New Characterizations of Simple Points in 2D, 3D, and 4D Discrete Spaces
A point of a discrete object is called simple if it can be deleted from this object without altering topology. In this paper, we present new characterizations of simple points, which hold in dimensions 2, 3, and 4 and 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. We develop this work in the framework of cubical complexes, which provides a sound topological basis for image analysis and retrieves the main notions and results of digital topology, in particular the notion of simple point.
simple point confluence collapse cubical complex thinning skeleton topology preservation 4d space