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Segmentation of coronary arteries in X-ray angiography is a fundamental tool to evaluate arterial diseases and choose proper coronary treatment. The accurate segmentation of coronary arteries has become an important topic for the registration of different modalities, which allows physicians rapid access to different medical imaging information from computed tomography (CT) scans or magnetic resonance imaging (MRI). In this paper, we propose an accurate fully automatic algorithm based on Graph-cuts for vessel centerline extraction, caliber estimation, and catheter detection. Vesselness, geodesic paths, and a new multiscale edgeness map are combined to customize the Graph-cuts approach to the segmentation of tubular structures, by means of a global optimization of the Graph-cuts energy function. Moreover, a novel supervised learning methodology that integrates local and contextual information is proposed for automatic catheter detection. We evaluate the method performance on three datasets coming from different imaging systems. The method performs as good as the expert observer with respect to centerline detection and caliber estimation. Moreover, the method discriminates between arteries and catheter with an accuracy of 96.5%, sensitivity of 72%, and precision of 97.4%.