Background and Objective: X-ray coronary angiography (XCA) remains the gold standard imaging technique for the diagnosis and treatment of cardiovascular disease. Automatic detection and grading of coronary stenoses in XCA are challenging problems due to the complex overlap of different background structures with intensity inhomogeneities. We present a new computerized image based method to accurately identify and quantify the stenosis severity on XCA. Methods: A unified framework, consisting of Hessian-based vessel enhancement, level-set skeletonization, improved measure of match measurement, and local extremum identification, is developed to distinctly reveal the vessel structures and accurately determine the stenosis grades. The methodology was validated on 143 consecutive patients who underwent diagnostic XCA through both qualitative and quantitative evaluations. Results: The presented algorithm was tested on a set of 267 vessel segments annotated by two expert cardiologists. The experimental results show that the method can effectively localize and quantify the vessel stenoses, achieving average detection accuracy, sensitivity, specificity, and F-score of 93.93%, 91.03%, 93.83%, 89.18%, respectively. Conclusions: A fully automatic coronary analysis method is devised for vessel stenosis detection and grading in XCA. The presented approach can potentially serve as a generalized framework to handle different image modalities. (C) 2018 Published by Elsevier B.V.