Revised mathematical morphological concepts: dilation, erosion, opening and closing

Thumbnail Image
Journal Title
Journal ISSN
Volume Title
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.
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,