ABSTRACT
This chapter describes how many of the concepts of “classical morphology” can be extended to spaces of images modeled by graphs. A graph consists of a collection of points, called vertices, and a binary relation between themml: two vertices either are related or they are not related. The structuring graph is used to construct a neighborhood function on the vertices by relating individual vertices to each other whenever they belong to a local instantiation of the structuring graph. Graph morphology provides nice tools for the study of heterogeneous media at a macroscopic level, based on information on their microstructure. The basic idea underlying classical morphology is to extract information from an image by probing it at any position with some small geometric shape called a structuring element. Graph morphology provides a collection of morphological tools for the investigation of populations of objects for which neighborhood relations are of interest.
