Revised mathematical morphological concepts: dilation, erosion, opening and closing
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Date
2015-02-20
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Abstract
Mathematical morphology is the theory and technique for the analysis and
processing of geometrical structures, based on set theory, lattice theory,
topology, and random functions. Mathematical Morphology is most com-monly applied to digital images, but it can be employed as well on graphs,
surface meshes, solids, and many other spatial structures. Mathematical
Morphology has a lots of operators but the most basic and important ones
are Dilation and Erosion. Since it development, Morphological operators
have been governed by algebraic properties, which we seek to improve in
this study. Mathematical proofs are outlined for propositions which were
discovered during the investigation of what happens to Dilation and Erosion
when the set or structural element in a morphological operation is parti-tioned before the operation is taken. It turns out that some of the operators
distribute over union and intersection with a few exceptions and it is also
possible to partitioned the set or structural element before carrying out the
morphological operation.
Description
A thesis submitted to the Department of Mathematics, Kwame Nkrumah
University of Science and Technology, Kumasi, in partial fulllment of the
requirement for the degree of M.Phil Pure Mathematics,