Stereological estimation of surface area from digital images

Johanna Ziegel, Markus Kiderlen

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    Abstract

    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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