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Flowers and wedges for the stereology of particles
Author(s) -
CRUZORIVE L.M.
Publication year - 2011
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 - 10.1111/j.1365-2818.2011.03485.x
Subject(s) - stereology , bounded function , regular polygon , surface (topology) , section (typography) , geometry , point (geometry) , mathematics , observable , invariant (physics) , polyhedron , population , mathematical analysis , physics , computer science , medicine , demography , quantum mechanics , sociology , mathematical physics , operating system
Summary Recently, a new decomposition has been found for the motion invariant density of straight lines in , with applications in stereology. The new principle, called the invariator, leads to new rotational formulae which express the surface area and the volume of a bounded subset (called a ‘particle’) in terms of an observable functional defined in an isotropically oriented section (called a pivotal section) through a fixed point (called the pivotal point). The results have been extended to intrinsic volumes of manifolds in general space forms. The purpose of this paper is to present new results and computational formulae for three‐dimensional particles. Explicit estimators are obtained for a convex polyhedral particle with a pivotal point in its interior, in terms of the coordinates of the vertices of the pivotal section. The results are applied to a population of polyhedral grains from a cemented carbide which was studied earlier by alternative methods.