Image Analysis -Topological Methods

Abstract

The aim of image analysis is to provide a symbolic description of the image structure, that can serve to supply information about the image for all kinds of different tasks. We will give a complete description of the topological structure of images, studied simultaneously at all levels of resolution. This can be achieved through the artifice of embedding an image into a continuous family of images that can be uniquely generated by it. We will show how the representation of the image structure on different levels of resolution may be linked in a logical manner, so that features existing at different levels of resolution get related to each other. Our method explains the succes of recently introduced 'pyramid' algorithms and is of value for the study of image morphology per se. Furthermore, it is not at all limited to two-dimensional images.