Coronary computed tomography angiography (CCTA) provides a non-invasive imaging solution that reliably depicts the anatomy of coronary arteries. Diagnosing coronary artery diseases (CAD) entails a clinical evaluation of stenosis and plaques, which is in turn essential for obtaining a reliable coronary-artery centerline from CCTA 3D imaging. This work proposes a centerline extraction algorithm by combining local semantic segmentation and recursive tracking. To this end we propose a Morphological Skeleton Loss (MS Loss) suited for 3D centerline segmentation based on an improved morphological skeleton algorithm coupled with a resource-efficient back-propagation scheme. This work employs 225 CCTA examinations paired with manually annotated coronary-artery centerlines. This method is compared against the deep-learning state of the art in the literature using a standardized evaluation method for coronary-artery tracking.