Image segmentation through operators based on topology

Abstract

We consider a cross-section topology that 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 acquire a homotopic kernel and a leveling kernel. Such kernels can 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 an irregular region. The iterative removal of irregular regions in a kernel enables us 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 to define and tune parameters.