Jordan surfaces in discrete antimatroid topologies

Authors:
Ralph Kopperman;John L. Pfaltz
Affiliations:
City University of New York, New York, NY;University of Virginia, Charlottesville, VA
Venue:
IWCIA'04 Proceedings of the 10th international conference on Combinatorial Image Analysis
Year:
2004

Citing 7
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Abstract

In this paper we develop a discrete, T0 topology in which (1) closed sets play a more prominent role than open sets, (2) atoms comprising the space have discrete dimension, which (3) is used to define boundary elements, and (4) configurations within the topology can have connectivity (or separation) of different degrees. To justify this discrete, closure based topological approach we use it to establish an n-dimensional Jordan surface theorem of some interest. As surfaces in digital imagery are increasingly rendered by triangulated decompositions, this kind of discrete topology can replace the highly regular pixel approach as an abstract model of n-dimensional computational geometry.