## 3 Method
### Model Structure  
Many studies have shown that the symmetric network of encoding and decoding is helpful to improve segmentation performance [13; 14; 20]. In this paper, the proposed model is similar to a 3D U-shaped full convolutional neural network proposed by [PERSON] et al. [43]. However, unlike their model, we design a 2.5D network to reduce the need for training parameters and VRAM occupancy. The 2.5D network is realized by inputting five adjacent slices to ensure that the occupation of VARM is reduced and that the exploration of 3D data spatial information is improved. In addition, the basic blocks of the proposed network are built by using the residual structure [6]. Each basic block based on the residual structure consists of two or three convolutional layers and a shortcut connection. The residual structure can avoid network degradation while training a deeper network and exploring more features to improve the model's performance. The residual structure is expressed as follows:  
\[x_{l+1}=x_{l}+F(x_{l},w_{l}), \tag{5}\]  
where \(x_{l}\) is the input in the \(l\) layer of the network, \(x_{l+1}\) is its output, \(F(\cdot)\) is the residual function, and \(w_{l}\) is the weight parameter of the corresponding residual block.  
Based on the basic block, that is, the residual structure, a 2.5D FCN network is designed, as shown in Figure 4. A common 2D network inputs an image and outputs a corresponding probabilistic map. Unlike normal 2D models, the input for our model consists of five cascading slices. The model outputs a segmentation feature map, which corresponds to the middle slice of the five slices. The descriptive formula of the structure of the full convolutional neural network is described as follows:  
\[\mathbf{I}=f_{2.5D}(\mathbf{X},\hat{L},\theta^{{}^{\prime}}), \tag{6}\]  
where \(f_{2.5D}\) is the formula of the 2.5D full convolutional network and \(\mathbf{X}\) represents five cascaded slices, which are input into the full convolutional network. \(\theta^{{}^{\prime}}\) describes the parameters that are used to train the network; \(\hat{L}\) is the corresponding loss function optimization; and \(I\) is the output result of the network \(f_{2.5D}\). Therefore, a larger image content on the \(x\)-\(y\) plane and \(z\)-_axis_ context information is provided. Compared with 3D networks, our network model not only maintains larger input image content but also add deeper layers to the networks. As described in Figure 4, two convolution blocks with the residual structure are used to structure the first two layers inside the model's  
Figure 3: (**a**) is the original image; (**b**) is the resulting image after we truncate HUs within [\(-150\), \(300\)]; (**c**) is the preprocessing image for the segmentation of the tumor, whose HUs are within [\(-135\), \(265\)]; and (**d**) is the image in which the gray values are reversed from (**c**).  
left part. The last three layers inside the left part of the model are structured by using three other convolution blocks with the residual structure, which can acquire more feature information. All convolution blocks consist of a convolution layer with a \(3\times 3\) kernel, a batch normalization layer and a ReLU activation layer. On the right part of the model is a symmetric decoding structure to restore the resolution of the input image and to output segmentation results. Compared with some 2.5D models [44; 45], our 2.5D FCN is different in that it incorporates interslice information into 2D CNNs to explore the spatial correlation. Specifically, since our model takes a set of adjacent slices as input and outputs the segmentation result corresponding to the centre slice, which makes it effective in reducing parameters and memory usage.