In this paper, a new skeleton-based algorithm for the segmentation of individual fibres in 3D tomographic images is described. The proposed method is designed to deal with low density materials featuring fibres with varied sizes, shapes and tortuosities, like composite fibreboards 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 fibres. Reconstruction of the path of the fibres 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 ordonned by the average radius of the fibres in order to reconstruct each identified fibres. As an application, the algorithm is used to segment a 3D tomographic image of hemp/polymer fibreboard for buildings insulation. Information such as the number of contacts, tortuosity, length, average radius, orientation of fibres are finally measured on both the segmented skeleton and reconstructed image, which allow for a thorough characterization of the fibre network.