Image Processing Reference
In-Depth Information
Figure 5.7 Digital logic implementation of the additive noise filter for the example in Fig. 2.1.
is designed to estimate the pixel value in the ideal image, the
differencing filter D estimates only those pixels changed by filtering. For example,
if x ={ X 0 , X 1 …, X c ,.. X n 1 }, where X c is the noisy pixel value at the center of win-
dow, then the filter output
Whereas the filter
ψ
if D ( x ) = 1.
Figure 5.8 shows the differencing filter values for the previous filter. It also
shows the structuring elements of the minimized differencing function. The differ-
encing filter may be implemented in digital hardware in a similar way to the direct
filter but including the addition of an XOR gate. This is shown in Fig. 5.9.
In theory, the differencing filter implementation should give precisely the same
filtering results as the direct filter. However, there are two main reasons for choos-
ing the differencing filter.
First, only a minority of pixels are likely to change. Therefore, the amount of
logic required for the differencing filter is usually less than for the direct filter. In
this case, there are just two structuring elements compared to four for the direct im-
plementation.
Second, when using large windows in practice (as seen in Chapter 4), there
may be some input combinations that have not been seen during training. In these
cases, it is not clear which value to allocate to the output. In the direct filter imple-
mentation, these unseen values may be given an arbitrary value resulting in, on av-
erage, 50% error for these inputs. A strategy that appears to give improved results
in practice involves leaving the input pixel unchanged. The value of pixels is only
changed when there is strong statistical evidence to do so. Using the differencing
filter design, these unseen inputs are allocated a value of 0 and so are left un-
changed by filtering.
ψ
( x
=
if D ( x ) = 0, and
ψ
( x
=
c
c
 
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