Centre for Mathematical Physics and Stochastics

Department of Mathematical Sciences, University of Aarhus

Funded by The Danish National Research Foundation

MPS-RR 2002-17

April 2002

Estimation methods for the directional measure of a stationary
planar random set * Z *, based only on discretized realizations
of * Z *, are discussed. Properties of the discretized set that
can be derived by comparing neighbouring grid points are used.
Larger grid configurations of more than two grid points are
considered. It is shown that the probabilities of observing the
various types of configurations can be expressed in terms of the first
contact distribution function of * Z * (with a finite structuring
element). An important prerequisite result concerning deterministic
dilation areas is also established. The inference on the mean normal
measure based on 2 x 2 configurations is discussed in detail.

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