pigmented colorants: dependence on media and time - Cornell ...

The L ∗ a ∗ b ∗ space is another perceptually based color system that is frequently
used. The value for L ∗ is the same as in Equation 3.9. The other variables are
given by:
where
a ∗ =500L ∗
X
f
b ∗ = 200L ∗
Y
f
⎧
⎪⎨
f (r) =
⎪⎩
Xn
Yn
Y
− f
Yn
Z
− f
Zn
r 1
3 ,r≥ .008856
7.787r + 16
116 , otherwise
83
(3.11)
Just as L ∗ corresponds to the luminance channel in the visual system, a ∗ cor-
responds to the red-green channel and b ∗ to the blue-yellow channel. This closely
models how our visual system encodes data from the real world. The Opponent
color theory [Her78] states that colors are detected by recording differences be-
tween cone responses. Processing is done in the cells that gather the information
from the photoreceptors in the eye, accentuating the differences among the re-
sponses. The three opponenent channels are: red versus green, yellow versus blue,
and black versus white. Responses to one color in a channel inhibit the other and
are mutually exclusive. This is why an object never appears both red and green.
The responses of the cones in the human visual system significantly overlap and
must be analyzed in unison to reduce redundancy. The achromatic, or luminance,
channel is the combination of the responses from the medium (M) and long (L)
wavelength cones (M+L). The yellow-blue channel is the difference of the short (S)
wavelength cone responses and the medium and long wavelength cone responses
(S-(M+L)). The red-green channel is the difference between the medium and long
wavelength cone responses (M-L). This processing results in a great decrease in