The study of the coronary vessel structure is crucial to the diagnosis of atherosclerosis and other cardiovascular diseases, which together account for about 35% of all deaths in the United States per year. Vessel Segmentation from CTA data is challenging because of non-uniform image intensity along the vessel, and the branching and thinning geometry of the vessel tree. We present a novel method for vessel extraction that models the vasculature as a tubular tree and individual vessels as 3D tubes. We create an initial tube from a few seed points within the vessel tree, and then evolve this initial tube using a variational energy optimization approach to capture the vessel while automatically detecting branches in the vessel tree. A significant advantage of our proposed framework is that the center-line of the blood vessel tree, which is useful in defining cross sectional area of the vessel and evaluating stenoses, is detected automatically as the tubular tree evolves. Existing approaches on the other hand need an explicit step for skeletonization of the vessel volume after segmentation. Another benefit is that the parent-child relationships between branches are also automatically obtained, which is useful in fly-through visualization as well as clinical reporting.