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Local Stereology of Tensors of Convex Bodies

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Abstract

In this paper, we present local stereological estimators of Minkowski tensors defined on convex bodies in ℝd. 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.

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Authors and Affiliations

  1. Department of Mathematics, Aarhus University, Ny Munkegade 118, 8000, Aarhus C, Denmark

    Eva B. Vedel Jensen

  2. Department of Mathematics and Statistics, Institute of Mathematical Statistics and Acturarial Science, University of Bern, Sidlerstrasse 5, 3012, Bern, Switzerland

    Johanna F. Ziegel

Authors
  1. Eva B. Vedel Jensen
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  2. Johanna F. Ziegel
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Correspondence to Johanna F. Ziegel.

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Jensen, E.B.V., Ziegel, J.F. Local Stereology of Tensors of Convex Bodies. Methodol Comput Appl Probab 16, 263–282 (2014). https://doi.org/10.1007/s11009-013-9337-8

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  • DOI: https://doi.org/10.1007/s11009-013-9337-8

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