We present a nearly automatic tool for the accurate segmentation of vascular structures in volumetric CTA images. Its inputs are a start and an end seed points inside the vessel. The two-step graph-based energy minimization method starts by computing the weighted shortest path between the vessel seed endpoints based on local image and seed intensities and vessel path geometric characteristics. It then automatically defines a Vessel Region Of Interest (VROI) from the shortest path and the estimated vessel radius, and extracts the vessels boundaries by minimize the energy on a corresponding graph cut. We evaluate our method within the 2009 MICCAI 3D Segmentation Challenge for Clinical Applications Workshop. Experimental results on the 46 carotid bifurcations from clinical CTAs, compared to ground-truth genrated by averaging three manual annotations, yield an average symmetric surface distance of 0.83mm and a Dice similarity of 81.8%, with only three input seeds. These results indicates that our method is easy to use, produces accurate segmentations of vessels lumen, and is robust to intensity variations inside the vessels, radius changes, bifurcations, and nearby anatomical structures with similar intensity values.