Corneal nerves changes have been linked to damage caused by surgical interventions or prolonged contact lens wear. Furthermore nerve tortuosity has been shown to correlate with the severity of diabetic neuropathy. For these reasons there has been an increasing interest on the analysis of these structures. In this work we propose a novel, robust, and fast fully automatic algorithm capable of tracing the sub-basal plexus nerves from human corneal confocal images. We resort to logGabor filters and support vector machines to trace the corneal nerves. The proposed algorithm traced most of the corneal nerves correctly (sensitivity of 0.88 ± 0.06 and false discovery rate of 0.08 ± 0.06). The displayed performance is comparable to a human grader. We believe that the achieved processing time (0.661 ± 0.07 s) and tracing quality are major advantages for the daily clinical practice.