Measurements of retinal blood vessel morphology have been shown to be related to the risk of cardiovascular diseases. The wrong identification of vessels may result in a large variation of these measurements, leading to a wrong clinical diagnosis. In this paper, we address the problem of automatically identifying true vessels as a postprocessing step to vascular structure segmentation. We model the segmented vascular structure as a vessel segment graph and formulate the problem of identifying vessels as one of finding the optimal forest in the graph given a set of constraints. We design a method to solve this optimization problem and evaluate it on a large real-world dataset of 2,446 retinal images. Experiment results are analyzed with respect to actual measurements of vessel morphology. The results show that the proposed approach is able to achieve 98.9% pixel precision and 98.7% recall of the true vessels for clean segmented retinal images, and remains robust even when the segmented image is noisy.