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Surface tensor estimation from linear sections
Authors:Astrid Kousholt  Markus Kiderlen  Daniel Hug
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.
Keywords:Crofton formula  Minkowski tensor  stereology  isotropic random line  anisotropic random line  vertical section estimator  minimal variance estimator  stationary particle process  stereological estimator  52A22  53C65  60D05  62G05  60G55
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