Statistical Analysis of Large-Scale Structure in the Universe

Lecture Notes in Physics

et al. 2002

Section: Going Beyond Scalar Minkowski Functionals -A Physical Motivamentioning

confidence: 99%

Vector- and Tensor-Valued Descriptors for Spatial Patterns

Beisbart

Dahlke

Lecture Notes in Physics

et al. 2002

“…[34]). There has been a long debate, whether and how strongly the clustering of galaxies depends on their luminosity and their morphological type (see, e.g.…”

Section: Segregation Effects In the Distribution Of Galaxiesmentioning

confidence: 99%

“…In this model the one-point density of the marks is M 1 (m) = w(m), and m k = u k etc. The conditional mark density is given by 34) and the mark-correlation functions defined in Sect. 1.1.4 read…”

Section: The Random Field Modelmentioning

confidence: 99%

Mark Correlations: Relating Physical Properties to Spatial Distributions

Beisbart

Kerscher

Morphology of Condensed Matter

2002

Self Cite

Abstract. Mark correlations provide a systematic approach to look at objects both distributed in space and bearing intrinsic information, for instance on physical properties. The interplay of the objects' properties (marks) with the spatial clustering is of vivid interest for many applications; are, e.g., galaxies with high luminosities more strongly clustered than dim ones? Do neighbored pores in a sandstone have similar sizes? How does the shape of impact craters on a planet depend on the geological surface properties? In this article, we give an introduction into the appropriate mathematical framework to deal with such questions, i.e. the theory of marked point processes. After having clarified the notion of segregation effects, we define universal test quantities applicable to realizations of a marked point processes. We show their power using concrete data sets in analyzing the luminosity-dependence of the galaxy clustering, the alignment of dark matter halos in gravitational N -body simulations, the morphologyand diameter-dependence of the Martian crater distribution and the size correlations of pores in sandstone. In order to understand our data in more detail, we discuss the Boolean depletion model, the random field model and the Cox random field model. The first model describes depletion effects in the distribution of Martian craters and pores in sandstone, whereas the last one accounts at least qualitatively for the observed luminosity-dependence of the galaxy clustering.

“…The application of these Minkowski functionals in statistical physics and cosmology are reviewed by [15,17] and [26], respectively.…”

Section: Continuitymentioning

confidence: 99%

Characterisation of irregular spatial structures by parallel sets and integral geometric measures

Arns

Knackstedt

Colloids and Surfaces A: Physicochemical and Engineering Aspect

2004

A new method of characterising the morphology of disordered systems is presented based on the evolution of a family of integral geometric measures during erosion and dilation operations. The method is used to determine the accuracy of model reconstructions of random systems. It is shown that the use of erosion/dilation operations on the original image leads to an accurate discrimination of morphology. We consider the morphology of an experimental system and use the method to optimally match a reconstructed model morphology.