Surface tensor estimation from linear sections

2014/04/28 by Astrid Kousholt, Kousholt, Astrid, Markus Kiderlen +3
Mathematics · #52A22 #53C65 #60D05 #60G55 #62G05 #FOS: Mathematics #Point processes and geometric inequalities #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.1404.6907

openalex publication_date 2014/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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