The invention relates to a method and a system for the simultaneous reconstruction of the three-dimensional vessel geometry and the flow characteristics in a vessel system. According to one realization of the method, vessel segments (41) of a parametric models are fitted to differently oriented X-ray projections (P1, Pk, PN) of the vessel system that are generated during the passage of a bolus of contrast agent, wherein the fitting takes the imaged contrast agent dynamics and physiological a priori knowledge into account. In an alternative embodiment, the vessel geometry is reconstructed progressively along each vessel, wherein a new segment of a vessel is added based on the continuity of the vessel direction, vessel radius and reconstructed contrast agent dynamics.