May 27 – 30, 2015
Mariehamn, Åland
Europe/Stockholm timezone

Integral Geometry and Physics of Random Spatial Structures

May 29, 2015, 3:30 PM
Conference room, Arkipelag (Mariehamn, Åland)

Conference room, Arkipelag

Mariehamn, Åland


Klaus Mecke (Universität Erlangen-Nürnberg)


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.

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