###### Abstract  
The aim of this study was to explore the feasibility of quantitatively evaluating a sapphire's color by analyzing gemstone images. The color characteristics of gemstones through photography and color extraction were accurately captured, and the key color parameters for different color regions of gemstones were extracted. Then, the color of sapphires was simulated by statistical method and function simulation method. The results indicate that the brightness value of the bright area was the highest and the chroma value of the \"fire\" area was the highest. The chroma (**C**) of the sapphires was linearly positively correlated with the absolute value of its **b** value, and the brightness (**L**) showed a quadratic correlation with its chromaticity parameters (**b** or **C**). The function simulation method with an average of **b** as the main independent variable had a larger standard deviation, which proves that this method has a stronger ability to distinguish the differences in a sapphire's color. This method can be extended to the color evaluation of other colored gemstones, and it can be used to form a gemstone color evaluation system. s +
Footnote †: journal: Applied sciences  
overall color. [PERSON] believes that, due to the reflection, refraction, and other effects of light, the human eye observes more facets than the actual facets of a gemstone, and these extra facets are called \"virtual\" facets [19]. These virtual facets present different colors and form \"invisible boundary patterns\" and \"brightness contrast\", which affect the evaluation of a gemstone's color [24]. The color of the table is observed when evaluating the color of colored gemstones. Transparent, faceted, and colored gemstones can exhibit different colors on each facet due to the reflection and refraction of light. The quantitative color evaluation of faceted, colored gemstones needs to consider the influence of each facet's color on the overall color. The color of faceted colored gemstones is related not only to the color of the original stone, but also optical effects such as brightness, fire, and darkness. These factors affect the human visual perception system, ultimately influencing the color presented in our brain. At present, the research on the color evaluation of colored diamonds is relatively comprehensive, and some difficulties have also been found. For example, pink diamonds with low saturation in brown or brown shades are often confused with pink diamonds that have orange tones [25]. This indicates that the human eye cannot accurately distinguish the hue of gemstone colors. Two blue diamonds with the same color difference are more likely to be in different color grades than two yellow diamonds with the same color difference [26], and the K-M, N-R, and S-Z color grades of the D-to-Z series diamonds overlap with the Faint, Very Light, and Light levels of yellow diamonds [27]. The colorimetric method is widely used for evaluating the color of gemstone, which operates by comparing the color with color cards or standard gemstones. [PERSON] et al. demonstrated the feasibility of using the Gemdialogue(tm) color card to evaluate sapphire colors [28]. [PERSON] et al. conducted semi-quantitative or quantitative evaluations of the colors of gemstones such as jadeite [29; 30], ruby [31; 32], manganese aluminum garnet [33], emerald [34], tourmaline [35], and citrine [36] in the CIE 1976 L* a* b* uniform color space by color cards for color comparison [37; 38] or by measuring color parameters with instruments. GIA and [PERSON] evaluated the color of gemstones using GemSet and GemDialogue, respectively [39]. The colorimetric method is subjective, and it can only be used for qualitative evaluation. Gem Research SwissLAB (GRS) used colorimetric methods to classify the color of rubies and sapphires into five levels: Intensity, Intensity to Vivid, Vivid, Vivid to Deep, and Deep. [PERSON] et al. [40] and [PERSON] et al.