## 2 Materials and Methods
### Manual Color Extraction  
The sapphires were placed in a light source box with D65 as the light source. The sapphire images were taken by a Canon EOS 200D which manufacturer was Canon (China), and with a neutral gray color card as the background. And the photograph condition was set as follows: a resolution of 720 dpi, an aperture value of f/8, and an exposure time of 1/200 s. The captured images were removed from the background by Adobe Photoshop CC 2018, and the width was adjusted to 300 pixels with the length changing proportionally. The sapphires' colors were divided into four regions based on the human perception of gemstone colors: brilliance, \"fire\", body color, and darkness. The color was manually selected in each region by Adobe Photoshop CC 2018 software based on the size of the region and the degree of color change (as shown in Figure 1). For Sample LBR01, Regions 1, 2, and 3 represent the brilliance, with one pixel color extracted from each region as a representative. The light shining on these three facets was mainly reflected to the human eye. But the amount of light reflected to the human eye was different, and the color seen was also different. As shown in Table 1, Numbers 1, 2, and 3 represent these three facets, and their color parameters and simulated color blocks are also listed. Regions 4, 5, 6, 7, 8, and 9 represent \"fire\", with one pixel color extracted from each region as a representative. Region 10 represents darkness, with one pixel color extracted as a representative. Region 11 represents body color, with one pixel color extracted as a representative.  
Figure 1: Schematic diagram of the manual color extraction on the Sample LBR01 image.  
Samples with noticeable optical effects were selected to extract the color parameters and to obtain representative color data. Six oval-shaped blue sapphires were selected (LBR01, LBR02, LBR03, LBR32, LBR33, and LBR34), and 73 sets of color parameters were manually extracted (including L, a, b, C, and h). Eleven pear-shaped blue sapphires were selected (LBP01, LBP02, LBP03, LBP04, LBP05, LBP07, LBP08, LBP14, LBP71, LBP72, and LBP80), and 120 sets of color parameters were manually extracted.  
The optical properties of each facet on the gemstones were nearly identical. Theoretically, there was a certain correlation among the color parameters of each pixel in the photographed image of the gemstone. Therefore, 193 sets of manually selected color parameters were subjected to correlation analysis. And correlation analysis was conducted on the color parameters of each region separately due to the significant differences in color among the four regions.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Number** & **Region** & **L** & **a** & **b** & **Simulated Color Block** \\ \hline
1 & Brilliance & 100 & 0 & 0 & \\
2 & Brilliance & 34 & 0 & \(-16\) & \\
3 & Brilliance & 57 & \(-1\) & \(-3\) & \\
4 & Fire & 22 & 30 & \(-62\) & \\
5 & Fire & 53 & 19 & \(-72\) & \\
6 & Fire & 27 & 30 & \(-67\) & \\
7 & Fire & 17 & 12 & \(-35\) & \\
8 & Fire & 7 & 14 & \(-32\) & \\
9 & Fire & 14 & 12 & \(-34\) & \\
10 & Darkness & 4 & 0 & \(-2\) & \\
11 & Body Color & 12 & 12 & \(-31\) & \\ \hline \hline \end{tabular}
\end{table}
Table 1: The color parameters of Sample LBR01.