Thesis (PDF) - Signal & Image Processing Lab

Chapter 6
Extrema-Watershed Tree example
Chapter 5 presents a general framework for producing morphological operators that
are compatible to a given tree representations. For every tree representation, a com-
plete inf-semilattice in the tree-representation domain is derived, and a set of mor-
phological operators on that inf-semilattice is obtained.
As for any general framework, the strength and usefulness of the proposed mor-
phological tree-based framework is measured by its ability to:
1) unify existing methods as much as possible, in a simple way, and
2) generate new and useful methods.
The purpose if this chapter is to present an example of a new method that is ob-
tained from the general framework, and to investigate its usefulness. This exemplifies
the strength of the general framework, as a tool for generating new, useful sets of
morphological operators.
Based on the general framework of Chapter 5, all that is needed in order to obtain
a new set of morphological operators is a given tree representation. The more this
tree representation is useful, the more useful these morphological operators are likely
to be, since many of the properties of the tree are inherited by the morphological
operators (like self-duality).
The tree representation selected for the method presented in this chapter is a
particular case of a “Binary Partitioning Tree”, which is a state-of-the-art, general
framework for tree generation, developed by Salembier in [10]. The proposed rep-
resentation is built using an iterative merging process as presented by Salembier,
Garrido and Garcia in [23].
75