CIE 1976 L*a*b* is based directly on CIE XYZ and is an attampt to linearize the perceptibility of color differences. The non-linear relations for L*, a*, and b* are intended to mimic the logarithmic response of the eye. Coloring information is referred to the color of the white point of the system, subscript n.
CIE 1976 L*u*u* (CIELUV) is based directly on CIE XYZ and is another attampt to linearize the perceptibility of color differences. The non-linear relations for L*, u*, and v* are given below:
XYZ to CIE L*a*b* (CIELAB) and CIELAB to XYZ conversions
where f(t) = t1/3 for t > 0.008856
Here Xn, Yn and Zn are the tristimulus values of the reference white.
The reverse transformation (for Y/Yn > 0.008856) is
where P = (L* + 16) / 116
XYZ to CIELUV & CIELUV to XYZ conversions
The quantities un' and vn' refer to the reference white or the light source; for the 2° observer and illuminant C, un' = 0.2009, vn' = 0.4610 [ 1 ]. Equations for u' and v' are given below:
The transformation from (u',v') to (x,y) is:
The transformation from CIELUV to XYZ is performed as following: