DigitalVideoAndHDTVAlgorithmsAndInterfaces.pdf

Eq 21.12
CIE L*a*b*
16
Eq 21.13 7. 787t
+
116
Providing that all of X/X n, Y/Y n, and Z/Z n are greater
than 0.008856, a* and b* are computed as follows:
⎡ 1 1 ⎤
⎡ 1 1 ⎤
⎢⎛
X ⎞ 3 ⎛ Y ⎞ 3 ⎥
⎢⎛
Y ⎞ 3 ⎛ Z ⎞ 3 ⎥
a*
= 500 ⎢⎜
X
⎟ − ⎜
Y
⎟ ⎥;
b*
= 200 ⎢⎜
Y
⎟ − ⎜
Z
⎟ ⎥
⎢⎝
n⎠⎝n⎠⎥ ⎢⎝
n⎠⎝n⎠⎥ ⎣⎢
⎦⎥
⎣⎢
⎦⎥
As in the L* definition, the transfer function incorporates
a linear segment. For any quantity X/Xn , Y/Yn , or
Z/Zn that is 0.008856 or smaller, denote that quantity t,
and instead of the cube root, use this quantity:
For details, consult CIE Publication N o 15.2, cited in the
margin of page 216.
As in L*u*v*, one unit of Euclidean distance in L*a*b* –
denoted ∆E* ab – approximates the perceptibility of color
differences:
2
2
2
Eq 21.14 ∆E* ab = ⎛L*
−L*
⎞ + ⎛ a* − a* ⎞ + ⎛b*
−b*
⎞
⎝ 2 1⎠
⎝ 2 1⎠
⎝ 2 1⎠
Eq 21.15
If ∆E* ab is unity or less, the color difference is taken to
be imperceptible. However, L*a*b* does not achieve
perceptual uniformity: It is merely an approximation.
A polar-coordinate version of the [a*, b*] pair can be
used to express chroma and hue:
b
C* a* 2
b* 2 −1
*
ab = + ; hab
= tan
a*
The equations that form a* and b* coordinates are not
projective transformations; straight lines in [x, y] do not
transform to straight lines in [a*, b*]. [a*, b*] coordinates
can be plotted in two dimensions, but such a plot
is not a chromaticity diagram.
CIE L*u*v* and CIE L*a*b* summary
Both L*u*v* and L*a*b* improve the 80:1 or so perceptual
nonuniformity of XYZ to about 6:1. Both systems
transform tristimulus values into a lightness component
ranging from 0 to 100, and two color components
ranging approximately ±100. One unit of Euclidean
228 DIGITAL VIDEO AND HDTV ALGORITHMS AND INTERFACES