Robust Morphological Measures for Large-Scale Structure in the Universe

Details Robust Morphological Measures for Large-Scale Structure in the Universe Robust Morphological Measures for Large-Scale Structure in the Universe

1993-12-14

arxiv.org/abs/astro-ph/9312028v1

Astron.Astrophys. 288 (1994) 697-704

Astronomy and Astrophysics

Astrophysics

submitted to A & A, Main Journal. TeX, 17 pages excl.figures; contact T. Buchert: TOB@ibma.ipp-garching.mpg.de

Scientific paper

We propose a novel method for the description of spatial patterns formed by a coverage of point sets representing galaxy samples. This method is based on a complete family of morphological measures known as Minkowski functionals, which includes the topological Euler characteristic and geometric descriptors to specify the content, shape and connectivity 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 applying it to a Poisson process, a `double-Poisson' process, and to the Abell catalogue of galaxy clusters.

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