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Local stereology of tensors of convex bodies. (English) Zbl 1319.60021

Summary: In this paper, we present local stereological estimators of Minkowski tensors defined on convex bodies in \(\mathbb R^d\). Special cases cover a number of well-known local stereological estimators of volume and surface area in \(\mathbb R^3\), 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.

MSC:

60D05 Geometric probability and stochastic geometry
53C65 Integral geometry
52A22 Random convex sets and integral geometry (aspects of convex geometry)
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