# Feasibility Study on Color Grading of Blue Iolite Based on GemDialogue Color Comparison Charts
## 3 Result and Discussion
### Color Grading of Color Charts  
According to the color characteristics of the GemDialogue color charts and idolite, the range of the hue angle, \(h^{\circ}\), was determined to be between 240-310\({}^{\circ}\), a total of 1930 data were selected. The selected data continuous are well, no obvious leap, and better cover the color range of blue idolite from low to high chroma. This paper uses K-Means clustering analysis to classify the data. The K-Means algorithm seeks the best partitioning of data through iterative optimization steps and minimization of square error [34], the basic idea is to divide the data space randomly into k classes specified in advance, and then update the centroid of each class through iterative calculation, when the results of two adjacent iterations are basically the same, the algorithm converges [35]. The selection of K value in K-Means clustering is often based on subjective experience, which cannot determine whether it is the best clustering number. Therefore, the elbow rule was chosen in this paper to determine the best K value of data. The basic principle of elbow rule is to determine the optimal cluster number by calculating the sum of the squared errors (SSE) under different cluster numbers, when the number of clusters increases to a certain extent, SSE will sharply slow down, forming an elbow, the number of clusters corresponding to the elbow is the optimal K value [36]. According to the results of the elbow rule (Figure 6), data works best when divided into 6 categories. Lightness, \(L^{*}\), chroma, C\({}^{+}\), and hue angle, \(h^{\circ}\), were selected as variables. K-Means clustering analysis was used to divide the color data into 6 categories, and the clustering results were shown in Table 2.  
Figure 5: The change of hue angle, \(h^{\circ}\), after three color charts superimposed with different color masks. According to the one-way ANOVA of the three parameters of the 6 categories (Table 3), the \(P\) values of the three parameters were all less than the significance level of 0.05, indicating that the fast clustering analysis of the test data divided into 6 categories was basically successful and the clustering effect was relatively ideal. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Cluster Center** & **Average Value** & **Simulated Color** & **Amount** \\ \hline \multirow{4}{*}{1} & \(L^{*}\) = 50.20 & \multirow{4}{*}{110} \\  & \(C^{*}\) = 45.20 & & 110 \\  & \(h^{\circ}\) = 303.03 & & \\ \hline \multirow{4}{*}{2} & \(L^{*}\) = 27.66 & \multirow{4}{*}{70} \\  & \(C^{*}\) = 82.25 & & 70 \\  & \(h^{\circ}\) = 294.36 & & \\ \hline \multirow{4}{*}{3} & \(L^{*}\) = 44.67 & \multirow{4}{*}{400} \\  & \(C^{*}\) = 19.48 & & 400 \\  & \(h^{\circ}\) = 250.78 & & \\ \hline \multirow{4}{*}{4} & \(L^{*}\) = 23.01 & \multirow{4}{*}{135} \\  & \(C^{*}\) = 25.78 & & 135 \\ \cline{1-1}  & \(h^{\circ}\) = 304.49 & & \\ \hline \multirow{4}{*}{5} & \(L^{*}\) = 25.30 & \multirow{4}{*}{735} \\  & \(C^{*}\) = 27.31 & & 735 \\ \cline{1-1}  & \(h^{\circ}\) = 255.84 & & \\ \hline \multirow{4}{*}{6} & \(L^{*}\) = 46.66 & \multirow{4}{*}{480} \\  & \(C^{*}\) = 45.49 & & \\ \cline{1-1}  & \(h^{\circ}\) = 262.17 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: K-Means cluster analysis results. Figure 6: The relationship between K and Sum of the Squared Errors (SSE). According to the classification results, the hue angle, \(h^{\circ}\), of the first and fourth categories are similar, ranging from 280\({}^{\circ}\) to 310\({}^{\circ}\), belonging to the range of bluepurple to purple hue. However, the lightness, \(L^{\star}\), and chroma, \(C^{\star}\), of the first category is much greater than the fourth category, which is blueviolet with a high lightness and medium chroma, some samples can reach light purple, with the best color in the 6 categories. While the fourth category gave the sample a bluepurple hue with a distinct blackgray tone due to a too low lightness and chroma.