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Medical image segmentation is usually regarded as one of the most important intermediate steps in clinical situations and medical imaging research. Thus, accurately assessing the segmentation quality of the automatically generated predictions is essential for guaranteeing the reliability of the results of the computer-assisted diagnosis (CAD). Many researchers apply neural networks to train segmentation quality regression models to estimate the segmentation quality of a new data cohort without labeled ground truth. Recently, a novel idea is proposed that transforming the segmentation quality assessment (SQA) problem intothe pixel-wise error map prediction task in the form of segmentation. However, the simple application of vanilla segmentation structures in medical image fails to detect some small and thin error regions of the auto-generated masks with complex anatomical structures. In this paper, we propose collaborative boundaryaware context encoding networks called AEP-Net for error prediction task. Specifically, we propose a collaborative feature transformation branch for better feature fusion between images and masks, and precise localization of error regions. Further, we propose a context encoding module to utilize the global predictor from the error map to enhance the feature representation and regularize the networks. We perform experiments on IBSR v2.0 dataset and ACDC dataset. The AEP-Net achieves an average DSC of 0.8358, 0.8164 for error prediction task,and shows a high Pearson correlation coefficient of 0.9873 between the actual segmentation accuracy and the predicted accuracy inferred from the predicted error map on IBSR v2.0 dataset, which verifies the efficacy of our AEP-Net.