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

    @article{3176b389c4854848b4ea9472b37b8ef9,
    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",
    doi = "10.5566/ias.v33.p147-155",
    language = "English",
    volume = "33",
    pages = "147--155",
    journal = "Image Analysis and Stereology",
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    publisher = "International Society for Stereology",
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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

    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 -