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Centre for Mathematical Physics and Stochastics
Department of Mathematical Sciences, University of Aarhus

Funded by The Danish National Research Foundation

MPS-RR 2001-44
December 2001

On the Oriental Analysis of Boolean Fibres from Digital Images


Eva B. Vedel Jensen

Salme Kärkkäinen, Dominique Jeulin


The orientational characteristics of fibres in digital images are studied. The fibres are modelled by a planar Boolean model whose typical grain is a thickened (coloured) fibre. The aim is to make stereological inference on the rose of directions of unobservable central fibres from observations made on a digital image of the thick fibres. For central fibres, the relation between the rose of directions and the point intensity, observed on a sampling line, is known. We derive, under regularity conditions, the relation between the unobservable point intensity and the scaled variogram observed on the line in a binary and greyscale image. Using such a relation, it is possible to draw inference about the rose of directions from the scaled variogram which is easy and fast to determine in a digital image.

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This paper has now been published in J. Microsc. 207, 69--77 (2003)