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Over the past several decades, deep neural networks have been extensively applied to medical image segmentation tasks, achieving significant success. However, the effectiveness of traditional deep segmentation networks is substantially limited by the small scale of medical datasets, a limitation directly stemming from current medical data acquisition capabilities. To this end, we introduce AttEUnet, a medical cell segmentation network enhanced by edge attention, based on the Attention U-Net architecture. It incorporates a detection branch enhanced with edge attention and a learnable fusion gate unit to improve segmentation accuracy and convergence speed on small medical datasets. The AttEUnet allows for the integration of various types of prior information into the backbone network according to different tasks, offering notable flexibility and generalization ability. This method was trained and validated on two public datasets, MoNuSeg and PanNuke. The results show that AttEUnet significantly improves segmentation performance on small medical datasets, especially in capturing edge details, with F1 scores of 0.859 and 0.888 and Intersection over Union (IoU) scores of 0.758 and 0.794 on the respective datasets, outperforming both convolutional neural networks (CNNs) and transformer-based baseline networks. Furthermore, the proposed method demonstrated a convergence speed over 10.6 times faster than that of the baseline networks. The edge attention branch proposed in this study can also be added as an independent module to other classic network structures and can integrate more attention priors based on the task at hand, offering considerable scalability. [ABSTRACT FROM AUTHOR]