Local Stereology of Tensors of Convex Bodies
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In this paper, we present local stereological estimators of Minkowski tensors defined on convex bodies in ℝ d . Special cases cover a number of well-known local stereological estimators of volume and surface area in ℝ3, but the general set-up also provides new local stereological estimators of various types of centres of gravity and tensors of rank two. Rank two tensors can be represented as ellipsoids and contain information about shape and orientation. The performance of some of the estimators of centres of gravity and volume tensors of rank two is investigated by simulation.
KeywordsEllipsoidal approximation Local stereology Minkowski tensors Particle shape Particle orientation Rotational integral geometry
AMS 2000 Subject Classification60D05 53C65 52A22
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- Beisbart C, Dahlke R, Mecke KR, Wagner H (2002) Vector- and tensor-valued descriptors for spatial patterns. In: Morphology of condensed matter, vol 600. Lecture notes in physics. Springer, Berlin, pp 249–271Google Scholar
- Dvořák J, Jensen EBV (2012) On semi-automatic estimation of surface area. CSGB Research Report 12-06, Centre for Stochastic Geometry and Advanced Bioimaging, Department of Mathematics, Aarhus University, Denmark. SubmittedGoogle Scholar
- Jensen EB, Gundersen HJG (1987) Stereological estimation of surface area of arbitrary particles. Acta Stereol 6:25–30Google Scholar
- Thórisdóttir O, Kiderlen M (2013) The invariator principle in convex geometry (in preparation)Google Scholar