We propose a Bayesian tracking and segmentation method of coronary arteries on coronary computed tomographic angiography (CCTA). The geometry of coronary arteries including lumen boundary is estimated in Maximum A Posteriori (MAP) framework. Three consecutive sphere based filtering is combined with a stochastic process that is based on the similarity of the consecutive local neighborhood voxels and the geometric constraint of a vessel. It is also founded on the prior knowledge that an artery can be seen locally disconnected and consist of branches which may be seemingly disconnected due to plaque build up. For such problem, an active search method is proposed to find branches and seemingly disconnected but actually connected vessel segments. Several new measures have been developed for branch detection, disconnection check and planar vesselness measure. Using public domain Rotterdam CT dataset, the accuracy of extracted centerline is demonstrated and automatic reconstruction of coronary artery mesh is shown.