# An Improved Multi-Scale Feature Fusion for Skin Lesion Segmentation
## 3 Proposed Methods
### Cross-Residual Encoder Module  
To improve the fitting ability of a model for different types or stages of skin lesions, complex calculations are required to extract features. Although theoretically, deeper networks have stronger fitting abilities, in practice, increasing the number of layers may lead to network degradation. Shallow features cannot be fully trained, resulting in problems such as gradient vanishing and gradient explosion. Therefore, balancing network depth and training effect is necessary, and appropriate techniques should be used to address these issues to improve model performance. ResNet [33] effectively solved the problem of model degradation in deep neural networks. It introduced a residual structure that allows certain layers in the neural network to skip the next feature extraction layer and connect to other layers, thereby weakening the strong inter-layer connections. The residual structure is shown in Figure 3. The residual structure introduces skip connections, allowing the network to capture subtle differences between the input and output more effectively. As the network depth increases, each residual block can learn additional feature variations, enhancing the expressive power and modeling ability of the network. It helps the network extract richer and more discriminative feature representations, making it well-suited for complex tasks.  
The UNet3+ model only used simple convolution and pooling operations during the feature extraction process. However, due to the contextual information lost during the upsampling and downsampling steps, the segmentation accuracy was poor. Despite the widespread effectiveness and popularity of the residual structure across various tasks, its performance improvement may not always be consistent in specific problems and application scenarios. Notably, when there are significant disparities in scale between input and output features, the simplistic addition operation in the residual structure may struggle to effectively align them, resulting in learning difficulties for the network. Therefore, it is crucial to carefully consider the network structure, make appropriate adjustments, and optimize it based on the specific circumstances at hand. In our approach, we introduced cross-residual connections in the encoder module to replace the original plain convolution operation, as shown in Figure 4.  
Figure 3: Two different types of residue in ResNet. **(a)** a building block for ResNet34. **(b)** a “bottleneck” building block for ResNet-50/101/152.  
The module consists of three convolution blocks and one connection block. Each convolution block includes a 3 \(\times\) 3 convolution layer, a batch normalization operation, and an activation function. Each connection block includes two addition operations and one convolution block. The input feature \(x_{0}\) goes through three convolution blocks to obtain the feature \(D_{3}(y_{2})\), which is then combined with the output feature \(D_{1}(x_{0})\) of the first convolution block as the input of the fourth convolution layer in the connection block. Next, the output feature \(D_{2}(y_{1})\) of the second convolution block is added to the connection block and added to the feature \(D_{4}(y_{1}+y_{3})\) generated by the fourth convolution operation. The final feature vector \(X_{out}\) is obtained by passing through a linear rectification unit. The calculation is shown in Equation (1):  
\[\left\{\begin{array}{l}y_{1}=D_{1}(x_{0})\\ y_{2}=D_{2}(y_{1})\\ y_{3}=D_{3}(y_{2})\\ y_{4}=D_{4}(y_{1}+y_{3})\\ X_{out}=y_{2}+y_{4}\end{array}\right. \tag{1}\]  
where \(D_{k}(x_{i})\) represents the output feature of the input feature \(x_{i}\) by the convolutional block \(k\). During the sampling process, the new network not only effectively preserves the shallow-level feature information of the encoder section to ensure that image details are not lost but also deepens the depth of the network's encoder, improving the network's fitting ability.