3.1. Rules of Color Charts
The color parameters of the five color charts B, P2B, B2P, B3P*, B4P*, and their overlapping blackgray (transparent) and brown (transparent) color masks were tested under a D65 light source. A total of 7250 data were collected. The changes in lightness, L*, chroma, C*, and hue angle, h°, were observed to study the change pattern of the color charts and the effect of color masks on color.
Without superimposed masks, the range of the lightness,
L*, of B, P2B, B2P, B3P*, and B4P* are, in order,
L*B ∈ (43.51, 77.38),
L*P2B ∈ (31.43, 81.33),
L*B2P ∈ (34.1, 79.18),
L*B3P* ∈ (20.48, 65.43), and
L*B4P* ∈ (17.44, 69.18); the range of chroma,
C*, are successively
C*B ∈ (26.29, 66.58),
C*P2B ∈ (15.76, 74.2),
C*B2P ∈ (21.18, 103.2),
C*B3P* ∈ (28.54, 93.61), and
C*B4P* ∈ (21.93, 90.28); the range of hue angle,
h°, are
h°B ∈ (237, 266.4),
h°P2B ∈ (258.6, 286.8),
h°B2P ∈ (307, 312.9),
h°B3P* ∈ (259.1, 302.5), and
h°B4P* ∈ (285.6, 303.6), in order. With the color band value from 100 to 10, the lightness,
L*, of the five color charts increased successively, the chroma,
C*, decreased successively, and the hue angle,
h°, showed an overall decreasing trend (
Figure 2). Very few samples did not follow this pattern, which may be related to the stability of the instrument. As can be seen from the figure, there are many overlapping parts of lightness,
L*, and chroma,
C*, in the five color charts, but the difference in hue angle,
h°, is obvious, which belongs to five different hue intervals, and the size relationship is:
h°B2P >
h°B4P* ≥
h°B3P* ≥
h°P2B ≥
h°B. The hue of B2P tends to be purple, the hue of B4P* lies in blue–purple, and the hue of B3P* partly lies in bluepurple and partly tends to blue. Color chart B and P2B are both located in blue, but the blue of B is lighter. Secondly, although the change trend of color parameters in each color chart is the same, the change speed is different, the chroma,
C*, and hue angle,
h°, are the most obvious.
3.1.1. The Influence of Color Mask on Lightness, L*
As shown in
Figure 3, when the color mask is not superimposed, it is the first part. The data obtained by superimposing a blackgray mask above the color charts, superimposing a blackgray mask below, superimposing a brown mask above, and superimposing a brown mask below are part II to V, respectively. It can be clearly seen that the lightness,
L*, is the highest when the color mask is not superimposed. After the color masks are superimposed, the lightness,
L*, of the three color charts is reduced, but the degree is different. Through data comparison and analysis, the decrease of lightness,
L*, after superposition of the blackgray mask is significantly higher than that of superposition of the brown mask, indicating that the blackgray mask has a greater impact on lightness,
L*, than the brown mask. Secondly, the superposition method of the color mask also affects the change degree of the lightness,
L*: both the blackgray mask and brown mask have a greater effect on the lightness,
L*, when the mask is placed at the bottom than when the mask is placed at the top.
3.1.2. The Influence of Color Mask on Chroma, C*
As shown in
Figure 4, when the color mask is not superimposed, the chroma,
C*, is the highest. After the color mask is superimposed, the chroma,
C*, decreases as a whole, which is the same as the change rule of the lightness,
L*. Overlaying different color masks or when the color mask overlay mode is different, the degree of change of chroma,
C*, is also different. It is found that compared with the blackgray color mask, the overall change of the chroma,
C*, is greater when the brown color mask is superimposed, indicating that the brown mask has a greater impact on the chroma,
C*. Secondly, the influence of the color mask on the chroma,
C*, is obviously greater than that of the color mask on the bottom, which is opposite to the law of the lightness,
L*, and the lighter the color, the greater the influence of the color mask.
3.1.3. The Influence of Color Mask on Hue Angle, h°
As shown in
Figure 5, it is found that the overall effect of the superimposed blackgray color mask on the hue angle,
h°, of the color standard is not significant, while the effect of the brown mask is obvious, especially for the color chart B2P. And it is observed that the superposition method of the color mask has little effect on the hue angle,
h°, that is, whether it is the superposition method of the color mask is on or under the color charts, the range of the hue angle,
h°, is not significantly different.
3.2. Color Grading of Color Charts
According to the color characteristics of the GemDialogue color charts and iolite, the range of the hue angle, h°, was determined to be between 240–310°, a total of 1930 data were selected. The selected data continuous are well, no obvious leap, and better cover the color range of blue iolite 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°, 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.
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.
According to the classification results, the hue angle, h°, of the first and fourth categories are similar, ranging from 280° to 310°, belonging to the range of bluepurple to purple hue. However, the lightness, L*, and chroma, C*, 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. The chroma, C*, of the second category is the highest in the 6 categories, indicating that its blue is the strongest and purest. Although the lightness is low, it has little influence on the color appearance. The mean values of hue angle, h°, of the third and fifth categories are similar, both have a hue angle between 240°and 300°, belonging to the blue color. While the lightness, L*, and chroma, C*, of the two are different. The lightness, L*, of the third category is higher than that of the fifth category, but the chroma is the lowest among the 6 categories, so the color of the third category belongs to the grayblue with low saturation. Although the saturation of the fifth category is slightly higher than that of the third category, due to the low lightness, it shows dark blue with obvious blackgray tone. The 6th category has similar lightness and chroma, its color appearance is light blue to blue.
For more accurate classification of the blue color charts, K-Means clustering analysis is performed again on categories 1 and 6 that have large color differences. The clustering results are shown in
Table 4.
Category 1 is further divided into three categories, whose color features are purple, light purple, and bluepurple, respectively. Category 6 is divided into two categories, with color characteristics of blue and light blue.
Based on the above analysis, the color characteristics and classification of 9 categories of color charts are summarized in
Table 5.
3.4. Application and Feasibility Study
Twenty-nine elliptic faceted blue iolites were selected for color test with the integrating sphere handheld spectroscopy, and color parameters
L*,
a*,
b*,
C*, and
h° were recorded. Due to the pleochroism of iolite, the table facet was selected as the color measurement surface in this paper. The color data were substituted into the discriminant functions of 9 categories, respectively, to obtain the category of each sample, and the results were shown in
Table 7.
The 29 samples were divided into three categories and classified into four color levels, among which 1 sample belonged to light purple with high lightness and medium chroma, 11 samples belonged to bluepurple with high lightness and medium chroma, 2 samples belonged to grayblue with low chroma, and 15 samples belonged to bluepurple with black and gray tones. After observation, it was found that the classification results were consistent with the visual observation, and the color comparison between some samples and the cluster centers is shown in
Figure 7.
Although not all categories were covered due to the limited number of samples, the results proved that this method is still feasible and can provide a more objective and stable basis for color classification of blue iolite than the visual evaluation.