Thesis (PDF) - Signal & Image Processing Lab

Chapter 5
Tree Semilattices
In this chapter, we propose a general framework for tree-based morphological image
processing, which unifies the schemes presented in previous chapters, and enables the
definition of new morphological operators that are based on tree representations. The
heart of the proposed approach is a novel complete inf-semilattice of tree representa-
tions of images. The proposed image processing scheme is shown is figure 5.1.
This chapter is organized as follows. First, Section 5.1 introduces the complete
inf-semilattice of tree representations. Then, in Section 5.2, morphological image
processing using the complete inf-semilattice of tree representations is developed. In
Section 5.3, we address the problem of whether the complete inf-semilattice of tree
representations induces a complete inf-semilattice structure on the set of images as
well. Finally, the chapter is summarized in Section 5.4.
Figure 5.1: Tree-based morphology.
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