Image Processing Reference
In-Depth Information
Figure 2.6
Design strategy. A table of observations is constructed by sliding the filter window
through the noisy image
I
n
and for each location, either column
N
0
or
N
1
is incremented de-
pending on whether the value of the corresponding pixel in the ideal image
I
o
is 0 or 1, respec-
tively.
However, even if the designer was willing to do this, the process does not scale well
and is impractical for anything other than very small filter windows.
Fortunately, there is a more intelligent strategy for identifying the optimum fil-
ter (see Fig. 2.6). The key feature here is the table of observations. The three col-
umns on the left show all combinations of the input variables
x
=(
X
0
,
X
1
,
X
2
).
This table is constructed by sliding the three-point window through image
I
n
.
All of the values in the two columns on the right are initially set to zero. At each lo-
cation, the pixel values within the input window correspond to one line in the table.
If the corresponding pixel value in the ideal image
I
o
is 0, then the value in column
N
0
is incremented; if it is 1 then the value in column
N
1
is incremented. This is re-
peated for every location in the image. At the end of this process the two columns on
the right,
N
0
and
N
1,
indicate the number of times that the value of the corresponding
pixel observed in the ideal image
I
o
was 0 or 1 for each input combination
x
.
At the end of the process, the two columns on the right contain counts of the
number of times the corresponding pixel in the ideal image was either 0 or 1 for
each input combination.
The resulting table can be used to:
•
Design the optimum filter,
•
Measure its error, and
•
Measure the increase in error by using any suboptimal filter.
2.7 Minimizing the MAE
Consider the line in the table of observation corresponding to
x
= (1, 0, 1). As previ-
ously explained, a pixel value of 1 corresponds to black and 0 corresponds to white.
