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The segmentation of coronary arteries in X-ray angiograms by convolutional neural networks (CNNs) is promising yet limited by the requirement of precisely annotating all pixels in a large number of training images, which is extremely labor-intensive especially for complex coronary trees. To alleviate the burden on the annotator, we propose a novel weakly supervised training framework that learns from noisy pseudo labels generated from automatic vessel enhancement, rather than accurate labels obtained by fully manual annotation. A typical self-paced learning scheme is used to make the training process robust against label noise while challenged by the systematic biases in pseudo labels, thus leading to the decreased performance of CNNs at test time. To solve this problem, we propose an annotation-refining self-paced learning framework (AR-SPL) to correct the potential errors using suggestive annotation. An elaborate model-vesselness uncertainty estimation is also proposed to enable the minimal annotation cost for suggestive annotation, based on not only the CNNs in training but also the geometric features of coronary arteries derived directly from raw data. Experiments show that our proposed framework achieves 1) comparable accuracy to fully supervised learning, which also significantly outperforms other weakly supervised learning frameworks; 2) largely reduced annotation cost, i.e., 75.18% of annotation time is saved, and only 3.46% of image regions are required to be annotated; and 3) an efficient intervention process, leading to superior performance with even fewer manual interactions. [ABSTRACT FROM AUTHOR]