MPS-RR 2002-34
October 2002

Directional Analysis of Digitized Planar Sets by Configuration Counts

Eva B. Vedel Jensen

M. Kiderlen

Abstract

The directional distribution of a random set Z can be used to quantify its anisotropy. A method for estimating this quantity from a digitization of Z in a sampling window, i.e. its pixel image, is presented. The image is analyzed locally by considering pixel squares of size n x n. This allows to count the number of different types of n x n configurations in the pixel image. In the present paper, it is shown that it suffices to restrict attention to the so-called informative configurations. The number of informative configurations increases only polynomially in n. An algorithm to find these informative configurations is presented. Furthermore, estimators of the directional distribution based on counts of observed informative configurations are derived. The procedure is illustrated by a simulated example and an anlysis of a microscopic image of steel

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