Related papers: Robust Morphological Measures for Large-Scale Stru…
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…
The Minkowski functionals are a mathematical tool to quantify morphological features of patterns. Some applications to the matter distribution in galaxy catalogues and N-body simulations are reviewed, with an emphasis on the effects of…
The morphological properties of large scale structure of the Universe can be fully described by four Minkowski functionals (MFs), which provide important complementary information to other statistical observables such as the widely used…
Methods for the statistical characterization of the large-scale structure in the Universe will be the main topic of the present text. The focus is on geometrical methods, mainly Minkowski functionals and the J-function. Their relations to…
A new method for the statistical analysis of 3D point processes, based on the family of Minkowski functionals, is explained and applied to modelled galaxy distributions generated by a toy-model and cosmological simulations of the…
Minkowski functionals provide a novel tool to characterize the large-scale galaxy distribution in the Universe. Here we give a brief tutorial on the basic features of these morphological measures and indicate their practical application for…
This article describes the theoretical foundation of and explicit algorithms for a novel approach to morphology and anisotropy analysis of complex spatial structure using tensor-valued Minkowski functionals, the so-called Minkowski tensors.…
We probe gravitational clustering in N-body simulations using geometrical descriptors sensitive to `connectedness': the genus curve, percolation and shape statistics. We find that both genus and percolation curves provide complementary…
Minkowski functionals constitute a family of order parameters which discriminate spatial patterns according to size, shape and connectivity. Here we point out, that these scalar descriptors can be complemented by vector-valued curvature…
In order to quantify higher-order correlations of the galaxy cluster distribution we use a complete family of additive measures which give scale-dependent morphological information. Minkowski functionals can be expressed analytically in…
In this work, we propose a powerful probe of neutrino effects on the large-scale structure (LSS) of the Universe, i.e., Minkowski functionals (MFs). The morphology of LSS can be fully described by four MFs. This tool, with strong…
In this study, we explore the potential of utilizing the four Minkowski functionals, which can fully describe the morphological properties of the large-scale structures, as a robust tool for investigating the modified gravity, particularly…
The morphology of galaxy clusters is quantified using Minkowski functionals, especially the vector-valued ones, which contain directional information and are related to curvature centroids. The asymmetry of clusters and the amount of their…
In a follow-up study to a previous analysis of the IRAS 1.2Jy catalogue, we quantify the morphological fluctuations in the PSCz survey. We use a variety of measures, among them the family of scalar Minkowski functionals. We confirm the…
The genus statistics of isodensity contours has become a well-established 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…
Higher-rank Minkowski valuations are efficient means for describing the geometry and connectivity of spatial patterns. We show how to extend the framework of the scalar Minkowski valuations to vector- and tensor-valued measures. The…
We apply Minkowski functionals and various derived measures to decipher the morphological properties of large-scale structure seen in simulations of gravitational evolution. Minkowski functionals of isodensity contours serve as tools to…
The influence of the microstructural geometry on the behavior of porous media is widely recognized, particularly in geomaterials, but also in biomaterials and engineered materials. Recent advances in imaging techniques, such as X-ray…
To study the global morphology of the galaxy distribution in our local neighbourhood we calculate the Minkowski functionals for a sequence of volume limited samples within a sphere of 8 Mpc centred on our galaxy. The well known strong…
We present a morphological analysis of atom probe data of nanoscale microstructural features, using methods developed by the astrophysics community to describe the shape of superclusters of galaxies. We describe second-phase regions using…