Image Processing Reference
In-Depth Information
Gamut RGB, sRGB, ROMMRGB, etc.). Gamuts produced by the chosen color
space should be compared to the gamut of the printer in Lab space prior to selecting
the
final working color space so that all colors that are reproducible by the printer
gamut are covered by the working color space. To limit our options, we choose
ProPhoto RGB as the color space. This choice was made because the ProPhoto RGB
space gives reasonable gamut coverage (see Figure 7.28).
To convert the RGB color space to Lab,we
first determine the matrix for
converting RGB to XYZ, then use the XYZ to Lab equation (see Appendix A).
Given the chromaticity coordinates of the RGB system (x
r
, y
r
), (x
g
, y
g
), and (x
b
, y
b
)
and its reference white (X
W
, Y
W
, Z
W
), the 3
3 conversion matrix, M, for converting
RGB to XYZ is given by
[
XYZ
] ¼ [
RGB
]
M
(
7
:
101
)
2
3
S
r
X
r
S
r
Y
r
S
r
Z
r
4
5
,
where, M
¼
S
g
X
g
S
g
Y
g
S
g
Z
g
S
b
X
b
S
b
Y
b
S
b
Z
b
X
i
¼
x
i
=
y
i
; Y
i
¼
1; Z
i
¼
(1
x
i
y
i
)
=
y
i
with index i
¼
r, g, b and,
2
3
1
X
r
Y
r
Z
r
X
g
Y
g
Z
g
X
b
Y
b
Z
b
4
5
[
S
r
S
g
S
b
] ¼ [
X
W
Y
W
Z
W
]
(
7
:
102
)
The XYZ values in Equation 7.101 are in the nominal range (0.0
1.0). For converting
XYZ to RGB the M matrix is inverted (i.e., M
1
). The RGB values must be linear (i.e.,
Equation 7.101 uses
-
g¼
1, see also Equations 7.105 and 7.106 for use with
g
6¼
1,
which gives non-linear relationship) and in the nominal range (0.0
1.0). They also have
to be scaled. If the values are in the range (0, 255), then divide the RGB values by 255.0.
It is important to note here that the reference whites are consistent with ICC
speci
-
cations. For example, if the sRGB color space is used as the working space,
then direct use of sRGB gives a mismatch between ICC profiles defined relative to
D50 reference white since sRGB is de
ned relative to D65 light source. Before they
can be used in a D50 environment, they should be adopted to a D50 reference white
from their native reference white. Chromatic adaptation algorithms can be used to
convert the source color (sRGB with D65 reference white) into the destination color
(sRGB with D50 reference white) by a linear transformation (Bradford, XYZ scaling,
and Von Kries are popular transforms), which is dependent on the source reference
white and the destination reference white.
For a 2-degree observer and a D50 illuminant [136], X
W
¼
0.96422, Y
W
¼
1.0,
Z
W
¼
0.82521. From Appendix A (Table A.2), chromaticity coordinates for a
ProPhoto RGB system are given by
x
r
¼
0
:
7347;
y
r
¼
0
:
2653;
x
g
¼
0
:
1596;
y
g
¼
0
:
8404;
(
7
:
103
)
x
b
¼
0
:
0366;
y
b
¼
0
:
0001;
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