Simulating stochastic geometries: morphology of overlapping grains Original Research Article

Integral geometry furnishes a family of morphological descriptors known as Minkowski functionals which are related to curvature integrals. We present an exact algorithm for the calculation of Minkowski functionals for overlapping grains each with arbitrary location, orientation and shape (Boolean model). The method is numerically robust even for small samples, independent of statistical assumptions, and yields global as well as local morphological information. We illustrate the method by applying it to distributions of overlapping and hard disks.