Thesis (PDF) - Signal & Image Processing Lab

4.1. FILTERING USING AN ADAPTIVE STRUCTURING ELEMENT 49
the resulting filter. As an example, Fig. 4.10 shows the filter effect for a filtering
depth limit of 1 on a noisy image of Lena. Notice that a number of noisy pixels
have survived the filtering. This artifact shows the typical problem of this approach.
Fig. 4.7 shows a simple example that explains the effect. In the image shown, the
upper pixel of component 3 is connected only to component 1. When in the erosion
process the shown structure element (SE) is placed on this pixel, the infimum is taken
between {103,-6,4} and {103,-5,2,-100}. The resulting infimum is {103,-5}. That
infimum length is 2, and the alternating sequences are of length 3 and 4, respectively.
Therefore, the length difference is 2, that is more than the filtering depth limit. In
that case the noisy pixel is left untouched because the resulting infimum is much
shorter then the source alternating sequence.
Figure 4.7: An example of filtering a dual-pixel noise : A black component - 3, is
located on brighter background - 1 and 2. After erosion with erosion depth limit of
1, the upper pixel of the 3-rd component is untouched.
This problem can be solved if we use a greater filtering depth limit. As an example,
in Fig. 4.11, the adaptive structuring element method succeeds to filter more salt and
pepper noise, but some of the “trenches” remain. Another solution is presented in
section 4.3.