Tensorial Minkowski functionals and anisotropy measures for planar patterns
Schröder-Turk G, Kapfer S, Breidenbach B, Beisbart C, Mecke K (2010)
Publication Status: Published
Publication Type: Journal article
Publication year: 2010
Journal
Publisher: WILEY-BLACKWELL
Book Volume: 238
Pages Range: 57-74
Journal Issue: 1
DOI: 10.1111/j.1365-2818.2009.03331.x
Abstract
Quantitative measures for anisotropic characteristics of spatial structure are needed when relating the morphology of microstructured heterogeneous materials to tensorial physical properties such as elasticity, permeability and conductance. Tensor-valued Minkowski functionals, defined in the framework of integral geometry, provide a concise set of descriptors of anisotropic morphology. In this article, we describe the robust computation of these measures for microscopy images and polygonal shapes. We demonstrate their relevance for shape description, their versatility and their robustness by applying them to experimental data sets, specifically microscopy data sets of non-equilibrium stationary Turing patterns and the shapes of ice grains from Antarctic cores.
Authors with CRIS profile
Gerd Schröder-Turk
Lehrstuhl für Theoretische Physik
Sebastian Kapfer
Lehrstuhl für Theoretische Physik
Klaus Mecke
Lehrstuhl für Theoretische Physik
Additional Organisation(s)
Involved external institutions
Germany (DE)How to cite
APA:
Schröder-Turk, G., Kapfer, S., Breidenbach, B., Beisbart, C., & Mecke, K. (2010). Tensorial Minkowski functionals and anisotropy measures for planar patterns. Journal of Microscopy, 238(1), 57-74. https://doi.org/10.1111/j.1365-2818.2009.03331.x
MLA:
Schröder-Turk, Gerd, et al. "Tensorial Minkowski functionals and anisotropy measures for planar patterns." Journal of Microscopy 238.1 (2010): 57-74.
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