Set-Valued Means of Random Particles

Authors:
Dietrich Stoyan;Ilya S. Molchanov
Affiliations:
TU Bergakademie Freiberg, D-09596 Freiberg (Sachs), Germany/ E-mail: stoyan@hrz.tu-freiberg.de;University of Glasgow, Department of Statistics, Glasgow, G12 8QW, Scotland, UK/ E-mail: ilya@stats.gla.ac.uk
Venue:
Journal of Mathematical Imaging and Vision
Year:
1997

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Abstract

Planar images of powder particles or sand grains can be interpreted as “figures”, i.e., equivalence classes of directlycongruent compact sets. The paper introduces a concept of set-valuedmeans and real-valued variances for samples of such figures. Inobtaining these results, the images are registered to have similarlocations and orientations. The method is applied to find a mean figure of a sample of polygonal particles.