Image Processing Reference
In-Depth Information
approach can be used to
find the right area coverages for measurements. In all these
cases, we need to ensure monotonicity in the measured (or reconstructed) tone
response. Otherwise, the static inverse methods described above will not work. In
Section 9.9.2 we show a control-based inversion technique, which can be used to
accurately construct the inverse tone response curve in the absence of the mono-
tonicity condition.
Example 9.8
Let the vector U
0
contain the input patch gray levels (or area coverages) for
controlling DMA on the photoconductor for the magenta separation shown in
Table 9.1 below. The vector x contains the normalized values of the measurements
corresponding to each gray level. This data was produced for a maximum DMA
value of 0.55 units with levels 1 and 2 controls enabled. Three patch DMA controls
were used in the level 2 loop. The targets were set to [0.0384 0.1301 0.3738] DMA
units. Three reference TRCs are sampled at the gray levels contained in the U
0
vector. They are shown in columns (x
d
)
1
,(x
d
)
2
, and (x
d
)
3
. The shape of the reference
TRCs for all gray levels are shown in Figure 9.22.
a. Construct the complete inverse TRC using static inversion process
described in Section 9.9.1 with end points
fixed at gray levels 0 and
255 for all three reference TRCs.
b. Show how the gray-level image appears when the image pixels are pro-
cessed with and without the inverted TRCs obtained with each reference.
S
OLUTION
Case (a): The data shown in vector x are
first interpolated are (see Chapter 6) to
form a smooth curve for each gray levels. The smooth function is then inverted
around the reference TRC using the static inversion technique described above.
Figure 9.23 shows three plots with inverted TRCs for each reference TRCs.
TABLE 9.1
TRC and Reference Samples at Discrete Input Gray Levels
Number of
Patches
U
0
x
(x
d
)
1
(x
d
)
2
(x
d
)
3
0
0.00
0.00
0.00
0.00
0.00
1
26.00
8.37
26.00
45.17
47.80
2
51.00
26.20
51.00
62.76
91.70
3
77.00
43.73
77.00
64.85
133.28
4
102.00
75.77
102.00
82.98
167.90
5
128.00
88.76
128.00
128.49
197.34
6
153.00
128.61
153.00
172.02
218.99
7
179.00
161.31
179.00
190.35
234.94
8
204.00
203.92
204.00
192.24
244.87
9
230.00
242.89
230.00
211.14
251.11
10
255.00
255.00
255.00
255.00
255.00
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