THE INVARIATOR DESIGN: AN UPDATE

Authors

  • Luis Manuel Cruz-Orive University of Cantabria (E-Santander)
  • Ximo Gual-Arnau Department of Mathematics-INIT, University Jaume I, E-12071 Castell\'o

DOI:

https://doi.org/10.5566/ias.1324

Keywords:

invariator, peak-and-valley formula, stereology, surface area, test line weighting, volume

Abstract

The invariator is a method to generate a test line within an isotropically oriented plane through a fixed point, in such a way that the test line is effectively motion invariant in three dimensional space. Generalizations exist for non Euclidean spaces. The invariator design is convenient to estimate surface area and volume simultaneously. In recent years a number of new results have appeared which call for an updated survey. We include two new estimators, namely the a posteriori weighting estimator for surface area and volume, and the peak-and-valley formula for surface area.

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Published

2015-11-10

Issue

Section

Original Research Paper

How to Cite

Cruz-Orive, L. M., & Gual-Arnau, X. (2015). THE INVARIATOR DESIGN: AN UPDATE. Image Analysis and Stereology, 34(3), 147-159. https://doi.org/10.5566/ias.1324

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