ROBUST MORPHOLOGICAL MEASURES FOR LARGE-SCALE STRUCTURE IN THE UNIVERSE

We propose a novel method for the description of spatial patterns form ed by a coverage of point sets representing galaxy samples. This metho d is based on a complete family of morphological measures known as Min kowski functionals, which includes the topological Euler characteristi c and geometric descriptors to specify the content, shape and connecti vity of spatial sets. 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 a pplying it to a Poisson process, a 'double-Poisson' process, and to th e Abell catalogue of galaxy clusters.