A segmentation algorithm is proposed which automatically extracts single fibers from tomographic 3D data of fiber-based materials. As an example, the algorithm is applied to a non-woven material used in the gas diffusion layer of polymer electrolyte membrane fuel cells. This porous material consists of a densely packed system of strongly curved carbon fibers. Our algorithm works as follows. In a first step, we focus on the extraction of skeletons, i.e., center lines of fibers. Due to irregularities like noise or other data artefacts, it is only possible to extract fragments of center lines. Thus, in a second step, we consider a stochastic algorithm to adequately connect these parts of center lines to each other, with the general aim to reconstruct the complete fibers such that the curvature properties of real fibers are reflected correctly. The quality of the segmentation algorithm is validated by applying it to simulated test data.