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Estimating the surface area of non-convex particles from central planar sections

By Ó. Thórisdóttir, A.H. Rafati and M. Kiderlen
CSGB Research Reports
No. 08, September 2013

In this paper, we present a new surface area estimator in local stereology. This new estimator is called the "Morse type surface area estimator" and is obtained using a two-stage sampling procedure. First a plane section through a fixed reference point of a three-dimensional structure is taken. In this section plane a modification of the area tangent count method is used. The Morse type estimator generalizes Cruz-Orive's pivotal estimator for convex objects to non-convex objects. The advantages of the Morse type estimator over existing local surface area estimators are illustrated in a simulation study. The Morse type estimator is well suited for computer assisted confocal microscopy and we demonstrate its practicability in a biological application: the surface area estimation of the nuclei of giant-cell glioblastoma from microscopy images. We also present an interactive software that allows the user to efficiently obtain the estimator.

Keywords: surface area, local stereology, area tangent count, invariator principle, Morse type surface area estimator

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