Thesis (PDF) - Signal & Image Processing Lab

92 CHAPTER 6. EXTREMA-WATERSHED TREE EXAMPLE
(a) (b)
Figure 6.18: Segmentation example. (a) Original pears image. (b) Sub-tree labels.
Trenches depth threshold 450.
The last operation in the algorithm is needed to deal with two problems. One
problem is that small regions are left sometimes near object borders. Those regions
are removed by the size criterion. It is important to notice that this size criterion does
not cause the algorithm to be a regular size-based pruning, because the size criteria
should be an order of magnitude smaller than the required objects. Another problem
is that in many cases a number of similar zones remain in the tree. Those zones have
a son-father relationship, and are stacked one above the other, with a slight difference
in size. The proposed solution of this problem is to prune vertices that have a slightly
bigger father. A threshold of 10% size difference was found to be a good choice.
An example of this segmentation is shown in Fig. 6.18. In this image the segmen-
tation roughly follows the pears boundary. Another example of segmentation can be
seen in Fig. 6.19.
6.3.2 Comparison to the Shape Tree
A natural alternative to the proposed representation is the shape tree, discussed in
Chapter 2.2.3. Monasse and Guichard list in [13] the properties of an opening operator
based on the shape tree. It may be a good idea to check which properties the two
approaches have in common and which they do not. Let us denote an opening operator
on an image u using the extrema watershed tree as γB(u), where B is a structuring