Issue No. 04 - April (2009 vol. 31)
Michel Couprie , Université Paris-Est, LABINFO-IGM, UMR CNRS, Noisy-Le-Grand
Gilles Bertrand , Université Paris-Est, LABINFO-IGM, UMR CNRS, Noisy-Le-Grand
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.
Image Processing and Computer Vision, Pattern Recognition
M. Couprie and G. Bertrand, "New Characterizations of Simple Points in 2D, 3D, and 4D Discrete Spaces," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 31, no. , pp. 637-648, 2008.