Coronary computed tomographic angiography (CCTA) is a non-invasive imaging modality for the visualization of the heart and coronary arteries. To fully exploit the potential of the CCTA datasets and apply it in clinical practice, an automated coronary artery extraction approach is needed. The purpose of this paper is to present and validate a fully automatic centerline extraction algorithm for coronary arteries in CCTA images. The algorithm is based on an improved version of Frangi's vesselness filter which removes unwanted step-edge responses at the boundaries of the cardiac chambers. Building upon this new vesselness filter, the coronary artery extraction pipeline extracts the centerlines of main branches as well as side-branches automatically. This algorithm was first evaluated with a standardized evaluation framework named Rotterdam Coronary Artery Algorithm Evaluation Framework used in the MICCAI Coronary Artery Tracking challenge 2008 (CAT08). It includes 128 reference centerlines which were manually delineated. The average overlap and accuracy measures of our method were 93.7% and 0.30 mm, respectively, which ranked at the 1st and 3rd place compared to five other automatic methods presented in the CAT08. Secondly, in 50 clinical datasets, a total of 100 reference centerlines were generated from lumen contours in the transversal planes which were manually corrected by an expert from the cardiology department. In this evaluation, the average overlap and accuracy were 96.1% and 0.33 mm, respectively. The entire processing time for one dataset is less than 2 min on a standard desktop computer. In conclusion, our newly developed automatic approach can extract coronary arteries in CCTA images with excellent performances in extraction ability and accuracy.