<title>Topological approach to image segmentation</title>

Abstract

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 information of an image. We define some basic notions relative to that topology. Furthermore, we indicate how to get an homotopic kernel. Such a kernel may be seen as an `ultimate' topological simplification 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 method of irregular regions in a kernel allows to selectively simplify the topology. 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.