In this paper, a new skeleton-based algorithm for the segmentation of individual fiber in 3D tomographic images is described. The proposed method is designed to deal with low-density materials featuring fibers of varied sizes, shapes and tortuosities, like composite fiberboards used for buildings insulation. To this end the paths of the skeleton are first classified according to their connectivity, the connectivity of their adjacent nodes, their orientation, their average radius and the variation of the distance transform along each path. This allows for the identification of spurious paths and paths linking two fibers. Reconstruction of the path of the fibers is done thanks to an optimal pairing algorithm which joins paths that show the most similar orientation and radius at each node/link. The segmented skeleton is finally dilated by means of a growing algorithm ordered by the average radius of the fibers in order to reconstruct each identified fiber. As an application, the algorithm is used to segment a 3D tomographic image of a hemp polymer fiberboard designed for buildings insulation. Information such as the number of contacts, tortuosity, length, average radius, orientation of fibers are measured on both the segmented skeleton and reconstructed image, which allow for a thorough characterization of the fiber network.