The L*a*b* color model is based on opposite color theory and reference white point (Wyszecki and Stiles, 1982). It is independent of devices used, and is suitable for applications with natural illumination. L*, a*, b* are nonlinearly related to R, G, B, through the middle terms X, Y, Z(tri-stimulus):

$X=0.4902R+0.3099G+0.1999B\text{}\text{}\text{}\text{}\text{}\left(8.54\right)$

$Y=0.1770R+0.8123G+0.0107B\text{}\text{}\text{}\text{}\text{}\left(8.55\right)$

$Z=0.0000R+0.0101G+0.9899B\text{}\text{}\text{}\text{}\left(8.56\right)$

L*, a*, b* are then computed by

${L}^{\ast}=\{\begin{array}{l}116{\left(Y/{Y}_{0}\right)}^{1/3}-16\text{}if\text{}Y/{Y}_{0}>0.008856\\ 903.3{\left(Y/{Y}_{0}\right)}^{1/3}\text{}\text{}if\text{}Y/{Y}_{0}>0.008856\end{array}\text{}\text{}\text{}\left(8.57\right)$

${a}^{\ast}=500\left[f\left(X/{X}_{0}\right)-f\left(Y/{Y}_{0}\right)\right]\text{}\text{}\text{}\text{}\left(8.58\right)$

${b}^{\ast}=200\left[f\left(Y/{Y}_{0}\right)-f\left(Z/{Z}_{0}\right)\right]\text{}\text{}\text{}\text{}\left(8.59\right)$

where

$$

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