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Markus Kiderlen

Surface tensor estimation from linear sections

Research output: Working paperResearch



  • Astrid Kousholt, Denmark
  • Markus Kiderlen
  • Daniel Hug, Department of Mathematics, Karlsruhe Institute of Technology (KIT)
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
PublisherCentre for Stochastic Geometry and advanced Bioimaging, Aarhus University
Number of pages31
Publication statusPublished - 2014
SeriesCSGB Research Reports

    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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