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Nail fold capillaroscopy (NC) an inexpensive, non-invasive method to assess capillary morphology, and is routinely used for the detection of scleroderma spectral disorders, Raynaud's phenomenon and other connective tissue diseases. Evaluation of NC requires expert knowledge and is typically performed by careful manual inspection of the images. Computer-aided approaches of capillary inspection would reduce the time required for diagnosis but have been little pursued due to the challenges present in NC images. In this paper, we present a capillary skeletonisation algorithm based on image enhancement followed by binarisation and skeleton extraction using a thinning algorithm. The extracted vessel skeleton can subsequently be utilised for auto measurement of capillary density and other parameters. We demonstrate that our algorithm works well and that it clearly outperforms previous approaches.