Thesis (PDF) - Signal & Image Processing Lab

4.3. FILTERING USING A COMBINED METHOD 55
4.3 Filtering using a combined method
It is possible to combine the features of the above two methods into a single method.
We can still look at all multiple path combinations and find such a combination that
results in the largest adapted SE and a longest alternating sequence. An example is
given in Fig. 4.13.
4.4 Results Comparison
4.4.1 Comparison of different methods for avoiding trenches
In this section, we summarize the comparison between different methods for solving
the trench problem. Figs. 4.14(c),(d) show the trench problem in BTV-based erosion
ˆεB and opening ˆγB of the noisy image in Fig. 4.14(b), respectively. Figures 4.15, 4.16
and 4.17 show the results of the three proposed methods. The multiple minimal paths
method is unacceptable, because it leaves trenches. The adaptive structure element
method and combined method results are very similar. The combined method results
are better than those of the adaptive structuring element method, but it is more
complex and more memory consuming.
4.4.2 Filtering of AS images versus traditional morphological
filtering
In this section, filtering results in the Alternating-Sequence inf-semilattice are com-
pared to the traditional erosion, dilation, opening, closing, open-close, close-open
operators in the complete lattice of gray level functions and a median filter.
In the example given in Fig. 4.19, traditional closing removes dark noise pixels,
but not the bright ones, and damages thin dark parts and edges. Traditional opening
removes bright noise, but not dark noise. In contrast, opening that was defined in
inf-semilattice of AS images is self-dual and removes both bright and dark noise.
However, it is possible to perform pseudo self-dual filtering in complete lattice of gray
level functions using traditional open-close or close-open operators, see Fig. 4.20.
The drawback is that such filtering contains two consecutive operations. Opening
removes bright noise, but damages thin bright parts or edges. Closing after opening