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Sufficiently Near Neighbourhoods of Points in Flow Graphs. A Near Set Approach

Peters J.F., Chitcharoen D.

Fundamenta Informaticae

2013

Vol. 124, nr 1/2

175--196

This paper introduces sufficiently near visual neighbourhoods of points and neighbourhoods of sets in digital image flow graphs (NDIFGs). An NDIFG is an extension of a Pawlak flow graph. The study of sufficiently near neighbourhoods in NDIFGs stems from recent work on near sets and topological spaces via near and far, especially in terms of visual neighbourhoods of points that are sufficiently near each other. From a topological perspective, non-spatially near sets represent an extension of proximity space theory and the original insight concerning spatially near sets by F. Riesz at the International Congress of Mathematicians (ICM) in 1908. In the context of Herrlich nearness, sufficiently near neighbourhoods of sets in NDIFGs provide a new perspective on topological structures in NDIFGs. The practical implications of this work are significant. With the advent of a study of the nearness of open as well as closed neighbourhods of points and of sets in NDIFGs, it is now possible to do information mining on a more global level and achieve new insights concerning the visual information embodied in the images that provide input to an NDIFG.