Integral-geometry morphological image analysis

This paper reviews a general method to characterize the morphology of two- and three-dimensional patterns in terms of geometrical and topological desc riptors. Based on concepts of integral geometry, it involves the calculatio n of the Minkowski functionals of black-and-white images representing the p atterns. The result of this approach is an objective, numerical characteriz ation of a given pattern. We briefly review the basic elements of morpholog ical image processing, a technique to transform images to patterns that are amenable to further morphological image analysis. The image processing tec hnique is applied to electron microscope images of nano-ceramic particles a nd metal-oxide precipitates. The emphasis of this review is on the practica l aspects of the integral-geometry-based morphological image analysis but w e discuss its mathematical foundations as well. Applications to simple latt ice structures, triply periodic minimal surfaces, and the Klein bottle serv e to illustrate the basic steps of the approach. More advanced applications include random point sets, percolation and complex structures found in blo ck copolymers. (C) 2001 Elsevier Science B.V. All rights reserved.