Lab color space

CIE L*a*b (CIELAB) is a color space, derived from CIE XYZ, for the purposes of measuring color differences, perceptual linearity and device independent, but is said to be not easy to use.

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.

XYZ to CIE L*a*b* (CIELAB) and CIELAB to XYZ conversions

L* = 116 (Y/Yn)1/3 - 16 for Y/Yn > 0.008856

L* = 903.3 Y/Yn otherwise

a* = 500 ( f(X/Xn) - f(Y/Yn) )

b* = 200 ( f(Y/Yn) - f(Z/Zn) )

where f(t) = t1/3 for t > 0.008856

f(t) = 7.787 t + 16/116 otherwise

Here Xn, Yn and Zn are the tristimulus values of the reference white. The reverse transformation (for Y/Yn > 0.008856) is

X = Xn * ( P + a* / 500 ) 3

Y = Yn * P 3

Z = Zn * ( P - b* / 200 ) 3

where P = (L* + 16) / 116

XYZ to CIELUV & CIELUV to XYZ conversions

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:

L* = 116 (Y/Yn)1/3 - 16

u* = 13L* ( u' - un' )

v* = 13L* ( v' - vn' )

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:

u' = 4X / (X + 15Y + 3Z) = 4x / ( -2x + 12y + 3 )

v' = 9Y / (X + 15Y + 3Z) = 9y / ( -2x + 12y + 3 ).

The transformation from (u',v') to (x,y) is:

x = 27u' / ( 18u' - 48v' + 36 )

y = 12v' / ( 18u' - 48v' + 36 ).

The transformation from CIELUV to XYZ is performed as following:

u' = u / ( 13L*) + un

v' = v / ( 13L* ) + vn

Y = (( L* + 16 ) / 116 )3

X = - 9Yu' / (( u' - 4 ) v' - u'v' )

Z = ( 9Y - 15v'Y - v'X ) / 3v'