Image Processing Reference
In-Depth Information
size. For an example of practical noise, the window size for acceptable results may
need to be5×5orlarger.
Figure 4.4 shows the error resulting from filtering an image with the optimum
filter in windows of increasing size.
It can be seen that the error declines exponentially as the window size in-
creases. Why does this happen? The filter is, in effect, an estimator that attempts to
determine the “true” value of the pixel in the ideal image. Depending on the statis-
tics of the image, the larger the window, the more information the filter has to make
a decision. From the values in the observation table, it is possible to compare two
sub-windows and also to determine the increase in error caused by reducing the size
of the window.
Consider the effect when instead of filtering with the 5-point window shown in
Fig. 4.5(a), the filtering takes place within the 3-point asymmetrical window
formed by omitting pixels
X
3
and
X
4
. This is shown in Fig. 4.5(b) and the intention
is still to estimate the true value of the pixel at location
X
2
.
The observation table generated for the original 5-point window is shown in
Fig. 4.6(a). The observation table for the 3-point window is calculated by combin-
ing all inputs with the same value of pixels for
X
0
,
X
1
, and
X
2
regardless of the val-
Figure 4.4
Effect of window size on MAE for optimum filter. In all cases the error falls with in-
creasing window size.
