Manual analysis of the bulk data generated by computed tomography angiography (CTA) is time consuming, and interpretation of such data requires previous knowledge and expertise of the radiologist. Therefore, an automatic method that can isolate the coronary arteries from a given CTA dataset is required. We present an automatic yet effective segmentation method to delineate the coronary arteries from a three-dimensional CTA data cloud. Instead of a region growing process, which is usually time consuming and prone to leakages, the method is based on the optimal thresholding, which is applied globally on the Hessian-based vesselness measure in a localized way (slice by slice) to track the coronaries carefully to their distal ends. Moreover, to make the process automatic, we detect the aorta using the Hough transform technique. The proposed segmentation method is independent of the starting point to initiate its process and is fast in the sense that coronary arteries are obtained without any preprocessing or postprocessing steps. We used 12 real clinical datasets to show the efficiency and accuracy of the presented method. Experimental results reveal that the proposed method achieves 95% average accuracy.