Regensburg 2010 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 1: Statistical Physics (general) I

DY 1.7: Talk

Monday, March 22, 2010, 11:45–12:00, H47

Tensorial Minkowski Functionals as Shape Measures for Experimental Data — •Sebastian Kapfer, Klaus Mecke, and Gerd E. Schröder-Turk — Friedrich-Alexander-Universität, Erlangen, Germany

In order to establish structure--function relationships for cellular and inhomogeneous materials, quantitative and robust `shape measures' are required that succinctly characterise the geometry of the material. In particular, if the quantities of interest are direction-dependent, tensor-valued shape measures are essential. We demonstrate that Minkowski Tensors characterise the anisotropy of disordered media in a robust way. We show that Minkowski tensors can be directly applied to experimental datasets. This is illustrated specifically for microscopy and tomography images.

Minkowski Tensors, also offering a firm mathematical foundation, consequently are promising candidates for shape measures.

For details see also: Schroeder-Turk et al., Journal of Microscopy 2009.