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Biomedical image segmentation plays a central role in quantitative analysis, clinical diagnosis, and medical intervention. In the light of the fully convolutional networks (FCN) and U-Net, deep convolutional networks (DNNs) have made significant contributions to biomedical image segmentation applications. In this paper, we propose three different multi-scale dense connections (MDC) for the encoder, the decoder of U-shaped architectures, and across them. Based on three dense connections, we propose a multi-scale densely connected U-Net (MDU-Net) for biomedical image segmentation. MDU-Net directly fuses the neighboring feature maps with different scales from both higher layers and lower layers to strengthen feature propagation in the current layer. Multi-scale dense connections, which contain shorter connections between layers close to the input and output, also make a much deeper U-Net possible. Besides, we introduce quantization to alleviate the potential overfitting in dense connections, and further improve the segmentation performance. We evaluate our proposed model on the MICCAI 2015 Gland Segmentation (GlaS) dataset. The three MDC improve U-Net performance by up to 1.8% on test A and 3.5% on test B in the MICCAI Gland dataset. Meanwhile, the MDU-Net with quantization obviously improves the segmentation performance of original U-Net., Comment: 10 pages, 5 figures, 6 tables, published in the Health Information Science and Systems journal