### Abstract

Original language | English |
---|---|

Pages (from-to) | 147-155 |

Number of pages | 9 |

Journal | Image Analysis and Stereology |

Volume | 33 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2014 |

MoE publication type | A1 Journal article-refereed |

### Fingerprint

### Keywords

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

### Cite this

*Image Analysis and Stereology*,

*33*(2), 147-155. https://doi.org/10.5566/ias.v33.p147-155

}

*Image Analysis and Stereology*, vol. 33, no. 2, pp. 147-155. https://doi.org/10.5566/ias.v33.p147-155

**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.

Research output: Contribution to journal › Article › Scientific › peer-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

N2 - 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.

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

U2 - 10.5566/ias.v33.p147-155

DO - 10.5566/ias.v33.p147-155

M3 - Article

VL - 33

SP - 147

EP - 155

JO - Image Analysis and Stereology

JF - Image Analysis and Stereology

SN - 1580-3139

IS - 2

ER -