0000000000483287
AUTHOR
Timo Lappalainen
Inclusion ratio based estimator for the mean length of the boolean line segment model with an application to nanocrystalline cellulose
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…
Determination of Fibre Orientation Distribution from Images of Fibre Networks
We recall two categories of algorithms for estimating fibre orientation distribution from an image of a spatial fibre system. In the first algorithm, the estimate is a magnitude-weighted distribution from angles perpendicular to the directions of the gradients in the image. The second algorithm is based on the scaled variogram of grey values scanned along a sampling line and its relation to the fibre orientation distribution. Using lines in several directions and assuming a parametric model for the orientation distribution, the orientation parameters are estimated numerically from a least-squares type procedure. Two versions of variogram-based methods are used in this work. We compare the p…