Related papers: Robust Morphological Measures for Large-Scale Stru…
A complete family of statistical descriptors for the morphology of large--scale structure based on Minkowski--Functionals is presented. These robust and significant measures can be used to characterize the local and global morphology of…
We suggest a set of morphological measures that we believe can help in quantifying the shapes of two-dimensional cosmological images such as galaxies, clusters, and superclusters of galaxies. The method employs non-parametric morphological…
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…
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…
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…
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…
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.…
Aims. H.E.S.S. observes an increasing number of large extended sources. A new technique based on the structure of the sky map is developed to account for these additional structures by comparing them with the common point source analysis.…
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…
We present a new ansatz which can successfully be used to determine the morphological properties of the supercluster-void network. The ansatz is based on a surface modelling scheme SURFGEN, which generates a triangulated surface from a…
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…
The study of shapes of the images of objects is an important issue not only because it reveals its dynamical state but also it helps to understand the object's evolutionary history. We discuss a new technique in cosmological image analysis…
Minkowski tensors are comprehensive shape descriptors that robustly capture n-point information in complex random geometries and that have already been extensively applied in the Euclidean plane. Here, we devise a novel framework for…
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 novel method for computing the Minkowski Functionals from isodensity surfaces extracted directly from the Delaunay tessellation of a point distribution. This is an important step forward compared to the previous cosmological…
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…
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…
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…