# CIELab 1976 Color Model

## CIELab

$L^*$, $a^*$, and $b^*$ are the 1976 CIELab lightness, red-green, and yellow-blue values, respectively. They are computed as $$L^* = 116 f\left ( \frac{Y}{Y_n} \right ) - 16$$ $$a^* = 500 \left [ f\left ( \frac{X}{X_n} \right ) - f\left ( \frac{Y}{Y_n} \right )\right ] \; \; \; \; b^* = 200 \left [ f\left ( \frac{Y}{Y_n} \right ) - f\left ( \frac{Z}{Z_n} \right )\right ]$$ where $$f(x) = \left\{\begin{matrix} x^{1/3} & x > 0.008856\\ 7.787x + 16/116 & x \leq 0.008856 \end{matrix}\right.$$

## Tristimulus values

Tristimulus values $X$, $Y$, and $Z$ are the relative luminances of total luminance $Y$, blue stimulation $Z$, and $X$ is a linear combination of the cone response curves, all from 0 to 100. $X_n$, $Y_n$, and $Z_n$ are the tristimulus values for the reference white. After performing either conversion, the specified color is plotted on the CIE1931 Chromaticity diagram.

References:
1. Color Vision and Colorimetry: Theory and Applications, Second Edition by Daniel Malacara, SPIE Press, 2011