Image Processing Reference
In-Depth Information
a. Find the derivatives at the patch values and the gain matrix for pole
values equal to 0.4. Use Equation 9.45 to
find the gain matrix.
b. Obtain the inverted tone values for (i.e., U(k)) iterations, k ¼
1,2,...,9.
Plot them with respect to iteration number, k.
c. Using end points 0 and 255 and a suitable curve
fitting algorithm com-
plete the full inverse TRC. Plot the inverted TRC. Mark the values of the
reference vector, x
d
, and the normalized values of the measurements, x,
corresponding to the patch gray levels.
d. Complete steps a through c for the new reference tone values.
S
OLUTION
Inverted tone values for (i.e., U(k)) iterations, k ¼
1, 2, . . . , 10 are plotted in Figures
9.27a, 9.28a, and 9.29a for three different reference TRCs as a function of the
iteration number, k. Corresponding full TRCs are shown in Figures 9.27b, 9.28b,
and 9.29b, respectively. Reference vector, x
d
, and the normalized values of the
measurements, x, are shown in these
figures corresponding to each patch gray level.
300
250
Reference TRC
Samples
TRC
Inverse TRC
250
200
200
150
150
100
100
50
50
0
0
1
2
3
4
5
6
7
8
9
10
0
50
100
150
200
250
300
(a)
Iteration #
(b)
Gray levels
FIGURE 9.27
(a) Convergence plot (poles
¼
0.4) for the inverse tone values. (b) Inverse
TRCs for 256 input gray levels shown for reference TRC 1.
250
300
Reference TRC
Samples
TRC
Inverse TRC
250
200
200
150
150
100
100
50
50
0
0
1
2
3
4
5
6
7
8
9
10
0
50
100
150
200
250
300
(a)
Iteration #
(b)
Gray levels
FIGURE 9.28
(a) Convergence plot (poles
¼
0.4) for the inverse tone values. (b) Inverse
TRCs for 256 input gray levels shown for reference TRC 2.
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