Author/Editor		Cruz-Orive, Luis M.
Title		Uniqueness properties of the invariator, leading to simple computations
Type		članek
Vol. and No.		Letnik 31, št. 2
Publication year		2012
Volume		str. 89-98
ISSN		1580-3139 - Image Analysis & Stereology online journal (Printed version).
Language		eng
Abstract		It is shown that, for a three dimensional particle (namely an arbitrary compact domain with piecewise smooth boundary in R^3) the mean wedge volume defined on a given pivotal section is equal to the average nucleator estimator of the particle volume defined on that section. Further, if the particle is convex and it contains the pivotal point, then the flower area of a given pivotal section equals the average surfactor estimator defined on that section. These results are intended to throw some light on the standing conjecture that the functional defined on a pivotal section according to the invariator has a unique general expression. As a plus, the former result leads to a computational formula for the mean wedge volume of a convex polygon which is much simpler than the one published recently, and it is valid whether the fixed pivotal point is interior or exterior to the particle.
Keywords		stereology surface area volume stereologija površina prostornina