Image Processing Reference
In-Depth Information
Figure 3.7 Comparison of optimum and median filters. The above filters implemented within
a five-point window are shown. The optimum filter performed more than twice as well as the
equivalent median.
med has over twice the error with 754 pixels. Fig-
ure 3.8 shows the observation table, which has 32 input combinations (= 2 5 ). The
difference in the error of the two filters of 394 pixels can be seen to correspond to
the sum of the advantages for the inputs where the two filters differ. It is interesting
to note that for the inputs where the two filters differ,
els, whereas the median filter
ψ
med = 1 and never
the other way around. Also for these inputs, the value of the pixel at the center of the
window X 2 = 0. The trained filter has therefore only learned to switch some of the
black pixels (= 1) to white (= 0). The noise in the training set was purely additive
and therefore the behavior of the correcting filter is subtractive. The median, on the
other hand, treats black and white pixels equally and would give the same result if
the input image were to be inverted, filtered, and re-inverted. The median filter is
therefore unsuitable for correcting noise processes other than those that are sym-
metrical, i.e., are both additive and subtractive by equal proportions.
The properties of the median and its variants are discussed in more detail in
Chapter 6.
ψ
opt = 0 and
ψ
3.2 Other Applications
3.2.1 Edge noise
The examples up to this point have focused on the removal of salt-and-pepper
noise. Some further examples will now be given. An interesting case is edge noise.
Search WWH ::




Custom Search