Inclusion ratio based estimator for the mean length of the Boolean line segment model with an application to nanocrystalline cellulose
Niilo-Rämä, M., Kärkkäinen, S., Gasbarra, D., & Lappalainen, T. (2014). Inclusion ratio based estimator for the mean length of the Boolean line segment model with an application to nanocrystalline cellulose. Image Analysis and Stereology, 33(2), 147-155. https://doi.org/10.5566/ias.v33.p147-155
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Image Analysis and StereologyDate
2014Copyright
© Niilo-Rämä et al. This is an open access article under a Creative Commons Attribution-NonCommercial License.
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.
Publisher
International Society for StereologyISSN Search the Publication Forum
1580-3139Keywords
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http://www.ias-iss.org/ojs/IAS/article/view/1072Publication in research information system
https://converis.jyu.fi/converis/portal/detail/Publication/23758486
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Except where otherwise noted, this item's license is described as © Niilo-Rämä et al. This is an open access article under a Creative Commons Attribution-NonCommercial License.
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