Estimation of Fibre Length Distributions from Fibre Endpoints

Estimating the fibre length distribution in composite materials is of practical relevance in materials science. We propose an estimator for the fibre length distribution using the point process of fibre endpoints as input. Assuming that this point process is a realization of a Neyman–Scott process, we use results for the reduced second moment measure to derive a consistent and unbiased estimator for the fibre length distribution. We introduce various versions of the estimator taking anisotropy or errors in the observation into account. The estimator is evaluated using a heuristic for its mean squared error as well as a simulation study. Finally, the estimator is applied to the fibre endpoint process extracted from a tomographic image of a glass fibre composite.