  The paper discusses local porosity theory and its relation with other
geometric characterization methods for porous media such as correlation
functions and contact distributions. Special emphasis is placed on the
charcterization of geometric observables through Hadwigers theorem in
stochastic geometry. The four basic Minkowski functionals are introduced into
local porosity theory, and for the first time a relationship is established
between the Euler characteristic and the local percolation probabilities. Local
porosity distributions and local percolation probabilities provide a scale
dependent characterization of the microstructure of porous media that can be
used in an effective medium approach to predict transport.
