  We investigate the problem of estimating geodesic tortuosity and
constrictivity as two structural characteristics of stationary random closed
sets. They are of central importance for the analysis of effective transport
properties in porous or composite materials. Loosely speaking, geodesic
tortuosity measures the windedness of paths whereas the notion of
constrictivity captures the appearance of bottlenecks resulting from narrow
passages within a given materials phase. We first provide mathematically
precise definitions of these quantities and introduce appropriate estimators.
Then, we show strong consistency of these estimators for unboundedly growing
sampling windows. In order to apply our estimators to real datasets, the extent
of edge effects needs to be controlled. This is illustrated using a model for a
multi-phase material that is incorporated in solid oxid fuel cells.
