Fraunhofer-Institut für Techno- und Wirtschaftsmathematik ITWMBeschreibung
The main idea of this research is modelling wood fibers. Fibres are sufficiently smooth simple curves in space, and can be modelled either as cylinders, as dilated curved lines or as chains of balls. The cross section can be modelled as circle, square, or triangular. Based on the natural microstructure of wood fibers, in here, fibers will be modelled as cylinders with rectangular cross section. Changing the shape of the cross section in the models requires the fitting of the cross section orientation distribution.
This research also focusses on characterizing the morphology of stochastic models like Boolean models, Poisson cylinder processes, or Gaussian random fields by the Minkowski functions. i.e. the densities of the Minkowski functionals, namely the volume fraction ( Vv ), the surface area ( Sv ), the integral of mean curvature ( Mv ) and the Euler characteristic ( χv ), after erosion and dilation of the set are considered. In particular, the capability of the Minkowski functions for choosing a suitable model class for an observed structure is investigated.