BEYOND GENUS STATISTICS - A UNIFYING APPROACH TO THE MORPHOLOGY OF COSMIC STRUCTURE

The genus statistics of isodensity contours has become a well-establis hed tool in cosmology. In this Letter we place the genus in the wider framework of a complete family of morphological descriptors. These are known as the Minkowski functionals, and we here apply them for the fi rst time to isodensity contours of a continuous random field. By takin g two equivalent approaches, one through differential geometry, the ot her through integral geometry, we derive two complementary formulae su itable for numerically calculating the Minkowski functionals. As an ex ample, we apply them to simulated Gaussian random fields and compare t he outcome to the analytically known results, demonstrating that both are indeed well suited for numerical evaluation. The code used for cal culating all Minkowski functionals is available from the authors.