Three-Dimensional Control of Color Management Systems - Control of Color Imaging Systems: Analysis and Design - page 367

function of a*orb* (horizontal axis) and using a* ¼ 0 (against b* as the horizontal

axis) or b* 0 (against a* as the horizontal axis) for different values of L*. The color

gamut with L* (vertical axis) and a* (horizontal axis) is shown in the center
sandwiched between these graphs. These curves show that the K values are weakly
dependent on either the a* or the b* values. L 0 ,

¼

are parameters of the
multidimensional K-function which satisfy following properties:

h , b , and a

1. K ! 1 when L* ! 0 so that maximum value of K is used at the dark end of

the color space.
2. The function is symmetrical with respect to a* and b*, and K increases
when the color is away from the neutral zone.
3. K !

! L 0 . Since L 0 is selected to be around 100 (top of the
gamut), only a small amount of black will be used near the white. Parameter
L 0 affects the middle part of the curve near the neutral region (shown by
double arrow), which is the place where most colors require adjustment to
obtain pleasing appearance on the paper. Figure 7.43 shows K as a function
of L* for a*

0 when L*

¼ 0 and b* ¼ 0 for three different values of L 0 with a¼ 0.01,

b¼ 1.5, and h¼ 0.5.

For a digital production printer gamut, typical values used for a , b , and h are

a¼ 0.01, b¼ 1.5, and h¼ 0.5. A large value of a gives a strong dependence of K

on a* and b*, while a small value of a means that K is mostly determined by

luminosity. The parameter determines the shape of the K-function curve at small

L* values (see left side of the graph in Figure 7.42). Larger value of

h

h means the

300

L 0 =102
L 0 =110
L 0 =160 250

200

150

100

50

0

0 10 20 30 40 50 60 70 80 90 100

L *

FIGURE 7.43 A neutral response of K-restricted GCR functions with a¼ 0.01, b¼ 1.5, and

h¼ 0.5 shown for three different values of L 0 .