Surface tensor estimation from linear sections

TL;DR

This paper develops new stereological estimators for surface tensors of convex bodies using linear sections, applicable in both design-based and model-based settings, advancing geometric analysis methods.

Contribution

It introduces novel estimators for surface tensors derived from Crofton's formula, utilizing linear sections in various random and structured configurations.

Findings

Derived estimators based on isotropic and non-isotropic lines

Provided estimators for stationary processes of convex particles

Enhanced surface tensor estimation techniques in Euclidean spaces

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.