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Liver cancer is one of the leading causes of cancer death. To assist doctors in hepatocellular carcinoma diagnosis and treatment planning, an accurate and automatic liver and tumor segmentation method is highly demanded in the clinical practice. Recently, fully convolutional neural networks (FCNs), including 2-D and 3-D FCNs, serve as the backbone in many volumetric image segmentation. However, 2-D convolutions cannot fully leverage the spatial information along the third dimension while 3-D convolutions suffer from high computational cost and GPU memory consumption. To address these issues, we propose a novel hybrid densely connected UNet (H-DenseUNet), which consists of a 2-D DenseUNet for efficiently extracting intra-slice features and a 3-D counterpart for hierarchically aggregating volumetric contexts under the spirit of the auto-context algorithm for liver and tumor segmentation. We formulate …