ON THE PRECISION OF THE ISOTROPIC CAVALIERI DESIGN
Keywords:brain, image analysis, isotropic Cavalieri, stereology, variance prediction, volume
AbstractThe isotropic Cavalieri design is based on a isotropically oriented set of parallel systematic sections a constant distance apart. Its advantage over the ordinary Cavalieri design is twofold - first, besides volume it allows the unbiased estimation of surface area, and second, the error variance predictor for the volume estimator is much simpler, involving only the surface area of the object, and the distance between sections. In an earlier paper, the two hemispheres of a rat brain were arranged perpendicular to each other before sectioning, aiming at reducing the error variance with respect to other arrangements (such as the aligned one) by exploiting an intuitively plausible antithetic effect. Because the total surface area of the objects is unchanged under any arrangements, however, the error variance predictor for the volume estimator does not depend on object shape, which looks intriguing. Using reconstructions of the mentioned hemispheres, we dilucidate the aparent paradox by means of automatic Monte Carlo replications of the relevant volume estimates under the antithetic and the aligned arrangements.
Cruz-Orive LM (2006). A general variance predictor for Cavalieri slices. J Microsc 222(3):158-65.
Cruz-Orive LM (2013). Variance predictors for isotropic geometric sampling, with applications in forestry. Statist Methods Appl 22(1):3-31.
Cruz-Orive LM, Gelsvartas J, Roberts N (2014). Sampling theory and automated simulations for vertical sections, applied to human brain. J
Cruz-Orive LM, Ramos-Herrera ML, Artacho-Pérula E (2010). Stereology of isolated objects with the invariator. J Microsc 240(2):94-110.
García-Fiñana M, Cruz-Orive LM (2004). Improved variance prediction for systematic sampling on R. Statistics 38(3):243-72.
González-Villa J, Cruz M, Cruz-Orive LM (2017). On the precision of the nucleator. Image Anal Stereol 36:123-34.
Gundersen HJG, Jensen EB (1987). The efficiency of systematic sampling in stereology and its prediction. J Microsc 147(3):229-63.
Kiêu K, Souchet S, Istas J (1999). Precision of systematic sampling and transitive methods. J Statist Plan Inf 77(2):263-79.
How to Cite
Copyright (c) 2018 Image Analysis & Stereology
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.