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Markus Kiderlen

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

Research output: Working paperResearch



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.
Original languageEnglish
PublisherCentre for Stochastic Geometry and Advanced Bioimaging, Aarhus University
Number of pages29
Publication statusPublished - 2013
SeriesCSGB Research Reports

    Research areas

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

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