Accurate detection and quantification of coronary artery stenoses is an essential requirement for treatment planning of patients with suspected coronary artery disease. We present a method to automatically detect and quantify coronary artery stenoses in computed tomography coronary angiography. First, centerlines are extracted using a two-point minimum cost path approach and a subsequent refinement step. The resulting centerlines are used as an initialization for lumen segmentation, performed using graph cuts. Then, the expected diameter of the healthy lumen is estimated by applying robust kernel regression to the coronary artery lumen diameter profile. Finally, stenoses are detected and quantified by computing the difference between estimated and expected diameter profiles. We evaluated our method using the data provided in the Coronary Artery Stenoses Detection and Quantification Evaluation Framework. Using 30 testing datasets, the method achieved a detection sensitivity of 29 % and a positive predictive value (PPV) of 24 % as compared to quantitative coronary angiography (QCA), and a sensitivity of 21 % and a PPV of 23 % as compared manual assessment based on consensus reading of CTA by 3 observers. The stenoses degree was estimated with an absolute average difference of 31 %, a root mean square difference of 39.3 % when compared to QCA, and a weighted kappa value of 0.29 when compared to CTA. A Dice of 68 and 65 % was reported for lumen segmentation of healthy and diseased vessel segments respectively. According to the ranking of the evaluation framework, our method finished fourth for stenosis detection, second for stenosis quantification and second for lumen segmentation.