Image Processing Reference
In-Depth Information
With a fewmatrix operations, we can express the weights as a function of the primaries
and the r vector as follows:
W T ¼ r T BB T B 1
(
7
:
53
)
The weight vector W can now be modeled in terms of a new parameter matrix
u 0 (with
linear af
cubic model parameters) and input variables, CMYK, using the
training samples as in Equations 7.44 through 7.47. The new parameter matrix
ne
=
quadratic
=
u 0 can
be estimated using the least square Equation 7.47 or RLS Equation 7.48.
Example 7.6
For a four-color CMYK printer, develop a spectral Neugebauer model (Equation
7.51) with Demichel weights for 16 Neugebauer primaries. Estimate the weights
using training samples with least-squares algorithms and Yule
-
Nielson factor (m)
as a free parameter.
a. Plot the accuracy of the model as a function of m.
b. For the best m, plot the model accuracy as a function of the number of
uniformly sampled data sets (e.g., 3 4 ,4 4 ,5 4 ,6 4 , etc.).
S OLUTION
When Yule
-
Nielson factor m is equal to 1, there is no light scattering in the paper,
and m¼
2 corresponds to Lambertian or perfectly diffused scattering in the paper
[31]. For an experimental printer considered in this simulation, we used Bayer
s
dithering technique to produce a halftone patch. As the halftone screen changes,
the optimal m could be different. A trial and error approach can be adopted to
come up with a best value for m. Figure 7.17 shows the model accuracy as a
function of parameter m and Figure 7.18 shows the model accuracy as a function
of the number of uniformly sampled data sets for best value of m from Figure 7.17.
'
30
90
Mean
95%
Mean
95%
80
25
70
20
60
50
15
40
10
30
20
5
10
0
0
1
1.5
2
2.5
3
3.5
4
1
1.5
2
2.5
3
3.5
4
Yule-Nielson factor
Yule-Nielson factor
FIGURE 7.17 The accuracy of the Neugebauer model for IT8 colors plotted as a function of
the Yule - Nielson factor. Demichel weights are modeled with respect to input CMYK values
using least-squares algorithm with linear affine and quadratic models.
Search WWH ::




Custom Search