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In medical image segmentation, it is often necessary to collect opinions from multiple experts to make the final decision. This clinical routine helps to mitigate individual bias. But when data is multiply annotated, standard deep learning models are often not applicable. In this paper, we propose a novel neural network framework, called Multi-Rater Prism (MrPrism) to learn the medical image segmentation from multiple labels. Inspired by the iterative half-quadratic optimization, the proposed MrPrism will combine the multi-rater confidences assignment task and calibrated segmentation task in a recurrent manner. In this recurrent process, MrPrism can learn inter-observer variability taking into account the image semantic properties, and finally converges to a self-calibrated segmentation result reflecting the inter-observer agreement. Specifically, we propose Converging Prism (ConP) and Diverging Prism (DivP) to process the two tasks iteratively. ConP learns calibrated segmentation based on the multi-rater confidence maps estimated by DivP. DivP generates multi-rater confidence maps based on the segmentation masks estimated by ConP. The experimental results show that by recurrently running ConP and DivP, the two tasks can achieve mutual improvement. The final converged segmentation result of MrPrism outperforms state-of-the-art (SOTA) strategies on a wide range of medical image segmentation tasks.