Image Processing Reference
In-Depth Information
Figure 3.3 A comparison of filters. The column on the right shows the increase in error result-
ing from the use of a filter with a different output for each input. In this case, the filters differ
only for inputs (0,1,1) and (1,0,0).
Figure 3.4 Original example. The original example from Fig. 2.1 has 10% additive noise. The
number of pixels in error is 5954, which corresponds to a MAE of 9%.
the observations table. This may be calculated by setting the filter function
=X 1
(i.e., the identity or “do nothing” filter) instead of the optimum. The error of 26 pix-
els may then be calculated by summing N 1 when
ψ
=X 1 =1.
Having described the method on a simple example, it will now be applied to the
original image shown in Fig. 2.1. The ideal image and the noise-corrupted version
with 10% additive noise are shown in Fig. 3.4. The total number of pixels in error is
5954 which is a MAE of 9%.
Before proceeding to optimum image filtering, it is interesting to apply the me-
dian filter. This will be applied within a 3 × 3 window. The median reduces the pix-
els in error to 468 (0.71%) but a repeated application has little further effect
reducing the error to only 443 pixels (0.67%). The corresponding images are
shown in Fig. 3.5. The optimum filter was designed within a 3 × 3 window using
the procedure described in Chapter 2. It was then applied to the noisy image reduc-
ψ
=X 1 = 0 and N 0 when
ψ
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