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Local Stereology of Tensors of Convex Bodies

  • Eva B. Vedel Jensen
  • Johanna F. Ziegel
Article

Abstract

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.

Keywords

Ellipsoidal approximation Local stereology Minkowski tensors Particle shape Particle orientation Rotational integral geometry 

AMS 2000 Subject Classification

60D05 53C65 52A22 

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of MathematicsAarhus UniversityAarhus CDenmark
  2. 2.Department of Mathematics and Statistics, Institute of Mathematical Statistics and Acturarial ScienceUniversity of BernBernSwitzerland

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