The quantitative analysis of retinal blood vessels is important for the management of vascular disease and tackling problems such as locating blood clots. Such tasks are hampered by the inability to accurately trace back problems along vessels to the source. This is due to the unresolved challenge of distinguishing automatically between vessel branchings and vessel crossings. In this paper, we present a new technique for tackling this challenging problem by developing a convolutional neural network approach for first locating vessel junctions and then classifying them as either branchings or crossings. We achieve a high accuracy of 94% for junction detection and 88% for classification. Combined with work in segmentation, this method has the potential to facilitate automated localisation of blood clots and other disease symptoms leading to improved management of eye disease through aiding or replacing a clinicians diagnosis.