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Markus Kiderlen

Stereological estimation of surface area from digital images

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  • Johanna Ziegel, Department of Mathematics and Statistics, The University of Melbourne, Australia
  • Markus Kiderlen
  • T.N. Thiele Centre
  • Centre for Stochastic Geometry and Advanced Bioimaging
  • Department of Mathematical Sciences
A sampling design of local stereology is combined with a method from digital stereology to yield a novel estimator of surface area based on counts of configurations observed in a digitization of an isotropic 2- dimensional slice with thickness s. As a tool, a result of the second author and J. Rataj on infinitesimal increase of volumes of morphological transforms is refined and used. The proposed surface area estimator is asymptotically unbiased in the case of sets contained in the ball centred at the origin with radius s and in the case of balls centred at the origin with unknown radius. For general shapes bounds for the asymptotic expected relative worst case error are given. A simulation example is discussed for surface area estimation based on 2×2×2-configurations.
Original languageEnglish
JournalImage Analysis and Stereology
Volume29
Pages (from-to)99-110
Number of pages12
ISSN1580-3139
Publication statusPublished - Jun 2010

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