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Directional analysis of digitized planar sets by configuration counts
Author(s) -
JENSEN E. B. V.,
KIDERLEN M.
Publication year - 2003
Publication title -
journal of microscopy
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.569
H-Index - 111
eISSN - 1365-2818
pISSN - 0022-2720
DOI - 10.1046/j.1365-2818.2003.01149.x
Subject(s) - pixel , digitization , planar , image (mathematics) , estimator , set (abstract data type) , window (computing) , computer science , algorithm , anisotropy , enumeration , sampling (signal processing) , mathematics , pattern recognition (psychology) , artificial intelligence , computer vision , statistics , combinatorics , optics , physics , computer graphics (images) , filter (signal processing) , programming language , operating system
Summary 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 × n . This allows us to count the number of different types of n × 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.