Image segmentation through operators based on topology

We consider a cross-section topology which is deened on grayscale images. The main interest of this topology is that it keeps track of the grayscale informations of an image. We deene 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 simpliications of an image. A kernel of a real image, though simpliied, 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 deening and tuning parameters.