Thesis (PDF) - Signal & Image Processing Lab

10 CHAPTER 1. INTRODUCTION
3. A general framework for producing morphological connected and non-connected
operators associated to a given tree representations is developed.
4. A new particular case of tree representation, named Extrema-Watershed Tree, is
proposed. A novel set of morphological operators was defined on the Extrema-
Watershed Tree, based on this general framework.
5. Some applications using morphological filtering, based on the Extrema-Watershed
Tree, are proposed. Those applications include pre-processing for OCR (Optical
Character Recognition) algorithms, intermediate step for image segmentation
and initial step for dust and scratch removal from images.
The thesis is organized as follows:
Chapter 2 provides a theoretical background on semilattices and graph theory,
and summarizes the work presented in [17, 16] . In Chapter 3, we propose an efficient
implementation of the methods defined in [16]. Chapter 4 proposes possible solutions
for the “trench” problem that arises when applying erosion and opening in the semi-
lattice defined in [16]. In Chapter 5 we develop a general framework for tree-based
morphological image processing, which unifies the schemes presented in [17, 16], and
enables the definition of new morphological operators that are based on tree represen-
tations. The heart of the proposed approach is a novel complete inf-semilattice of tree
representations of images. For every tree representation, a complete inf-semilattice
on the tree-representation domain is derived, and a set of morphological operators on
that inf-semilattice is obtained.
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 will likely be,
since many of the properties of the tree are inherited by the morphological operators
(like self-duality).
Chapter 6 is devoted to the Extrema-Watershed Tree semilattice; a particular
case, obtained from the general framework, and to the investigation of its usefulness.
The Extrema-Watershed Tree is a kind of “Binary Partitioning Tree”, which is
a state-of-the-art general framework for tree generation, developed by Salembier in
[10]. It was designed in order to be used for tasks such as self-dual filtering. The