M.Sc Thesis

M.Sc StudentVichik Alla
SubjectSelf-dual Morphological Operators Based on Tree
Representations of Images
DepartmentDepartment of Electrical and Computer Engineering
Supervisors DR. Renato Kresch


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 infsemilattice in the corresponding tree-representation domain is derived. Morphological 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 are 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 arises, when applying erosion and opening based on the semilattice, is studied. Possible solutions for the trench problem are proposed. Moreover, the trenches are used in order to exploit the implicit segmentation property of the Extrema-Watershed Tree.