Speaker
Klaus Mecke
(Universität Erlangen-Nürnberg)
Description
A morphometric analysis of stochastic geometries is
introduced by using tensorial valuations, i.e.,
tensor-valued Minkowski functionals. Tensorial physical
properties such as elasticity, permeability and conductance
of microstructured heterogeneous materials require
quantitative measures for anisotropic characteristics of
random spatial structure. Tensor-valued Minkowski
functionals, defined in the framework of integral geometry,
provide a concise set of descriptors. The talk provides an
overview on the application on stochastic geometries used in
physics. A robust computation of these measures is presented
for microscopy images and polygonal shapes by linear-time
algorithms. Their relevance for shape description, their
versatility and their robustness is demonstrated by applying
them to experimental datasets, specifically microscopy
datasets. Applications are shown in two dimensions on
Turing patterns and on sections of ice grains from Antarctic
cores. In three dimensions Minkowski tensors have been used
to quantify the anisotropy of fluids and granular matter,
of confocal microscopy images of sheared biopolymers and of
triply-periodic minimal surface models for amphiphilic
self-assembly.
