The Adaptive Topology of a Digital Image

Authors:
Herbert Edelsbrunner;Olga Symonova
Affiliations:
-;-
Venue:
ISVD '12 Proceedings of the 2012 Ninth International Symposium on Voronoi Diagrams in Science and Engineering
Year:
2012

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Abstract

In order to enjoy a digital version of the Jordan Curve Theorem, it is common to use the closed topology for the foreground and the open topology for the background of a 2-dimensional binary image. In this paper, we introduce a single topology that enjoys this theorem for all thresholds decomposing a real-valued image into foreground and background. This topology is easy to construct and it generalizes to n-dimensional images.