A knowledge-driven approach to the three-dimensional reconstruction of coronary artery trees by means of two X-ray projections is proposed. The spatial reconstruction of the tree skeleton is discussed. A binary tree model of the arterial structure and its projections is employed. Consequently, the reconstruction of the three-dimensional tree skeleton is achieved by (a) matching the skeletons of corresponding pairs of vascular segments in the two views and (b) back-projecting the coupled skeleton projections. From a geometrical point of view, the matching problem is, in general, ill-conditioned. For this reason, additional information sources were used. Thus, the matching phase is accomplished by using both the imaging geometry information, as well as anatomical and topological knowledge, about the coronary arteries coded in a rule base. As far as the back-projection phase is concerned, an algorithm was developed based on: (1) the imaging geometry, (2) the bounding of the back-projection error and (3) a contiguity criterion.