The learning rate starts at a low initial value during training, then increases rapidly to reach its peak, and finally decreases to a value lower than the initial setting. This approach prevents the model from getting stuck in local optima, allowing for rapid convergence. Once the model has converged, minor adjustments are made to ensure optimal weight exploration.
The model’s loss function employed the Δ E * , a metric for quantitatively evaluating color differences, instead of the Mean Squared Error (MSE) commonly used for regression problems. Humans typically do not perceive differences in brightness, hue, and saturation of colors uniformly. In certain color ranges, even small color variations may be strongly perceived, while in other ranges, substantial color shifts may be perceived as negligible [42]. Color differences can be calculated as the Euclidean distance in the LAB color space ( Δ E a b * ). However, this study used Δ E 00 * as the loss function to more accurately reflect visible color differences, which is critical in the printing industry where color accuracy is essential. The Δ E 00 * color difference formula, developed by the CIE, objectively corrects for color differences by accounting for the nonuniformity of human perception. This complex formula captures the interplay between color brightness, hue, and saturation [43,44] (Appendix A).

3. Results

Experiments were conducted to evaluate the mixed ink color prediction model developed in this study. The model was developed in a Python 3.8 environment using Pytorch 1.12.1 (CUDA 11.3). The experiments were conducted on a system equipped with a 3.2 GHz Hexadeca Core CPU, NVIDIA-A100-SXM4-40GB GPU, 1 TiB RAM, running Ubuntu 20.04.5 LTS.

3.1. Preprocessing Validation

In this study, an experiment was designed to validate the performance and effectiveness of the proposed preprocessing method. The main objective was to determine the differences in the performance of the prediction model, specifically focusing on the mean loss value on the evaluation set, when preprocessing was applied versus when it was not. Two models with identical architecture and hyperparameter settings were used. The first model was trained on the raw data set, while the second model used the data set that had undergone the proposed preprocessing. Based on this experimental setup, both models underwent 30 independent training and evaluation iterations. The mean loss values from these iterations were then compared for statistical analysis.
A t-test was conducted to statistically compare the mean loss values of the two models. As shown in Table 4, the results showed a significant decrease in the mean loss value for the model trained with the preprocessed data. Specifically, the model using preprocessed data consistently showed a lower mean loss of 0.4692 compared to its counterpart, with a p-value less than 0.05, highlighting the statistical significance of the observed difference. These results show the effect of the proposed preprocessing technique in reducing the loss of the prediction model, thus demonstrating its importance in the field of ink color prediction.

3.2. Hyperparameter Optimization

Before evaluating the model, hyperparameter optimization was conducted to optimize its performance. The effectiveness of a DNN depends heavily on the number of hidden layers and the number of neurons within each layer [45]. Therefore, we experimented with different combinations of hyperparameters to determine the ideal set. Individual model tests for each combination used the K-fold cross-validation method to evaluate performance on unseen data.
Table 5 shows that the model with 5 hidden layers and 512 neurons in each layer achieved the best performance on the validation dataset, with K set to 9. In this configuration, the model predicted colors with an average difference of 3.6280. Therefore, the model will be further evaluated based on these findings.

3.3. Experimental Results

We conducted experiments on the pre-split test data using the model derived in Section 3.2. Figure 3 shows the progression of training and validation losses over the course of 100 epochs during the model’s learning process. In the given graph, both losses decrease sharply at first and then level off, showing a converging trend. This indicates that the model is learning and generalizing well, as the validation loss decreases in tandem with the training loss, and both plateau in a similar range. If overfitting were occurring, we would expect the validation loss to either begin to increase or remain significantly higher than the training loss as the epochs increase. The close proximity of the two lines at the end of the graph suggests that the model has learned the patterns from the training data without overfitting, which is a good sign of a well generalized model.
Figure 4 shows the distribution of Δ E 00 * values between the predicted colors and the actual colors. The data is concentrated within a smaller range, with an average of 3.6679. In the printing industry, a Δ E 00 * value of 4.0 is regarded as an acceptable range for color difference [46]. About 72% of the test results fall below this threshold. With a median value of 2.1672, the majority of the values are between 1.1495 and 4.4487, as shown in the Table 6. Therefore, it can be concluded that the prediction model created in this study can effectively estimate the majority of spot colors.
Diving deeper into the color space (Figure 5), we see that the predictions are consistently accurate for darker shades with L* values below 33. The mid-range L* values, from 33 to 67, show a wider range of predictions, indicating occasional discrepancies. Lighter shades with L* values above 67 are consistently predicted, with a few notable exceptions. When looking at a* and b* values, colors in the positive quadrant for both show consistent model performance. However, colors with only positive a* values or only positive b* values occasionally deviate, especially in the mid-range L* values. Finally, the quadrant with negative values for both a* and b* predominantly shows stable performance, with some exceptions in the mid L* range. In addition, Table 7 provides a visual comparison of randomly selected test data, showing the model’s predicted colors alongside their actual counterparts. This allows visual interpretation of the performance of the numerical model. For colors predicted by Δ E 00 * below 4, it is difficult to visually see the difference from the actual color. This is kept at about 4, but it can be seen that the colors predicted by Δ E 00 * greater than 4 show a slight difference from the actual color.
However, notable discrepancies were observed in certain predictions, likely due to the model’s training process. Because this approach relies primarily on ink mixing ratios without specific color information, this approach may lead to a situation where if certain data patterns are underepresented compared to others, the model might struggle to learn and account for them effectively. Therefore, some strategies such as generating synthetic data using data augmentation techniques or introducing more comprehensive data could be explored in future studies to improve the accuracy and adaptability of the model.

4. Discussion

The significance of color in product packaging cannot be overstated, acting as a pivotal brand communication tool. Spot colors assure consistent color representation, offering standardization to brands. Despite this, the conventional CMYK mixing process, which is widely adopted in the packaging printing sector, presents difficulties in reproducing particular colors with precision, resulting in potential discrepancies and inefficiencies. Our study addressed the challenge of reducing color perception discrepancies in printing by introducing a deep learning model capable of predicting ink mixing outcomes, without the need for actual mixing. By exclusively using the usage data obtained through the color-matching process of a printing company, our model hopes to minimize inconsistencies in color perception. The model’s performance level of 3.6679 is a promising development that, in turn, suggests its potential utility as a dependable reference tool for industry experts. The outcome emphasizes the model’s ability to predict color, which, when fused with the proficiency of experts, can create a balanced combination of automation and human intervention. This can boost the precision and productivity of color mixing procedures.
However, our approach does have noteworthy restrictions. The use of a simplified model could overlook complex relationships among factors that impact ink colors. Moreover, relying on data from only one company introduces risks associated with the particular quality and features of that dataset. Our preprocessing methods attempted to rectify incorrect data. However, the intrinsic nature of the algorithms presents challenges in detecting anomalies for uncommon patterns. Given these limitations, there are two directions to enhance the potential of this research. Firstly, it is essential to refine the model by thoroughly exploring and identifying the various factors influencing the quality of printed colors. The refined model must directly incorporate these factors and account for the intricacies of the printing process, raw materials, and other relevant attributes. Ideally, a more segmented approach would be taken in conducting such an endeavour, catering to the unique requirements of each sector or segment. Refinement of our preprocessing methods is possible, in addition to the reduction of data dependency. For example, conceptualizing each data point as a node and building edges based on pattern similarities could lead to the formation of graphs. Graph neural network (GNN) techniques can be utilized to improve anomaly detection in graphs, leading to higher data quality and potential productivity enhancements. GNN also has the potential to lay the foundation for various data-driven productivity enhancements. Incorporating these directions into future research would likely enhance the applicability and robustness of the color prediction model in real-world printing scenarios.

Author Contributions

Conceptualization, J.M., G.Y. and H.T.; methodology, J.M. and G.Y.; software, J.M. and G.Y.; validation, J.M. and G.Y.; formal analysis, J.M. and G.Y.; investigation, J.M. and G.Y.; resources, J.M. and G.Y.; data curation, J.M. and G.Y.; writing—original draft preparation, J.M. and G.Y.; writing—review and editing, J.M., G.Y. and H.T.; visualization, J.M. and G.Y.; supervision, H.T.; project administration, H.T.; funding acquisition, H.T. All authors have read and agreed to the published version of the manuscript.

Funding

This study was carried out with the support of ’R&D Program for Forest Science Technology (Project No. 2021383A00-2323-0101)’ provided by Korea Forest Service(Korea Forestry Promotion Institute). This work was supported by the Korea Institute of Industrial Technology as “Development of holonic manufacturing system for future industrial environment [KITECH EO-230006]”.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The data presented in this study are available on request from the corresponding author. The data are not publicly available due to legal restrictions.

Conflicts of Interest

The authors declare no conflict of interest.

Appendix A. Δ E 00 * Calculation Formula

  • Computation of adjusted chroma C i ′ and hue h i ′ .
    For each color, C i ′ is computed as
    C i * = ( a i * ) 2 + ( b i * ) 2 i = 1 , 2
    where a i * and b i * are the chromaticity coordinates in the CIE L*a*b* color space. This step determines the chroma, which is a measure of color saturation or vividness.
    A factor G is is computed as
    G = 0.5 1 − C ¯ 7 C ¯ 7 + 25 7
    where C ¯ = C 1 * + C 2 * 2 is the average chroma. This adjustment factor G modifies the chroma values to reflect the viewing conditions.
    The adjusted chroma C i ′ and hue h i ′ are calculated as
    C i ′ = ( a i ′ ) 2 + ( b i * ) 2 i = 1 , 2
    h i ′ = arctan ( b i * , a i ′ )
    where a i ′ = a i * ( 1 + G ) . These adjusted values provide a nuanced representation of each color’s properties.
  • Determination of color difference components Δ L ′ , Δ C ′ , Δ H ′ .
    The difference in lightness Δ L ′ is calculated as
    Δ L ′ = L 2 * − L 1 *
    where L 2 * and L 1 * are the lightness values of the two colors.
    The difference in chroma Δ C ′ is given by
    Δ C ′ = C 2 ′ − C 1 ′
    The difference in hue Δ h ′ is computed with special handling for angles exceeding 180 degrees, ensuring accuracy across the hue spectrum.
    Δ h ′ = h 2 ′ − h 1 ′ | h 1 ′ − h 2 ′ | ≤ 180 ∘ ( h 2 ′ − h 1 ′ ) + 360 ∘ | h 1 ′ − h 2 ′ | > 180 ∘ , h 2 ′ ≤ h 1 ′ ( h 2 ′ − h 1 ′ ) − 360 ∘ | h 1 ′ − h 2 ′ | > 180 ∘ , h 2 ′ > h 1 ′
    Δ H ′ = 2 C 1 ′ C 2 ′ sin Δ h ′ 2
    where Δ H ′ is a more refined value that incorporates both the hue difference and the chroma values of the colors, providing a measure that is more aligned with human perception of color differences.
  • Final calculation of color difference Δ E 00 * .
    The average values for lightness, chroma, and hue ( L ¯ ′ , C ¯ ′ , and h ¯ ′ ) are computed.
    L ¯ ′ = L 1 * + L 2 * 2 , C ¯ ′ = C 1 ′ + C 2 ′ 2
    h ¯ ′ = h 1 ′ + h 2 ′ 2 | h 1 ′ − h 2 ′ | ≤ 180 ∘ h 1 ′ + h 2 ′ + 360 ∘ 2 | h 1 ′ − h 2 ′ | > 180 ∘ , h 1 ′ + h 2 ′ < 360 ∘ h 1 ′ + h 2 ′ − 360 ∘ 2 | h 1 ′ − h 2 ′ | > 180 ∘ , h 1 ′ + h 2 ′ ≥ 360 ∘ h 1 ′ + h 2 ′ C 1 ′ C 2 ′ = 0
    A rotational function T is calculated to address the non-linear perception of colors, especially in the blue region.
    T = 1 − 0.17 cos ( h ¯ ′ − 30 ∘ ) + 0.24 cos ( 2 h ¯ ′ ) + 0.32 cos ( 3 h ¯ ′ + 6 ∘ )                           − 0.20 cos ( 4 h ¯ ′ − 63 ∘ )
    The rotational term R T is calculated to account for the interaction between chroma and hue in the blue region.
    R T = − 2 ( C ¯ ′ ) 2 ( C ¯ ′ ) 2 + 25 7 sin 60 ∘ exp − h ¯ ′ − 275 ∘ 25 ∘ 2
    The comprehensive color difference Δ E 00 * is calculated as a weighted Euclidean distance using the formula
    Δ E 00 * = Δ L ′ k L S L 2 + Δ C ′ k C S C 2 + Δ H ′ k H S H 2 + R T Δ C ′ k C S C Δ H ′ k H S H
    where S L = 1 + 0.015 ( L ¯ ′ − 50 ) 2 20 + ( L ¯ ′ − 50 ) 2 , S C = 1 + 0.045 C ¯ ′ , S H = 1 + 0.015 C ¯ ′ T are scaling factors. These are applied to the lightness, chroma, and hue differences, respectively, to adjust for perceptual non-uniformities.

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Applsci 13 13100 g001
Figure 1. Correlation coefficients between the input features.
Figure 1. Correlation coefficients between the input features.
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Applsci 13 13100 g002
Figure 2. Architecture of spot color prediction model.
Figure 2. Architecture of spot color prediction model.
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Applsci 13 13100 g003
Figure 3. Training and validation losses over epochs.
Figure 3. Training and validation losses over epochs.
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Applsci 13 13100 g004
Figure 4. Distribution and cumulative frequency of Δ E 00 * .
Figure 4. Distribution and cumulative frequency of Δ E 00 * .
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Figure 5. Color distribution according to Δ E 00 * .
Figure 5. Color distribution according to Δ E 00 * .
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Table 1. Collected data on spot color ink manufacturing.
Table 1. Collected data on spot color ink manufacturing.
FeaturesUnit/Range
Spot ColorL* (luminance)[0, 100]
a* (green-red coordinate)[−128, 127)
b* (blue-yellow coordinate)[−128, 127)
Spectral reflectance 1%
Basic InkAmount used for mixing 2mg
PaperWidthmm
Heightmm
Weightmg
Spectral reflectance 1%
1 Divided into 31 sections from 400 nm to 710 nm. 2 By 62 inkcodes.
Table 2. Illustration of color sharing mixing formula.
Table 2. Illustration of color sharing mixing formula.
Mixed Basic Ink (Amount)Spot Color CodePaper ColorL*a*b* ValueSpot Color
20120015 (150 mg),
20120037 (1000 mg),
20120014 (30 mg),
20120019 (520 mg)		18991Applsci 13 13100 i001(50.95, −9.77, −20.27)Applsci 13 13100 i002
18999Applsci 13 13100 i003(60.41, −7.69, −16.96)Applsci 13 13100 i004
20220025 (4000 mg),
20220013 (400 mg),
20120004 (10 mg)		76Applsci 13 13100 i005(27.57, −0.87, −3.97)Applsci 13 13100 i006
82Applsci 13 13100 i007(86.84, −1.29, −0.57)Applsci 13 13100 i008
229Applsci 13 13100 i009(39.27, −2.58, −4.76)Applsci 13 13100 i010
20120002 (496 mg),
20120015 (558 mg),
20120021 (535 mg)		2177Applsci 13 13100 i011(26.32, 16.98, 19.45)Applsci 13 13100 i012
2216Applsci 13 13100 i013(28.99, 16.28, 19.73)Applsci 13 13100 i014
2224Applsci 13 13100 i015(79.11, 7.67, 13.36)Applsci 13 13100 i016
2244Applsci 13 13100 i017(26.63, 15.66, 18.26)Applsci 13 13100 i018
2252Applsci 13 13100 i019(28.74, 16.31, 19.52)Applsci 13 13100 i020
Table 3. NBS ratings [38].
Table 3. NBS ratings [38].
NBS UnitCritical Remarks of Color Difference
0–0.5TraceExtremely slight change
0.5–1.5SlightSlight change
1.5–3.0NoticeablePerceivable
3.0–6.0AppreciableMarked change
6.0–12.0MuchExtremely marked change
12.0+Very muchChange to other color
Table 4. Data preprocessing validation experiment results.
Table 4. Data preprocessing validation experiment results.
MeanStdtp
Raw Dataset4.57860.193510.61550.00
Preprocessed Dataset4.10940.1454
Table 5. Performance under various combinations of hyperparameters.
Table 5. Performance under various combinations of hyperparameters.
The Number of Hidden Layers Δ E 00 * The Number of Neurons
64128256512
3Mean4.42224.14583.93533.8109
Std0.11970.13580.13270.1198
4Mean4.35834.00183.79373.6750
Std0.12980.14310.13040.1273
5Mean4.22773.95053.74833.6280 *
Std0.11190.13410.12170.1060 *
6Mean4.19653.84623.66533.6292
Std0.11890.14270.13710.1525
* Minimum value.
Table 6. Statistical values of Δ E 00 * .
Table 6. Statistical values of Δ E 00 * .
StatisticsValueStatisticsValue
Count715Mean3.6679
25th percentile1.1495Std4.5817
50th percentile2.1672Min0.0738
75th percentile4.4487Max44.1385
Table 7. Illustration of the prediction result comparison on random samples.
Table 7. Illustration of the prediction result comparison on random samples.
Paper ColorMixed Basic Ink (Amount)Measured Value of Δ E 00 * Actual Color vs. Predicted Color
Applsci 13 13100 i02120220008 (1500 mg), 20220016 (3000 mg)0.7308Applsci 13 13100 i022
Applsci 13 13100 i02320220009 (250 mg), 20220016 (180 mg),
20220015 (9 mg), 20220056 (3500 mg),
20220014 (48 mg), 20220005 (40 mg)		0.4896Applsci 13 13100 i024
Applsci 13 13100 i02520120002 (13 mg), 20120015 (40 mg),
20120021 (83 mg), 20120037 (2000 mg)		0.7491Applsci 13 13100 i026
Applsci 13 13100 i02720120002 (1000 mg), 20120015 (450 mg),
20120014 (2000 mg)		1.1794Applsci 13 13100 i028
Applsci 13 13100 i02920220009 (90 mg), 20220022 (300 mg),
20120054 (1000 mg)		1.5656Applsci 13 13100 i030
Applsci 13 13100 i03120220008 (150 mg), 20220016 (1000 mg),
20220025 (1000 mg)		6.7326Applsci 13 13100 i032
Applsci 13 13100 i03320220014 (400 mg), 20220004 (500 mg),
20220005 (5000 mg)		1.4632Applsci 13 13100 i034
Applsci 13 13100 i03520120002 (100 mg), 20120007 (34 mg),
20120014 (10 mg), 20120009 (1000 mg)		0.5292Applsci 13 13100 i036
Applsci 13 13100 i03720220009 (590 mg), 20220015 (1000 mg),
20220005 (4000 mg)		4.0906Applsci 13 13100 i038
Applsci 13 13100 i03920120007 (230 mg), 20120015 (46 mg),
20120037 (2000 mg), 20120014 (11 mg)		8.1258Applsci 13 13100 i040
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Moon, J.; Yang, G.; Tae, H. A Study on DNN-Based Practical Model for Predicting Spot Color. Appl. Sci. 2023, 13, 13100. https://doi.org/10.3390/app132413100

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Moon J, Yang G, Tae H. A Study on DNN-Based Practical Model for Predicting Spot Color. Applied Sciences. 2023; 13(24):13100. https://doi.org/10.3390/app132413100

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Moon, Jaekyeong, Geonhee Yang, and Hyunchul Tae. 2023. "A Study on DNN-Based Practical Model for Predicting Spot Color" Applied Sciences 13, no. 24: 13100. https://doi.org/10.3390/app132413100

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