Three-Dimensional Control of Color Management Systems - Control of Color Imaging Systems: Analysis and Design - page 369

Example 7.9

Construct a K-restricted GCR for a uniformly sampled printer input output data using

the analytic functions of Equations 7.90 and 7.91 and a 4-to-3 control-based inver-
sion approach. Show the advantages with respect to gamut and image quality (IQ).

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S OLUTION
Figure 7.44 shows the CMYK response curves (also called corner plots) for a rst

inverted LUT produced with a 4-to-3, K-constrained control-based algorithm.
These plots are drawn from white (C¼M¼Y¼K¼ 0) to the dark black (C¼ 0,

M¼ 0, Y¼ 0, K¼ 255), dark red (C¼ 0, M¼Y¼K¼ 255), dark green (C¼ 255,

M¼ 255) corners of the

gamut (see Section 7.7.2 to understand more about the corner plots). Values 0

0, Y¼K¼ 255) and dark blue (C¼M¼ 255, Y¼ 0, K¼

100
on the x-axis represent points starting fromwhite with 100 on the corner. The x-axis is
extended to reach out-of-gamut colors until it touches the sides of the cube formed by
the device-independent space. Solid curves represent CMYK response after one post

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filtering step. Clearly, the CMYK response shown by dashed curves for both in-gamut
colors and out-of-gamut colors is not smooth. This is because the starting CMYK
values obtained in step (c) contain local minima (depending on the resolution of the
CMYK grid). This LUT produces contours in some images (see the region

shown in Figure 7.45) due to nonsmooth CMYK formulations caused by the inversion
algorithm. Also, the K response shown by dashed dot curve in Figure 7.44 (d,f,h) is
calculated from Equations 7.90 and 7.91. The inversion algorithm tries to follow the
general trend. Except for a nonsmooth CMYK response, the pro

neck

'' ''

le LUT is, in general,

in the right direction.
To avoid the formulation jumps (i.e., non-smooth CMYK response), we apply the
preconditioning steps mentioned in step (h) above and generate the second inverted
LUT. We

filter the LUT by applying the multidimensional smoothing algorithm and

re ne the accuracy by applying a 4-to-3 control-based inversion on the printer model

using post- ltered CMYK values as the starting points for the inversion. After perform-

ing this step a few times, we obtain a

final inverted LUT to produce smooth CMYK
response (see response curves in Figure 7.46 shown just before and after the sixth
preconditioning step). In Figure 7.46, the differences between solid and dashed
curves are negligible as compared with similar figures in Figure 7.44. Solid curves

represent the responses before nal filtering. The dashed curves are smooth. They are

obtained after the filtering step. Figures 7.47 and 7.48 show the image quality

improvement due to preconditioning steps. Table 7.10 shows the round trip accuracy
at the end of each preconditioning step. It is to be noted that each precondition step
includes

nal

filtering and 4-to-3 control-based inversion (Figure 7.41) carried out using

post- ltered CMYK values as the initial CMYK LUT in the inversion process. Filtering

is applied to all nodes (i.e., in-gamut and out-of-gamut nodes) in themultidimensional
pro le.Without the control-based inversion on the post- lteredCMYK values, there is

signi cant loss in the round trip accuracy. In this example, with limited node size

(33 3 ), we see an effective gamut utilization of greater than 94%.
The CMYK formulations between adjacent nodes have to be smooth. As shown
in this example, multidimensional filtering (Section 6.6) combined with additional

iterative control procedure on filtered data may be necessary to soften the kinks in

CMYK formulations. Alternatively, step (c) can be started with previously inverted
LUTs using methods such as the MM.