The development of realistic neuroanatomical models of peripheral nerves for simulation purposes requires the reconstruction of the morphology of the myelinated fibres in the nerve, including their nodes of Ranvier. Currently, this information has to be extracted by semimanual procedures, which severely limit the scalability of the experiments. In this contribution, we propose a supervised machine learning approach for the detailed reconstruction of the geometry of fibres inside a peripheral nerve based on its high-resolution serial section images. Learning from sparse expert annotations, the algorithm traces myelinated axons, even across the nodes of Ranvier. The latter are detected automatically. The approach is based on classifying the myelinated membranes in a supervised fashion, closing the membrane gaps by solving an assignment problem, and classifying the closed gaps for the nodes of Ranvier detection. The algorithm has been validated on two very different datasets: (i) rat vagus nerve subvolume, SBFSEM microscope, 200 ?? 200 ?? 200 nm resolution, (ii) rat sensory branch subvolume, confocal microscope, 384 ?? 384 ?? 800 nm resolution. For the first dataset, the algorithm correctly reconstructed 88% of the axons (241 out of 273) and achieved 92% accuracy on the task of Ranvier node detection. For the second dataset, the gap closing algorithm correctly closed 96.2% of the gaps, and 55% of axons were reconstructed correctly through the whole volume. On both datasets, training the algorithm on a small data subset and applying it to the full dataset takes a fraction of the time required by the currently used semiautomated protocols. Our software, raw data and ground truth annotations are available at http://hci.iwr.uni-heidelberg.de/Benchmarks/. The development version of the code can be found at https://github.com/RWalecki/ATMA.