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- Title
UNIQUENESS PROPERTIES OF THE INVARIATOR, LEADING TO SIMPLE COMPUTATIONS.
- Authors
CRUZ-ORIVE, LUIS M.
- Abstract
It is shown that, for a three dimensional particle (namely an arbitrary compact domain with piecewise smooth boundary in ℝ3) 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.
- Subjects
UNIQUENESS (Mathematics); POLYGONS; VOLUME (Cubic content); COMPUTATIONAL geometry; STEREOLOGY; CONVEX geometry; LOGICAL prediction
- Publication
Image Analysis & Stereology, 2012, Vol 31, Issue 2, p89
- ISSN
1580-3139
- Publication type
Article
- DOI
10.5566/ias.v31.p89-98