The topological consistence of path connectedness in regular and irregular structures
In this paper an overview of regular adjacency structures compatible with topologies in 2 dimensions is given. This means that the different discrete structures are investigated on the equivalence of topological-connectedness and path-connectedness which is induced by the underlying adjacency.
In the second part a method is suggested how to construct topologies on irregular graphs and their compatibility to the adjacency structure is analyzed. Examples of basic adjacency structures are given. These topologies on regular grids and especially on irregular graphs are appropriate to be applied to image hierarchies in the field of image processing.
KeywordsTopological Structure Regular Graph Adjacency Structure Adjacent Vertex Dual Graph
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