# Liver Tumor Computed Tomography Image Segmentation Based on an Improved U-Net Model
## 2 The Traditional U-Net  
As shown in the figure above, the ReLU function can convert negative values to 0, while positive values are unchanged; such a unilateral suppression operation can make neurons have sparse activation activity and can better explore features after sparseness. In addition, the ReLU function is more powerful than other excitation functions, and because its slope in the nonnegative interval is constant, there is no problem of slope elimination.  
U-Net is a new approach based on an FCN (fully convolutional networks for semantic segmentation) proposed by [PERSON] et al.  
U-Net is a symmetric neural network with an encoder-decoder architecture, resembling the letter \"U\", hence its name. Figure 1 shows a typical U-Net network. The network consists of operations such as convolution, downsampling, upsampling, and concatenation. The left half of the network is the contracting path, while the right half is the expanding path. The contracting path is responsible for extracting important features from the image and reducing its resolution, composed of four blocks. Each block includes two 3\(\times\)3 convolutions, ReLU activation, and one downsampling operation. The use of 3\(\times\)3 convolutional kernels aims to reduce the complexity of the neural network while maintaining segmentation accuracy. U-Net performs mirror edge padding on the input image, adding symmetric edges that mirror the edge pixels. This mirror operation helps to handle edge information better. Then, two 3 \(\times\) 3 convolutions and ReLU activation are applied. The ReLU activation function accelerates the convergence and prevents the gradient from vanishing. Subsequently, downsampling is performed using 2 \(\times\) 2 max pooling to reduce the image resolution while preserving important information, although pooling may lead to some loss of features. After each downsampling operation, the dimensions of the image increase to twice the original dimensions, halving the size. By repeating these four operations, the dimension of the feature map increases from the initial 64 to 512, and the size of the feature map becomes 32 \(\times\) 32 pixels.  
The expanding path of the U-Net is used to gradually restore the image details for the precise localization of lesions and to restore the image to the size of the input image. The expanding path also consists of four blocks, each containing two 3 \(\times\) 3 convolutions, ReLU activation, and one upsampling operation. The upsampling operations decode the abstract features obtained through downsampling back to the original size of the image. After each upsampling operation, the size of the feature map doubles, while the number of channels halves, and the final output feature map has the same size as the input. Skip connections are added between the contracting and expanding paths for pixel-level localization. Unlike the summation operation used in an FCN, the U-Net uses concatenation to crop the feature maps from the same layer of the contracting path to match the size of the expanding path and then performs concatenation. This helps to recover information lost during the downsampling process.