Improved estimation of fiber length from 3-dimensional images

A new method is presented for estimating the specific fiber length from 3D images of macroscopically homogeneous fiber systems. The method is based on a discrete version of the Crofton formula, where local knowledge from 3 x 3 x 3-pixel configurations of the image data is exploited. It is shown that the relative error resulting from the discretization of the outer integral of the Crofton formula amounts at most 1.2 %. An algorithmic implementation of the method is simple and the runtime as well as the amount of memory space are low. The estimation is significantly improved by considering 3 x 3 x 3-pixel configurations instead of 2 x 2 x 2, as already studied in literature.