Tensorial Minkowski functionals and anisotropy measures for planar patterns

• Published in: Journal of Microscopy
• Main Authors: Schröder-Turk, G.E., Kapfer, S., Breidenbach, B., Beisbart, C., Mecke, K.
• Format: Article in Journal/Newspaper
• Language: English
• Published: Wiley 2010
• Subjects: Antarc*; Antarctic
• Online Access: https://doi.org/10.1111/j.1365-2818.2009.03331.x; https://researchportal.murdoch.edu.au/esploro/outputs/journalArticle/Tensorial-Minkowski-functionals-and-anisotropy-measures/991005545116807891

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.