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.
| Original language | English |
|---|---|
| Journal | Mathematische Nachrichten |
| Volume | 288 |
| Issue | 14-15 |
| Pages (from-to) | 1647-1672 |
| Number of pages | 26 |
| ISSN | 0025-584X |
| DOIs | |
| Publication status | Published - 2015 |
Keywords
- Crofton formula
- Minkowski tensor
- stereology
- isotropic random line
- anisotropic random line
- vertical section estimator
- minimal variance estimator
- stationary particle process
- stereological estimator