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

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    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
    Issue number2
    Publication statusPublished - 2014
    MoE publication typeA1 Journal article-refereed



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

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