Delineation and reconstruction of curvilinear structures in medical images are critical for the diagnosis of various vascular diseases and related surgical procedures. In this paper, we present a novel method for vascular structure segmentation and reconstruction, including the automatic detection of bifurcation points. First, we perform a pre-selection of tubular structures. Second, we trace the vessels based on the eigenanalysis of the Hessian matrix. This provides us the estimated direction of vessels as well as the cross-sectional planes orthogonal to the vessels. A Scan-Conversion method is then applied to cross-sectional planes to automatically detect the bifurcation points of the vessels. This method has a 96.59% success rate for detecting bifurcation correctly. Finally, vessels are delineated and reconstructed using deformable models. Our method is efficient and allows for completely automatic delineation and reconstruction of vessels as well as automatic detection of bifurcation points.