X-ray angiography is the most commonly used imaging modality for the detection of coronary stenoses due to its high spatial and temporal resolution of lumen contour and its utility to guide coronary interventions in real time. However, the high inter- and intra-observer variability in interpreting the geometry of 3D vascular structure based on multiple 2D image projections is a limitation in the accurate determination of lesion severity. This could be addressed by the 3D reconstruction of the coronary arterial (CA) tree. The automated reconstruction of 3D CA tree from 2D projections is challenging due to the existence of several imaging artifacts, such as vessel overlap, foreshortening, and most importantly respiratory and cardiac motion. Along with these artifacts, the acquisition geometry introduces the possibility of generating false vessel segments in the reconstruction. Our approach aims to reduce the motion artifacts in angiographic projections by developing a new method for rigid and non-rigid motion correction. A novel point-cloud based approach is subsequently introduced for reconstruction of 3D vessel centerlines by iteratively minimizing the reconstruction error. The performance of the proposed 3D reconstruction is evaluated using angiographic projections from 45 patients, producing average reprojection errors of mm and mm for 3D centerlines reconstruction, when co-registered with the parent vessels on projection planes that were/were not used to derive the 3D reconstruction, respectively. A comparison of the reconstructed 3D lumen surface with optical coherence tomography (OCT) measurements has been performed, showing no statistically significant difference in the luminal cross-sections reconstructed with our method, compared to OCT.