# A Multi-Organ Segmentation Network Based on Densely Connected RL-Unet
## 2 Method
### RLSwin-Transformer Module  
In the process of medical image segmentation, the main role of the RLSwin-Transformer module is to replace the traditional convolutional module for feature learning and information extraction. The RLSwin-Transformer module structure is shown in Figure 2. Features are input into the normalization layer (LN) to ensure the stability of data feature distribution; thenk feature information is learned by the window-based multi-head self-attention (W-MSA) module. Finally, W-MSA output is input into LN and residual multi-layer perceptrons (Res-MLP) successively. At the same time, the local induction bias (LIB) module is introduced in the process of residual connection to obtain the final output. The other layer is a similar process [27; 36]. After adding local inductive bias module into RLSwin-Transformer module, on the one hand, rich contextual semantic information can be obtained by stacking convolutional layers with different receptive fields without changing scale. On the other hand, RLSwin-Transformer module can calculate adjacent pixels through the convolution operation to obtain local details of edges and corners. The calculation process of RLSwin-Transformer module is summarized as follows:  
Figure 1: The general structure of Residual Local induction bias-Unet (RL-Unet). \[\dot{z}^{l}=W\_MSA(LN(z^{l-1}))+z^{l-1} \tag{1}\] \[z^{l}=ResMLP(LN(z^{l}))+LIB(\dot{z}^{l})\] (2) \[\dot{z}^{l+1}=SW\_MSA(LN(z^{l}))+z^{l}\] (3) \[z^{l+1}=ResMLP(LN(z^{l+1}))+LIB(\dot{z}^{l+1}) \tag{4}\]  
where \(l\) represents the number of index layers, \(\dot{z}^{l}\) represents the output of W-MSA module, \(\dot{z}^{l+1}\) indicates the output of SW-MSA module, and \(z^{l}\) and \(z^{l+1}\) represent the output of the Res-MLP module. Equations (5) and (6) illustrate the specific structure of Res-MLP clearly. \[z^{\prime\prime}=GeLU(W^{\prime}z^{\prime}+b^{\prime}) \tag{5}\] \[ResMLP(z^{\prime})=z^{\prime}+GeLU(W^{\prime\prime}z^{\prime \prime}+b^{\prime\prime}) \tag{6}\]  
where \(z^{\prime}\) represents the output of layernorm; \(W\) and \(b\) represent weight matrix and bias vector, respectively; and \(GeLU\) is the \(GeLU\) nonlinear activation function. The local induction bias module is embedded in the residual connection process of the RLSwin-Transformer module. The right half of Figure 2 provides a detailed description of the precise structure. The Seq2 Img layer performs a simple reconstruction function, converting the input one-dimensional sequence into a two-dimensional feature \(\dot{x}^{l}\in\mathbb{R}^{C\times H\times W}\). \[M_{Res},M_{Cov}=CSp(\dot{x}^{l}_{i,:,:})_{(i=C/2)} \tag{7}\]  
where \(M_{Res}\in\mathbb{R}^{C/2\times H\times W}\) and \(M_{Cov}\in\mathbb{R}^{C/2\times H\times W}\) represent the feature maps of residual connections and feature extraction branches, respectively. Let \(CSp(\cdot)\) be the channel split module. \(\dot{x}^{l}_{i,:,:}\) indicates that input feature map is truncated at the \(i\)-th channel in the channel dimension. Then channel split module evenly divides the channel number of input features into two parts: one is used for feature extraction and the other is used for residual connection. In the feature extraction part, the feature map is input into three Conv layers with the receptive field of \(1\times 1\), \(3\times 3\), \(1\times 1\) to extract local multi-scale features \(M_{Lm}\in\mathbb{R}^{C/2\times H\times W}\). The \(3\times 3\) convolution has been deeply optimized on GPUs, offering higher computational density compared to other convolution kernels [37]. Therefore, we opted for the most efficient combination of \(1\times 1\), \(3\times 3\), and \(1\times 1\) convolutions. This combination was chosen to balance between capturing fine details and maintaining computational efficiency. \[x^{l}=CSh((M_{Res},M_{Lm})_{i,:,:})_{(i=C/2)} \tag{8}\]  
where \(x^{l}\in\mathbb{R}^{C}\times H\times W\) represents the output feature map of the channel shuffle module. Let \(CSh(\cdot)\) be the channel shuffle module.