Percolation is an important property of porous media, as it describes the connectivity of pores. We propose a novel, direction-dependent percolation probability which can be efficiently estimated from three-dimensional images obtained by microtomography. Furthermore, in order to describe the penetrability of the pore space by particles of a given diameter or a fluid of a given surface tension, we introduce a percolation probability depending on the width of the pores, from which we may also derive a measure of the mean pore channel width. As application examples, we consider the penetrability of porous beryllium pebbles, the connectivity of pores in arctic firn, the percolation of the pore space of aluminum foams and the mean width of the percolating space between the fibers in a laminate's percolating pore space

A large spatio-temporal data set monitoring the annual progress of bark beetle infestation in the Bavarian Forest National Park (Germany) is statistically analysed by means of complex image analysis algorithms. The infestation data were obtained by color-infrared (CIR) aerial image interpretation and cover 10 subsequent years (2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010). Newly emerged infestation patches are hypothesized as spatially correlated to locations of previous year's infestation. Both areas, source patches and subsequently emerged patches, are considered as two disjoint random sets. Their spatio-temporal dependence is analysed by two methods: the classical approach based on the measurement of cross-covariance functions, and a second one based on nearest neighbor distances. The resulting characteristics can be interpreted as pre-disposition probabilities of bark beetle infestation depending on distance to sources. Both methods show a strong short-range preference, which decreases with increasing distances.