Analysis Of Digital Images Based On A Grid Point Topology

A topological method is one of the important methods in digital image analysis.The thesis focuses on the analysis of' 3D digital images based on a grid point topology?simply,M-topology?.In order to study the transformation of digital images,we discuss some properties of M-continuous maps and M-homeomorphisms.However these maps are somewhat rigid and some common rotations and translations are not even M-continuous maps.For more effective analysis of digital images,the thesis introduces an MA-map and an MA-isomorphism,and then gives a definition of an M-adjacent category,with which the other two categories are compared.Classification of a number of simple closed curves in these categories are discussed.The thesis proves that in 3D digital space Z³,an M-adjacency is equivalent to a digital 6-adjacency;an MA-map is equivalent to a digital 6-continuous map,is connectedness-preserving as a generalization of an M-continuous map;an MA-isomorphism is a generalizations of an M-homeomorphism.Moreover the thesis also proves that SC_M^3,l₁ is M-homeomorphic to SC_M^3,l₂ if and only if l₁ =l₂ where SC3,lM means a simple closed M-curve with l elements in Z3;SC_MA^3,l₁ is MA-isomorphic to SC3,l2MA if and only if l₁ =l₂,where SC_MA^3,l means a simple closed MA-curve with l elements in Z3.Finally,the notion of MA-retract map is introduced to thin digital images and it is more effective in the thinning of 3D digital images,compared with the topology retract.