Image Segmentation Through Operators Based Upon Topology
Gilles Bertrand, Jean-Christophe Everat, Michel Couprie · 1997
: We consider a cross-section topology which is defined on grayscale images. The main interest of this topology is that it keeps track of the grayscale informations of an image. We define some basic notions relative to that topology. Furthermore, we indicate how to get an homotopic kernel and a leveling kernel. Such kernels may be seen as "ultimate" topological simplifications of an image. A kernel of a real image, though simplified, is still an intricated image from a topological point of view. We introduce the notion of irregular region. The iterative removal of irregular regions in a kernel allows to selectively simplify the topology of the image. Through an example, we show that this notion leads to a method for segmenting some grayscale images without the need of defining and tuning parameters. Keywords: discrete topology, cross-section topology, topological numbers, regularization, segmentation. 1 Introduction The topology of discrete binary two-dimensional images has receiv...