title: Directional analysis of digitized planar sets by configuration counts.
abstract: The oriented rose of normal directions 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 analysed locally by considering pixel squares of size n x n. This allows us to count the number of different types of n x n configurations in the pixel image. We show 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 oriented rose based on counts of observed informative configurations are derived. The procedure is illustrated by a simulated example and an analysis of a microscopic image of steel.
authors: Laboratory for Computational Stochastics and MaPhySto, Department of Mathematical Sciences, University of Aarhus, Ny Munkegade, DK-8000 Aarhus C, Denmark. eva@imf.au.dk
authors: E B V
authors: EB
authors: Jensen
authors: M
authors: M
authors: Kiderlen
mesh_terms: D000465:Algorithms; D016880:Anisotropy; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D013232:Steel / Q000737:chemistry
chemical_list: D013232:Steel