Minkowski Tensors of Anisotropic Spatial Structure

Details Minkowski Tensors of Anisotropic Spatial Structure Minkowski Tensors of Anisotropic Spatial Structure

2010-09-13

arxiv.org/abs/1009.2340v1

Physics

Condensed Matter

Soft Condensed Matter

Scientific paper

We describe a novel approach to morphology and anisotropy analysis of complex spatial structure using tensor-valued Minkowski functionals, or Minkowski tensors. Minkowski tensors are generalizations of the well-known scalar Minkowski functionals and are explicitly sensitive to anisotropic aspects of morphology, relevant for example for elastic moduli or permeabilities of porous materials. We provide explicit linear-time algorithms to compute these measures for three-dimensional shapes given by triangulations of their bounding surface, including triangulations obtained from experimental gray-scale image data by isosurface extraction. Eigenvalue ratios of Minkowski tensors provide a robust and versatile definition of intrinsic anisotropy. This analysis is applied to biopolymer networks under shear and to cellular complexes of dense bead packs. We validate our numerical method by computing Minkowski tensors of triply-periodic minimal surfaces (often used as structural models for self-assembled amphiphilic phases) for which analytic expressions of these tensors can be derived from the Weierstrass parametrization.

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