Surface tensor estimation from linear sections

Astrid Kousholt; Markus Kiderlen; Daniel Hug

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arXiv · 1404.6907

Surface tensor estimation from linear sections

Astrid Kousholt·Markus Kiderlen·Daniel Hug

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Abstract

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.

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Astrid Kousholt, Markus Kiderlen, Daniel Hug. 2014-04-28. Surface tensor estimation from linear sections. https://arxiv.org/abs/1404.6907

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