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Particle size‐shape distributions: the general spheroid problem: II. Stochastic model and practical guide
Author(s) -
Orive LuisM. Cruz
Publication year - 1978
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.1365-2818.1978.tb01162.x
Subject(s) - spheroid , ellipse , histogram , population , variable (mathematics) , plane (geometry) , probability density function , covariance , mathematics , mathematical analysis , physics , statistical physics , geometry , statistics , computer science , biochemistry , sociology , in vitro , image (mathematics) , chemistry , demography , artificial intelligence
SUMMARY Mathematical relationships linking the size‐shape probability density function (pdf) of an infinite population of variable spheroids uniformly and isotropically scattered in space on the one hand, with the size‐shape pdf of the ellipses produced by a plane of section on the other, have recently been published (Cruz Orive, 1976). In the present paper, an independent model is developed for estimating the size‐shape bivariate histogram of a finite population of variable spheroids (either prolate, or oblate) uniformly and isotropically scattered within an arbitrary specimen, from the corresponding histogram of the elliptical profiles produced by an arbitrary section (or sections) through the whole specimen. The approach is stochastic, allowing the estimation of the variance‐covariance matrix of the ‘unfolded’ size‐shape spheroid frequencies. The numerical reliability of the methods is checked by means of an example, whereas a practical guide illustrates and summarizes the unfolding procedure. Natural ways of estimating spheroid properties, alternative to those found in Cruz Orive (1976), are presented.