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Automatic medical image segmentation plays a critical role in scientific research and medical care. Existing high-performance deep learning methods typically rely on large training datasets with high-quality manual annotations, which are difficult to obtain in many clinical applications. Here, we introduce Annotation-effIcient Deep lEarning (AIDE), an open-source framework to handle imperfect training datasets. Methodological analyses and empirical evaluations are conducted, and we demonstrate that AIDE surpasses conventional fully-supervised models by presenting better performance on open datasets possessing scarce or noisy annotations. We further test AIDE in a real-life case study for breast tumor segmentation. Three datasets containing 11,852 breast images from three medical centers are employed, and AIDE, utilizing 10% training annotations, consistently produces segmentation maps comparable to …