Aarhus Universitets segl

Astrid Kousholt

Surface tensor estimation from linear sections

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Surface tensor estimation from linear sections. / Kousholt, Astrid; Kiderlen, Markus; Hug, Daniel.
I: Mathematische Nachrichten, Bind 288, Nr. 14-15, 2015, s. 1647-1672.

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avisTidsskriftartikelForskningpeer review

Harvard

Kousholt, A, Kiderlen, M & Hug, D 2015, 'Surface tensor estimation from linear sections', Mathematische Nachrichten, bind 288, nr. 14-15, s. 1647-1672. https://doi.org/10.1002/mana.201400147

APA

CBE

MLA

Vancouver

Kousholt A, Kiderlen M, Hug D. Surface tensor estimation from linear sections. Mathematische Nachrichten. 2015;288(14-15):1647-1672. doi: 10.1002/mana.201400147

Author

Kousholt, Astrid ; Kiderlen, Markus ; Hug, Daniel. / Surface tensor estimation from linear sections. I: Mathematische Nachrichten. 2015 ; Bind 288, Nr. 14-15. s. 1647-1672.

Bibtex

@article{3145ba02e64d431cb669bbff50a214e6,
title = "Surface tensor estimation from linear sections",
abstract = "From Crofton{\textquoteright}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",
author = "Astrid Kousholt and Markus Kiderlen and Daniel Hug",
year = "2015",
doi = "10.1002/mana.201400147",
language = "English",
volume = "288",
pages = "1647--1672",
journal = "Mathematische Nachrichten",
issn = "0025-584X",
publisher = "Wiley - V C H Verlag GmbH & Co. KGaA",
number = "14-15",

}

RIS

TY - JOUR

T1 - Surface tensor estimation from linear sections

AU - Kousholt, Astrid

AU - Kiderlen, Markus

AU - Hug, Daniel

PY - 2015

Y1 - 2015

N2 - 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.

AB - 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.

KW - Crofton formula

KW - Minkowski tensor

KW - stereology

KW - isotropic random line

KW - anisotropic random line

KW - vertical section estimator

KW - minimal variance estimator

KW - stationary particle process

KW - stereological estimator

U2 - 10.1002/mana.201400147

DO - 10.1002/mana.201400147

M3 - Journal article

VL - 288

SP - 1647

EP - 1672

JO - Mathematische Nachrichten

JF - Mathematische Nachrichten

SN - 0025-584X

IS - 14-15

ER -