Image Processing Reference
In-Depth Information
Thus
1
a
1
a
1
a
Q 11 ¼
, Q 22 ¼
, Q 33 ¼
(
9
:
129
)
2
1
2
2
2
3
Similarly, we choose matrix R to be diagonal, with diagonal elements chosen as
1
u 1 max
1
u 2 max
1
u 3 max
1
u 4 max
R 11 ¼
, R 22 ¼
, R 33 ¼
, R 44 ¼
Recursive algorithm (steady-state):
If N is chosen to be suf
ciently large, the feedback gain matrix becomes a constant
matrix. This constant gain can be obtained by either solving the algebraic Equations
9.123 and 9.124, or the recursive equations given by Equations 9.120 and 9.121.
Since the algebraic equations are nonlinear,
it would be computationally more
ef
cient and easier to solve the recursive Equations 9.120 and 9.121. We start with
the boundary condition P(N)
0 and solve Equation 9.121 backward from P(N)to
P(0). The steady-state solution for P is the initial value P(0). Once P is found,
Equation 9.123 can be used to compute the gain matrix K.
¼
9.14 OPTIMAL MEASUREMENTS
TRCs are updated over time by periodically printing test patches at various gray
levels. Printed test patches are sensed by the sensor to determine the appropriate
compensation so that the new TRCs provide compensation for the current state of the
print engine. TRCs in level 3 control are used for linearizing each separation.
Whereas, the spatial TRCs, although serving a similar purpose, are generally used
to adjust the pixel values (0
fine resolution to compensate for the
characteristics of the print engine so that images are rendered uniformly [50
-
255) at a relatively
52]. In
such systems, one may select an appropriate compensating TRC for a pixel location
in a rendered image space based on the contone value of the input pixel.
A problem usually encountered in such a control system is the ability to de
-
ne a
minimal sampling procedure for creating and updating the compensation TRCs.
In particular, there is a need to determine the optimum minimal set of gray levels or
colors for use during the calibration process. De
ning a minimal set of samples
becomes increasingly important when the images have to be controlled under multi-
tude of variables, particularly for production printers, under TRC-based control
methodologies (e.g., colors, halftones, media, printers, etc.). The amount of unneces-
sary measurement time spent by the printer and the sensing system can be otherwise
utilized for making prints useful to the customer. Minimizing the number of samples
reduces the computation,
ink usage, and memory requirements of
the system, as well as the spatial extent of the test patches when the test patches
are rendered in the IDZ areas. This results in a reduction in cost and enables more
frequent
time,
toner
=
=
cient sampling, particularly when the method corrects time-dependent
print quality errors in production color printers.
ef
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