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Stereological estimation of integral mixed curvature with application
Author(s) -
Beneš V.,
Hlawiczková M.,
Voleník K.
Publication year - 2000
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 - 10.1046/j.1365-2818.2000.00742.x
Subject(s) - estimator , curvature , bounded function , bias of an estimator , mathematics , variance (accounting) , space (punctuation) , function (biology) , mean curvature , point (geometry) , minimum variance unbiased estimator , mathematical analysis , computer science , statistics , geometry , accounting , evolutionary biology , business , biology , operating system
This article addresses a bounded system of compact smooth surfaces in three‐dimensional space. Recently, an unbiased estimator of the integral mixed curvature of the given system based on a vertical sampling design has been proposed. The aims of the present paper are: (i) to show that the proposed estimator may have an infinite variance; (ii) to suggest a modification that has better statistical properties; (iii) to extend the point estimator to a function that monitors the curvature along the gradient microstructures; (iv) to present an application of the method to real microscopic images.