Image Processing Reference
In-Depth Information
TABLE 7.4
Accuracy of Clustered Spectral PCA Model (
D
E
2000
and
D
E
a
*
Space)
D
E
a
*
D
E
2000
No. of
Models
Basis Vectors
Mean
95%
Max
Mean
95%
Max
RLS
1
4.98
10.94
53.00
7.98
23.30
162.73
2
4.11
9.51
41.81
7.29
20.33
102.39
3
3.76
7.32
31.23
6.51
16.46
100.60
4
3.40
7.82
32.47
5.67
14.46
92.96
5
3.14
7.25
30.88
5.13
12.64
91.39
6
3.07
7.12
53.74
5.02
12.49
137.04
7
3.01
7.10
50.57
4.89
12.23
127.96
8
2.92
6.47
20.89
4.73
11.11
57.62
9
2.74
6.68
19.95
4.23
10.58
49.31
10
2.72
6.49
22.61
4.23
10.79
39.65
to the physical effects of light scattering and mechanical dot growth [24,52,56].
The approach is similar to normal PCA, except that the re
ectance spectra are raised
to the power of (1
=
m), where m is determined by trial and error to achieve the best
prediction.
1
=
m
R
(l) !
R
(l)
(
7
:
50
)
Values of m are somewhat arbitrary and could be set anywhere between 1 (for a
glossy substrate) and 2 (for a perfect diffuser). It can also exceed 2.0.
As clearly seen from previous discussions, successful printer characterization
based purely on experimental data and its piecewise linear representation may need a
large number of measurements. Consequently, models based on the fundamental
physical process are much more preferred, if available, since the nonlinearities of the
physical process can be captured in the analytical functions. Often physics-based
approaches would require fewer measurements. The following sections illustrate
various color models studied by many researchers.
7.4.3 N
EUGEBAUER
M
ODEL
One well-known spectral modeling technique is the Neugebauer color mixing model
[25
64] commonly used to model the output color in digital printing processes.
The Neugebauer model determines the spectral re
-
ectance function in terms of the
weighted sum of spectral re
ectance functions obtained from one, two, and more
combinations of available colorants and a substrate on which the colorants are
formed. The resulting colorant combinations are referred to as the Neugebauer
primaries. In a three-color system, for example, having cyan, magenta, yellow
(CMY) colorants,
there are 8 (2
3
¼
8) Neugebauer primaries. In a four-color
system, for example, having cyan, magenta, yellow, black (CMYK) colorants, there
will be 16 (2
4
16) Neugebauer primaries. In an N color system, there will be 2
N
known spectral re
¼
ectance functions. In mathematical form, the vector corrected
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