Related papers: Morphometry of Spatial Patterns
A space curve is determined by conformal arc-length, conformal curvature, and conformal torsion, up to M\"obius transformations. We use the spaces of osculating circles and spheres to give a conformally defined moving frame of a curve in…
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.…
The second-order formula of Minkowski functionals in weakly non-Gaussian fields is compared with the numerical $N$-body simulations. Recently, weakly non-Gaussian formula of Minkowski functionals is extended to include the second-order…
We present a new harmonic-domain approach for extracting morphological information, in the form of Minkowski Functionals (MFs), from weak lensing (WL) convergence maps. Using a perturbative expansion of the MFs, which is expected to be…
We pursue a novel morphometric analysis to detect sources in very-high-energy gamma-ray counts maps by structural deviations from the background noise. Because the Minkowski functionals from integral geometry quantify the shape of the…
Modern redshift surveys such as the 2 degree field Galaxy Redshift Survey (2dFGRS) and the Sloan Digital Sky Survey (SDSS) reveal the fully 3 dimensional distribution of a million or so galaxies over a large cosmological volume. Visually…
Using general but simple covariance arguments, we classify the `quantum' Minkowski spaces for dimensionless deformation parameters. This requires a previous analysis of the associated Lorentz groups, which reproduces a previous…
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…
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…
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 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…
Galaxy clusters exhibit a rich morphology during the early and intermediate stages of mass assembly, especially beyond their boundary. A classification scheme based on shapefinders deduced from the Minkowski functionals is examined to fully…
Recently, Minkowski Tensors (MT) have gained popularity for morphological analysis tasks. As opposed to the scalar Minkowski functionals (MF; in 2D given by area, perimeter and Euler characteristic), MT can characterize symmetry and…
Shape is one of the most important visual attributes to characterize objects, playing a important role in pattern recognition. There are various approaches to extract relevant information of a shape. An approach widely used in shape…
Minkowski functionals quantify the morphology of smooth random fields. They are widely used to probe statistical properties of cosmological fields. Analytic formulae for ensemble expectations of Minkowski functionals are well known for…
Pairs of metrics in a two-dimensional linear vector space are considered, one of which is a Minkowski type metric. Their simultaneous diagonalizability is studied and canonical presentations for them are suggested.
A complete classification of continuous, dually epi-translation invariant, and rotation equivariant valuations on convex functions is established. This characterizes the recently introduced functional Minkowski vectors, which naturally…
Many statistical methods have been proposed in the last years for analyzing the spatial distribution of galaxies. Very few of them, however, can handle properly the border effects of complex observational sample volumes. In this paper, we…
Observations reveal that on large scales the universe is spanned by a percolating network of superclusters interspersed with large and almost empty regions -- voids. This thesis reports the construction of a sophisticated computational…