Title: Learning to Segment from Noisy Annotations: A Spatial Correction Approach. Abstract: Noisy labels can significantly affect the performance of deep neural networks (DNNs). In medical image segmentation tasks, annotations are error-prone due to the high demand in annotation time and in the annotators' expertise. Existing methods mostly tackle label noise in classification tasks. Their independent-noise assumptions do not fit label noise in segmentation task. In this paper, we propose a novel noise model for segmentation problems that encodes spatial correlation and bias, which are prominent in segmentation annotations. Further, to mitigate such label noise, we propose a label correction method to recover true label progressively. We provide theoretical guarantees of the correctness of the proposed method. Experiments show that our approach outperforms current state-of-the-art methods on both synthetic and real-world noisy annotations.