One-Dimensional, Two-Dimensional, and Spot-Color Management and Control Methods - Control of Color Imaging Systems: Analysis and Design - page 444

C

250

200

150

100

50

0 M+Y

0 50 100 150 200 250 300 350 400 450 500

FIGURE 8.11 Scatter plot of grid control point for 2-D cyan TRC in (C, M þ Y) plane.

Note that the LUT includes the control grid points of Figure 8.11. The complete
LUT for every point in the (C, MþY) plane is constructed using interpolation

=

smoothing. Similar LUTs are constructed for magenta and yellow TRCs.
To evaluate the performance of 2-D calibration against 1-D, a total of 180
in-gamut patches were generated. The patch values are processed through the
calibration LUTs and the simulated printer for both 1-D and 2-D calibrations. The
accuracy results are compiled in Table 8.7. Two-dimensional calibration outper-
forms 1-D with respect to mean and 95th percentile DE a * .

8.6 ONE-DIMENSIONAL AND TWO-DIMENSIONAL PRINTER
CALIBRATION WITH STATE-FEEDBACK METHODS
The approach of the previous section regarding the gray-balance and channel-
independent calibrations is based on printer model constructed using a high-resolution
LUT or an accurate printer model. In this section, we show how control approaches
using state-feedbackmethods [2,3] can be used to design 1-D and 2-D calibration TRCs.
Other, more robust, control approaches are also available [6].
Consider the gray-balance control loop with the gain-weighted MIMO (multi-
input and multi-output) integral controller shown in Figure 8.12. In this gure,

[L*(k) a*(k) b*(k)] T are the states, as de x(k) ned by the state variable model for

a CMY ! L*a*b* printer described in Section 7.5.2.2, and, in this case, the states are
also the output of the system. The outputs are the measured L*a*b* values from the
color sensor. V(k)

¼

d Y(k)] T . r ¼ [ L *
target

a *
target

b *

target ] T is the target

¼ [ d C(k) d M(k)

L*a*b*, and K is the 3 3 feedback gain matrix. The printer in this loop can be an

(accurate) printer model or an actual printer. The sensor can be an inline or of ine

spectrophotometer. If an inline sensor is used, then the processes can be automated to