Surface tensor estimation from linear sections

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DOI

    Astrid Kousholt, Denmark
  • Markus Kiderlen
  • Daniel Hug, Department of Mathematics, Karlsruhe Institute of Technology (KIT), Denmark
From Crofton’s formula for Minkowski tensors we derive stereological estimators of translation invariant surface tensors of convex bodies in the n-dimensional Euclidean space. The estimators are based on one-dimensional linear sections. In a design based setting we suggest three types of estimators. These are based on isotropic uniform random lines, vertical sections, and non-isotropic random lines, respectively. Further, we derive estimators of the specific surface tensors associated with a stationary process of convex particles in the model based setting.
Original languageEnglish
JournalMathematische Nachrichten
Volume288
Issue number14-15
Pages (from-to)1647-1672
Number of pages26
ISSN0025-584X
DOIs
Publication statusPublished - 2015

    Research areas

  • Crofton formula, Minkowski tensor, stereology, isotropic random line, anisotropic random line, vertical section estimator, minimal variance estimator, stationary particle process, stereological estimator

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