# An Enhanced Feature Extraction Network for Medical Image Segmentation
## 3 Proposed Method
### Structure of EFEN  
Compared with traditional medical image analysis methods, using fully convolutional networks can achieve better performance. Fully convolutional networks are more accurate and robust in tasks such as cardiac MR [39], brain tumors [40] and abdominal CT [41; 42] image segmentation. Among them, the fully convolutional network U-Net has been proved to be the best performing medical image segmentation architecture. The network proposed in this paper improves the structure on the basis of U-Net. The encoder of VGG-19 is used as a sub-network of our encoder, and a symmetrical decoder is designed. The decoding part of U-Net adopts an improved skip-connection for feature compensation, which can  
Figure 1: Structure of the EFEN. The feature maps of different colors represent the results obtained via different methods of processing. supervise the compensation information and reduce noise or interference effectively. Given an input image \(I\in\mathbb{R}^{3\times H\times W}\), \(I\) is mapped to a set of feature maps \(F_{i}^{E1}\). The process can be formulated as follows:  
\[F_{i}^{E1}=\Phi^{E1}\Big{(}F_{i-1}^{E1}\Big{|}W_{i}^{E1}\Big{)}\,, \tag{1}\]  
where \(i\) is the \(ith\) stage in the processes of feature extraction and \(E1\) refers to the first encoding process. \(F_{i}^{E1}\in\mathbb{R}^{C_{i}\times\frac{H}{2}\times\frac{W}{2}}\), where \(C_{i}\) is the channel number of the \(ith\) stage during encoding. \(H\) and \(W\) are the number of pixels along the height and width of the feature map, respectively. When \(i=1\), \(F_{0}^{E1}\) is the input image \(I\). \(W_{i}^{E1}\) refers to the weights of the convolutional network during encoding. \(\Phi^{E1}\) refers to the operations of mapping feature maps \(F_{i-1}^{E1}\) to \(F_{i}^{E1}\) during the encoding process, which usually includes convolution, pooling, and ReLu, etc. The decoding process begins when we obtain the features from the deepest layer, and it can be formulated as follows:  
\[F_{j}^{D1}=\Psi^{D1}\Big{(}\,\Phi^{D1}\Big{(}F_{j-1}^{D1}\Big{)},\ R_{j}^{D1} \Big{(}F_{i}^{E1},\ F_{j}^{D1}\Big{)}\Big{)}\,, \tag{2}\]  
where \(j\) is the \(jth\) stage in the process of decoding and \(D1\) refers to the first decoding process. \(F_{j}^{D1}\) refers to the feature map in the \(jth\) stage during decoding process. \(\Phi^{D1}\) refers to the operation of transposed convolution. \(R_{j}^{D1}\) is the operation of improved skip-connection and is described in detail in Section 3.2. \(\Psi^{D1}\) includes two layers of \(3\times 3\) convolution and one layer of \(1\times 1\) convolution. First, we discard the last \(1\times 1\) convolution layer of the U-Net decoder, and then fuse its outputs with the inputs of the encoder using improved skip-connection. The fused features have both semantic information and shallow information. After that, we continue to build a feature extraction network to enhance the feature extraction capability, and features in each stage in the second feature extraction process are fused with the corresponding layer features which are extracted in the down-sampling process of U-Net. This process can be formulated as follows:  
\[F_{k}^{E2}=op_{k}^{E2}(\,\Phi^{E2}\Big{(}F_{k-1}^{E2}\Big{|}W_{k}^{E2}\Big{)},F_{j}^{D1}\Big{)}\,, \tag{3}\]  
where \(k\) is the \(kth\) stage in the process of feature extraction, \(E2\) refers to the feature re-extraction process, and \(F_{k}^{E2}\in\mathbb{R}^{C_{k}\times\frac{H}{2}\times\frac{W}{2}}\). \(\Phi^{E2}\) refers to the operations of mapping feature maps \(F_{k-1}^{E2}\) using the weights of \(W_{k}^{E2}\), which usually include convolution, pooling, and ReLu, etc. The size of \(F_{j}^{D1}\) is the same as the outputs of \(\Phi^{E2}\). \(op_{k}^{E2}\) is the fusion method which includes the operations of two layers of \(3\times 3\) convolution and one layer of \(1\times 1\) convolution.