Journal article
Minkowski tensors of anisotropic spatial structure
New Journal of Physics, Vol.15
2013
Abstract
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 so-called 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 permeability of microstructured materials. Here we derive explicit linear-time algorithms to compute these tensorial measures for three-dimensional shapes. These apply to representations of any object that can be represented by a triangulation of its bounding surface; their application is illustrated for the polyhedral Voronoi cellular complexes of jammed sphere configurations and for triangulations of a biopolymer fibre network obtained by confocal microscopy. The paper further bridges the substantial notational and conceptual gap between the different but equivalent approaches to scalar or tensorial Minkowski functionals in mathematics and in physics, hence making the mathematical measure theoretic formalism more readily accessible for future application in the physical sciences.
Details
- Title
- Minkowski tensors of anisotropic spatial structure
- Authors/Creators
- G.E. Schröder-Turk (Author/Creator)W. Mickel (Author/Creator)S.C. Kapfer (Author/Creator)F.M. Schaller (Author/Creator)B. Breidenbach (Author/Creator)D. Hug (Author/Creator)K. Mecke (Author/Creator)
- Publication Details
- New Journal of Physics, Vol.15
- Publisher
- Institute of Physics Publishing
- Number of pages
- 38
- Identifiers
- 991005545080907891
- Copyright
- 2013 IOP Publishing and Deutsche Physikalische Gesellschaft
- Murdoch Affiliation
- Murdoch University
- Language
- English
- Resource Type
- Journal article
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InCites Highlights
These are selected metrics from InCites Benchmarking & Analytics tool, related to this output
- Collaboration types
- Domestic collaboration
- Citation topics
- 9 Mathematics
- 9.50 Applied Statistics & Probability
- 9.50.1564 Convex Body
- Web Of Science research areas
- Physics, Multidisciplinary
- ESI research areas
- Physics