[MaPhySto logo]
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 of the Directional Measure of Planar Random Sets by Digitization


Eva B. Vedel Jensen

Markus Kiderlen


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.

Availability: [ gzipped ps-file ] [ pdf-file ]

[ Help on down-loading/viewing/printing ]

This paper has now been published in Adv. Appl. Prob. (SGSA) 35 (2003)