Aspects of Mathematical Morphology

In this paper we review the basic concepts of integral-geometry-based morphological image analysis. This approach yields an objective, numerical characterization of twoand threedimensional patterns in terms of geometrical and topological descriptors called Minkowski functionals. We review its mathematical foundation and show that it is easy to put the theory into practice by presenting simple computer algorithms to perform the analysis. Illustrative examples are given of applications of this approach to simple lattice structures, random point sets and minimal surfaces. As a more advanced application we show how the technique can be used to obtain a morphological characterization of computer tomography images of metal foams.