Inclusion ratio based estimator for the mean length of the boolean line segment model with an application to nanocrystalline cellulose

M. Niilo-Rämä (Corresponding Author), S. Kärkkäinen, D. Gasbarra, Timo Lappalainen

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)

Abstract

A novel estimator for estimating the mean length of fibres is proposed for censored data observed in square shaped windows. Instead of observing the fibre lengths, we observe the ratio between the intensity estimates of minus-sampling and plus-sampling. It is well-known that both intensity estimators are biased. In the current work, we derive the ratio of these biases as a function of the mean length assuming a Boolean line segment model with exponentially distributed lengths and uniformly distributed directions. Having the observed ratio of the intensity estimators, the inverse of the derived function is suggested as a new estimator for the mean length. For this estimator, an approximation of its variance is derived. The accuracies of the approximations are evaluated by means of simulation experiments. The novel method is compared to other methods and applied to real-world industrial data from nanocellulose crystalline.
Original languageEnglish
Pages (from-to)147-155
Number of pages9
JournalImage Analysis and Stereology
Volume33
Issue number2
DOIs
Publication statusPublished - 2014
MoE publication typeA1 Journal article-refereed

Fingerprint

Cellulose
Line segment
cellulose
estimators
Inclusion
inclusions
Sampling
Estimator
Fibers
Crystalline materials
sampling
Fiber
Model
fibers
Censored Data
Approximation
approximation
Experiments
Simulation Experiment
Biased

Keywords

  • Boolean model
  • nanocellulose
  • fibres
  • length distribution
  • mean length
  • simulation

Cite this

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title = "Inclusion ratio based estimator for the mean length of the boolean line segment model with an application to nanocrystalline cellulose",
abstract = "A novel estimator for estimating the mean length of fibres is proposed for censored data observed in square shaped windows. Instead of observing the fibre lengths, we observe the ratio between the intensity estimates of minus-sampling and plus-sampling. It is well-known that both intensity estimators are biased. In the current work, we derive the ratio of these biases as a function of the mean length assuming a Boolean line segment model with exponentially distributed lengths and uniformly distributed directions. Having the observed ratio of the intensity estimators, the inverse of the derived function is suggested as a new estimator for the mean length. For this estimator, an approximation of its variance is derived. The accuracies of the approximations are evaluated by means of simulation experiments. The novel method is compared to other methods and applied to real-world industrial data from nanocellulose crystalline.",
keywords = "Boolean model, nanocellulose, fibres, length distribution, mean length, simulation",
author = "M. Niilo-R{\"a}m{\"a} and S. K{\"a}rkk{\"a}inen and D. Gasbarra and Timo Lappalainen",
year = "2014",
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Inclusion ratio based estimator for the mean length of the boolean line segment model with an application to nanocrystalline cellulose. / Niilo-Rämä, M. (Corresponding Author); Kärkkäinen, S.; Gasbarra, D.; Lappalainen, Timo.

In: Image Analysis and Stereology, Vol. 33, No. 2, 2014, p. 147-155.

Research output: Contribution to journalArticleScientificpeer-review

TY - JOUR

T1 - Inclusion ratio based estimator for the mean length of the boolean line segment model with an application to nanocrystalline cellulose

AU - Niilo-Rämä, M.

AU - Kärkkäinen, S.

AU - Gasbarra, D.

AU - Lappalainen, Timo

PY - 2014

Y1 - 2014

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AB - A novel estimator for estimating the mean length of fibres is proposed for censored data observed in square shaped windows. Instead of observing the fibre lengths, we observe the ratio between the intensity estimates of minus-sampling and plus-sampling. It is well-known that both intensity estimators are biased. In the current work, we derive the ratio of these biases as a function of the mean length assuming a Boolean line segment model with exponentially distributed lengths and uniformly distributed directions. Having the observed ratio of the intensity estimators, the inverse of the derived function is suggested as a new estimator for the mean length. For this estimator, an approximation of its variance is derived. The accuracies of the approximations are evaluated by means of simulation experiments. The novel method is compared to other methods and applied to real-world industrial data from nanocellulose crystalline.

KW - Boolean model

KW - nanocellulose

KW - fibres

KW - length distribution

KW - mean length

KW - simulation

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DO - 10.5566/ias.v33.p147-155

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