Characterizing Cluster Morphology Using Vector-valued Minkowski Functionals

The morphological and dynamical evolution of simulated galaxy clusters

We explore the morphological and dynamical evolution of galaxy clusters in simulations using scalar and vector-valued Minkowski valuations and the concept of fundamental plane relations. In this context, three questions are of fundamental interest: 1. How does the average cluster morphology depend on the cosmological background model? 2. Is it possible to discriminate between different cosmolog...

Minkowski tensors of anisotropic spatial structure

This paper 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 socalled Minkowski tensors. Minkowski tensors are generalizations of the wellknown scalar Minkowski functionals and are explicitly sensitive to anisotropic aspects of morphology, relevant...

A Representation for Characteristic Functionals of Stable Random Measures with Values in Sazonov Spaces

Extended morphometric analysis of neuronal cells with Minkowski valuations

Minkowski valuations provide a systematic framework for quantifying different aspects of morphology. In this paper we apply vector- and tensor-valued Minkowski valuations to neuronal cells from the cat's retina in order to describe their morphological structure in a comprehensive way. We introduce the framework of Minkowski valuations, discuss their implementation for neuronal cells and show ho...

Tensor Valuations and Their Local Versions

The intrinsic volumes, recalled in the previous chapter, provide an array of size measurements for a convex body, one for each integer degree of homogeneity from 0 to n. For measurements and descriptions of other aspects, such as position, moments of the volume and of other size functionals, or anisotropy, tensor-valued functionals on convex bodies are useful. The classical approach leading to ...