Graph-Based Methods Volume I: Graph-Based Learning and its applications for Biomedical Data Analysis

It is a challenge to automatically and accurately segment the liver and tumors in computed tomography (CT) images, as the problem of over-segmentation or under-segmentation often appears when the Hounsfield unit (Hu) of liver and tumors is close to the Hu of other tissues or background. In this paper, we propose the spatial channel-wise convolution, a convolutional operation along the direction of the channel of feature maps, to extract mapping relationship of spatial information between pixels, which facilitates learning the mapping relationship between pixels in the feature maps and distinguishing the tumors from the liver tissue. In addition, we put forward an iterative extending learning strategy, which optimizes the mapping relationship of spatial information between pixels at different scales and enables spatial channel-wise convolution to map the spatial information between pixels in high-level feature maps. Finally, we propose an end-to-end convolutional neural network called Channel-UNet, which takes UNet as the main structure of the network and adds spatial channel-wise convolution in each up-sampling and down-sampling module. The network can converge the optimized mapping relationship of spatial information between pixels extracted by spatial channel-wise convolution and information extracted by feature maps and realizes multi-scale information fusion. The proposed ChannelUNet is validated by the segmentation task on the 3Dircadb dataset. The Dice values of liver and tumors segmentation were 0.984 and 0.940, which is slightly superior to current best performance. Besides, compared with the current best method, the number of parameters of our method reduces by 25.7%, and the training time of our method reduces by 33.3%. The experimental results demonstrate the efficiency and high accuracy of Channel-UNet in liver and tumors segmentation in CT images.