Automatic coronary centerline extraction and lumen segmentation facilitate the diagnosis of coronary artery disease (CAD), which is a leading cause of death in developed countries. Various coronary centerline extraction methods have been proposed and most of them are based on shortest path computation given one or two end points on the artery. The major variation of the shortest path based approaches is in the different vesselness measurements used for the path cost. An empirically designed measurement (e.g., the widely used Hessian vesselness) is by no means optimal in the use of image context information. In this paper, a machine learning based vesselness is proposed by exploiting the rich domain specific knowledge embedded in an expert-annotated dataset. For each voxel, we extract a set of geometric and image features. The probabilistic boosting tree (PBT) is then used to train a classifier, which assigns a high score to voxels inside the artery and a low score to those outside. The detection score can be treated as a vesselness measurement in the computation of the shortest path. Since the detection score measures the probability of a voxel to be inside the vessel lumen, it can also be used for the coronary lumen segmentation. To speed up the computation, we perform classification only for voxels around the heart surface, which is achieved by automatically segmenting the whole heart from the 3D volume in a preprocessing step. An efficient voxel-wise classification strategy is used to further improve the speed. Experiments demonstrate that the proposed learning based vesselness outperforms the conventional Hessian vesselness in both speed and accuracy. On average, it only takes approximately 2.3 seconds to process a large volume with a typical size of 512×512×200 voxels.