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Background: The curved planar reformation (CPR) technique is one of the most commonly used methods in clinical practice to locate coronary arteries in medical images. Purpose: The artery centerline is the cornerstone for the generation of the CPR image. Here, we describe the development of a new fully automatic artery centerline tracker with the aim of increasing the efficiency and accuracy of the process. Methods: We propose a COronary artery Centerline Tracker (COACT) framework which consists of an ostium point finder (OPFinder) model, an intersection point detector (IPDetector) model and a set of centerline tracking strategies. The output of OPFinder is the ostium points. The function of the IPDetector is to predict the intersections of a sample sphere and the centerlines. The centerline tracking process starts from two ostium points detected by the OPFinder, and combines the results of the IPDetector with a series of strategies to gradually reconstruct the coronary artery centerline tree. Results: Two coronary CT angiography (CCTA) datasets were used to validate the models. Dataset1 contains 160 cases (32 for test and 128 for training) and dataset2 contains 70 cases (20 for test and 50 for training). The results show that the average distance between the ostium points predicted by the OPFinder and the manually annotated ostium points was 0.88 mm, which is similar to the differences between the results obtained by two observers (0.85 mm). For the IPDetector, the average overlap of the predicted and ground truth intersection points was 97.82% and this is also close to the inter‐observer agreement of 98.50%. For the entire coronary centerline tree, the overlap between the results obtained by COACT and the gold standard was 94.33%, which is slightly lower than the inter‐observer agreement, 98.39%. Conclusions: We have developed a fully automatic centerline tracking method for CCTA scans and achieved a satisfactory result. The proposed algorithms are also incorporated in the medical image analysis platform TIMESlice (https://slice‐doc.netlify.app) for further studies. [ABSTRACT FROM AUTHOR]