Thesis (PDF) - Signal & Image Processing Lab

94 CHAPTER 6. EXTREMA-WATERSHED TREE EXAMPLE
tree and shape tree on the corrupted image shown in Fig. 6.20. A difference between
the two approaches is shown in Fig. 6.21. It is interesting that there is a major
difference in the erosion result, but almost no difference in the opening result. This
is because in the erosion picture of the extrema watershed tree trenches are revealed.
The trenches in extrema watershed tree exposes flat zones located deep into the tree.
There is no similar effect in a shape tree because its tree structure is different.
Note that noise connected to the image border is not filtered in the Tree of shapes
and is filtered in the EWT tree. Noise is left by the shape tree filter because its
“fillhole” operator does not consider this boundary noise as a hole that can be filled
during tree creation process.
6.3.3 Filtering using Extrema watershed tree versus tradi-
tional morphological filtering
In this section, filtering results using the EWT are compared with traditional erosion,
dilation, opening, closing, open-close, close-open operators and median filter in a
complete lattice of gray level functions. In Figs. 6.24 and 6.24, results of conventional
morphological filters (erosion, dilation, opening, closing) are shown. As expected,
their results are not symmetric with respect to a gray and dark pixels. Because of
that, those filters cannot be compared with the extrema-watershed tree.
An additional morphological filter that has a pseudo symmetrical effect is a com-
bined open-close or close-open filters as described in Chapter 8 of [3]. Their results
are shown in Fig. 6.26. In Fig. 6.27 a median filter result is shown and compared to
the EWT result. Those two figures enable a comparison between the proposed filter
and traditional approaches. It can be seen the the EWT filtered result is in general
similar to an open-close and close-open results, but without a bias towards dark pixels
as a close-open or towards a light pixels as an open-close filter. The median filter
is unbiased, but a number of noisy pixels have survived the filtering by it, and the
median filter lacks other important features. For example it is not an idempotent
filter.