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STEREOLOGICAL ESTIMATION OF SURFACE AREA FROM DIGITAL IMAGES
June 2010
JOHANNA ZIEGEL AND MARKUS KIDERLEN
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.
Configurations, Digital Stereology, Local Stereology, Surface Area
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