Parameters extracted from the vasculature on the retina are correlated with various conditions such as diabetic retinopathy and cardiovascular diseases such as stroke. Segmentation of the vasculature on the retina has been a topic that has received much attention in the literature over the past decade. Analysis of the segmentation result, however, has only received limited attention with most works describing methods to accurately measure the width of the vessels. Analyzing the connectedness of the vascular network is an important step towards the characterization of the complete vascular tree. The retinal vascular tree, from an image interpretation point of view, originates at the optic disc and spreads out over the retina. The tree bifurcates and the vessels also cross each other. The points where this happens form the key to determining the connectedness of the complete tree. We present a supervised method to detect the bifurcations and crossing points of the vasculature of the retina. The method uses features extracted from the vasculature as well as the image in a location regression approach to find those locations of the segmented vascular tree where the bifurcation or crossing occurs (from here, POI, points of interest). We evaluate the method on the publicly available DRIVE database in which an ophthalmologist has marked the POI.