Planar images of powder particles or sand grains can be interpreted as ``figures'', i.e., equivalence classes of directly congruent compact sets. The paper introduces a concept of set-valued means and real-valued variances for samples of such figures. In obtaining these results, the images are registered to have similar locations and orientations. The method is applied to find a mean figure of a sample of polygonal particles.

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CWI
Department of Operations Research, Statistics, and System Theory [BS]

Stoyan, D, & Molchanov, I.S. (1995). Set-valued means of random particles. Department of Operations Research, Statistics, and System Theory [BS]. CWI.