Thesis (PDF) - Signal & Image Processing Lab

Abstract
This research addresses a new image filtering methodology, based on mathematical
morphology.
In this thesis a new general framework for producing morphological, self-dual
operators that are compatible to a given tree representation is proposed.
For every tree representation, a set of morphological operators on a complete
inf-semilattice in the corresponding tree-representation domain is derived. Morpho-
logical erosion, opening, and opening by reconstruction operators are defined using
this framework. The proposed image filtering scheme consists of three steps:
1. Transform the input image to the corresponding tree representation,
2. perform morphological operators in the tree representation domain, and
3. transform the resulting tree representation back to the image domain.
A particular case of this general framework is presented and studied. It involves a
new tree representation,which we also developed in this research, called the Extrema-
Watershed Tree. The particular case example emphasizes the ability of the general
framework to generate new and useful sets of morphological operators.
A number of potential applications for the Extrema-Watershed Tree is proposed.
The new morphological operators excel in tasks suited for the application of classical
morphological operators, but that require, in addition, self-duality. The proposed
applications are pre-processing for OCR (Optical Character Recognition) algorithms,
de-noising of images, and preprocessing for dust and scratch detection. In addition
we show that the tree has an implicit segmentation property that could be used in
image segmentation algorithms.
In a previous work, Keshet has defined a complete inf-semilattice of images of
alternating sequences. In this research an efficient implementation of morphological
operators in this semilattice is proposed. In addition, the “trench” problem that
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