A new topological classification of points in 3D images

Abstract

We propose, in this paper, a new topological classification of points in 3D images. This classification is based on two connected components numbers computed on the neighborhood of the points. These numbers allow to classify a point as an interior or isolated, border, curve, surface point or as different kinds of junctions. The main result is that the new border point type corresponds exactly to a simple point. This allows the detection of simple points in a 3D image by counting only connected components in a neighborhood. Furthermore other types of points are better characterized. This classification allows to extract features in a 3D image. For example, the different kinds of junction points may be used for characterizing a 3D object. An example of such an approach for the analysis of medical images is presented.