Image Processing Reference
In-Depth Information
80
50
75
β=1
40
70
30
65
20
β=0
β = 0.5
60
10
55
0
50
45
-10
0 102030405060708090100
0 102030405060708090100
Color index,
i
Color index,
i
30
25
20
15
10
5
0
-5
0 102030405060708090100
Color index,
i
FIGURE 7.60
Soft gamut-mapping curves for L* (top left), a* (top right), and b* (bottom
center) for
b¼
0, 0.5, 1 shown with and without smoothing.
7.6.4 G
AMUT
M
APPING FOR
C
ONSTANT
L
IGHTNESS AND
H
UE
An algorithm that preserves the lightness and hue angle of the node Lab color
coordinates is shown below. For convenience, the
s are removed from the
color coordinates, L*a*b*. If the original color in the CIELab color space is denoted
by [Lab] and its corresponding mapped color by [L
0
a
0
b
0
], then, to preserve
the lightness and hue relationship, the following constraints must be satis
*
''
''
ed:
¼ tan
1
b
a
tan
1
b
0
a
0
L
0
¼
L
and
(
:
)
7
99
Graphically, as illustrated in Figure 7.61, this can be shown on a chroma plane at
constant L* by drawing a ray from the desired color to the centroid of the gamut.
First we need to determine whether a given input color is inside or outside the
printer gamut. This is achieved by the following two steps:
1. Transform the color gamut into spherical coordinates where the center of the
sphere is at the centroid of the gamut, approximately equal to Lab
¼
[5000].
In these new color coordinates, each node color is speci
ed by its spherical
coordinates r,
a
,and
u
given by the equations,
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