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The Cavalieri estimator with unequal section spacing revisited

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The Cavalieri estimator with unequal section spacing revisited. / Kiderlen, Markus; Dorph-Petersen, Karl Anton.

I: Image Analysis and Stereology, Bind 36, Nr. 2, 2017, s. 135-141.

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

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Kiderlen, Markus ; Dorph-Petersen, Karl Anton. / The Cavalieri estimator with unequal section spacing revisited. I: Image Analysis and Stereology. 2017 ; Bind 36, Nr. 2. s. 135-141.

Bibtex

@article{f7f2db50d51442b882eb709cab770957,
title = "The Cavalieri estimator with unequal section spacing revisited",
abstract = "The Cavalieri method allows to estimate the volume of a compact object from area measurements in equidistant parallel planar sections. However, the spacing and thickness of sections can be quite irregular in applications. Recent publications have thus focused on the effect of random variability in section spacing, showing that the classical Cavalieri estimator is still unbiased when the stack of parallel planes is stationary, but that the existing variance approximations must be adjusted. The present paper considers the special situation, where the distances between consecutive section planes can be measured and thus where Cavalieri's estimator can be replaced by a quadrature rule with randomized sampling points. We show that, under mild conditions, the trapezoid rule and Simpson's rule lead to unbiased volume estimators and give simulation results that indicate that a considerable variance reduction compared to the generalized Cavalieri estimator can be achieved.",
keywords = "Cavalieri estimator, Perturbed spacing, Randomized Newton-Cotes quadrature, Variance approximations",
author = "Markus Kiderlen and Dorph-Petersen, {Karl Anton}",
year = "2017",
doi = "10.5566/ias.1723",
language = "English",
volume = "36",
pages = "135--141",
journal = "Image Analysis and Stereology",
issn = "1580-3139",
publisher = "INT SOC STEREOLOGY",
number = "2",

}

RIS

TY - JOUR

T1 - The Cavalieri estimator with unequal section spacing revisited

AU - Kiderlen, Markus

AU - Dorph-Petersen, Karl Anton

PY - 2017

Y1 - 2017

N2 - The Cavalieri method allows to estimate the volume of a compact object from area measurements in equidistant parallel planar sections. However, the spacing and thickness of sections can be quite irregular in applications. Recent publications have thus focused on the effect of random variability in section spacing, showing that the classical Cavalieri estimator is still unbiased when the stack of parallel planes is stationary, but that the existing variance approximations must be adjusted. The present paper considers the special situation, where the distances between consecutive section planes can be measured and thus where Cavalieri's estimator can be replaced by a quadrature rule with randomized sampling points. We show that, under mild conditions, the trapezoid rule and Simpson's rule lead to unbiased volume estimators and give simulation results that indicate that a considerable variance reduction compared to the generalized Cavalieri estimator can be achieved.

AB - The Cavalieri method allows to estimate the volume of a compact object from area measurements in equidistant parallel planar sections. However, the spacing and thickness of sections can be quite irregular in applications. Recent publications have thus focused on the effect of random variability in section spacing, showing that the classical Cavalieri estimator is still unbiased when the stack of parallel planes is stationary, but that the existing variance approximations must be adjusted. The present paper considers the special situation, where the distances between consecutive section planes can be measured and thus where Cavalieri's estimator can be replaced by a quadrature rule with randomized sampling points. We show that, under mild conditions, the trapezoid rule and Simpson's rule lead to unbiased volume estimators and give simulation results that indicate that a considerable variance reduction compared to the generalized Cavalieri estimator can be achieved.

KW - Cavalieri estimator

KW - Perturbed spacing

KW - Randomized Newton-Cotes quadrature

KW - Variance approximations

UR - http://www.scopus.com/inward/record.url?scp=85020986390&partnerID=8YFLogxK

U2 - 10.5566/ias.1723

DO - 10.5566/ias.1723

M3 - Journal article

AN - SCOPUS:85020986390

VL - 36

SP - 135

EP - 141

JO - Image Analysis and Stereology

JF - Image Analysis and Stereology

SN - 1580-3139

IS - 2

ER -