Three-Dimensional Control of Color Management Systems - Control of Color Imaging Systems: Analysis and Design - page 338

weights of the Neugebauer primaries to the dot area coverages (c, m, y, k)is
modeled by Demichel dot model. Obtain the dot growth functions showing
the relationship between the digital input C, M, Y, K and the corresponding dot
area coverages c, m, y, k (0

c, m, y, k 1) for measured spectral samples shown

in Table 7.7 using

a. The least square error minimization (Equation 7.60a)
b. The weighted least square error minimization (Equation 7.60b)

S OLUTION
Figure 7.21 shows the dot growth functions constructed for each separation
using the least-squares error minimization formula, Equation 7.60, and synthe-
sized spectral curves from Table 7.7. To complete the function, dot areas for
intermediate digital counts are obtained through linear interpolation. To predict
the spectral re ectance for any new color, we need to know their digital counts

and follow the Neugebauer calculations shown in the block diagram of Figure
7.19. Given the digital counts (CMYK), we use the individual dot growth functions
to find their corresponding dot area coverages. All the dot area coverages are

substituted in the weight Equation 7.54. Then the spectra are calculated using
basis vectors from Table 7.6, these weights, and Equation 7.51.

The usual ideas of error minimization (Equation 7.57) led to a closed form
optimal solution for determining the dot area coverages (i.e., CMYK values) corre-
sponding to their digital counts (i.e., CMYK values). However, this operation is done
with one important assumption: each dot area coverage value for a given separation
is independent of other three separations. To further improve the dot area coverage
solution, samples with mixed colors have to be used while calculating the dot growth
functions. To accommodate the use of mixed color samples, the error minimization
steps should be performed with a mixture model so that the factors involved with
multiple separations are also taken into consideration.

7.4.3.4 Cellular Neugebauer Model (Lab-NB)

The basic Neugebauer model, Equation 7.51, used basis vectors that are combin-
ations of the spectral curves for primary colors with 0% or 100% area coverages and
their over prints. These area coverages form the grid points of a cube when CMY
separations are involved. Intermediate area coverages, such as 50%, were not
included. Figure 7.22 shows the structure of the cube for a cellularized Neugebauer
model with grid points also having 50% area coverage combinations. For these grid
points, the Neugebauer primaries will increase from 2 3 8to3 3 27. Weights for

the cellular model are obtained using Demichel weights, Equation 7.54 for random
screens, or Equation 7.55 for dot-on-dot screen or using various least-squares
regressions. A much

¼ ¼

finer division of the cube can be obtained by using a larger
number of grid points, which presumably can lead to improved accuracy.
Other physics-based models considered in printing systems are Clapper Yule

[38,55,65] model, which introduces correction for errors by modeling the internal
scattering, the ink transmissions, and the surface re

-

ectance.