New Characterizations of Simple Points in 2D, 3D, and 4D Discrete Spaces

Authors:
Michel Couprie;Gilles Bertrand
Affiliations:
Université Paris-Est, LABINFO-IGM, UMR CNRS, Noisy-Le-Grand;Université Paris-Est, LABINFO-IGM, UMR CNRS, Noisy-Le-Grand
Venue:
IEEE Transactions on Pattern Analysis and Machine Intelligence
Year:
2009

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Abstract

A point of a discrete object is called simple if it can be deleted from this object without altering topology. In this article, we present new characterizations of simple points which hold in dimensions 2, 3 and 4, and which lead to efficient algorithms for detecting such points. In order to prove these characterizations, we establish two confluence properties of the collapse operation which hold in the neighborhood of a point in spaces of low dimension. This work is settled in the framework of cubical complexes, which provides a sound topological basis for image analysis, and allows to retrieve the main notions and results of digital topology, in particular the notion of simple point.