# SARFNet: Selective Layer and Axial Receptive Field Network for Multimodal Brain Tumor Segmentation
## 3 Methodology
### Selective Layer Receptive Field Attention Module (SL\({}_{i}\)RF)  
Spatial features are very important for medical image segmentation; however, the challenge of losing effective information during the downsampling stage has still not been addressed. Receptive field attention (RFA) [59] was introduced to address the issue of considering the significance of each feature in the receptive field to further improve the efficiency of the extraction features and the performance of the model. Inspired by RFA, we propose the selective layer receptive field attention module (SL\({}_{i}\)RF), which is shown in Figure 3. The module is used in downsampling, which utilizes convolutions with different kernels to reduce the image size and capture more useful information on each channel and spatial feature. Generally, downsampling uses pooling or convolution with a stride of 2, which leads to information loss. The SL\({}_{i}\)RF module consists of SL\({}_{i}\)Conv, group convolution, and spatial and channel attention. SL\({}_{i}\)Conv, which adopts different convolution kernels in each layer, can expand the receptive field while completing the size change. One of its main functions is to retain important feature information during downsampling. Group convolution can extract spatial features with a larger receptive field. Batch Normalization (BN) and Rectified Linear Unit (ReLU) are used together to enhance the model's ability to learn nonlinear mappings. The spatial and channel weights can be obtained while ensuring a large receptive field to improve segmentation performance using the global average pooling and maximum pooling operations in the spatial and channel attention mechanism. Based on the above operations, the SL\({}_{i}\)RF module can ensure a large receptive field to effectively reduce the loss of important information during downsampling operations. Formally, as shown in Figure 3, \(x\) is the input feature \(x\in R^{C\times H\times W\times D}\) of the SL\({}_{i}\)RF module, where C, H, W, and D represent the number of channels, height, width, and  
Figure 3: An illustration of the proposed SL\({}_{i}\)RF block. Figure 2: The structure of CAM. Input A and input B are one level apart. depth of the feature map, respectively. The SL\({}_{i}\)Conv algorithm selects different convolution kernels according to the position of the layer, which can be represented as follows:  
\[U_{i}=f_{sli}(x) \tag{1}\]  
where \(f_{sli}\) denotes the convolution with different kernels of the SL\({}_{i}\)Conv module, whose kernel sizes are \(\{3\times 3\times 3\), \(5\times 5\times 5\), \(7\times 7\times 7\times 7\), \(7\times 7\times 7\)}. \(U_{i}\) is the result calculated by the SL\({}_{i}\)Conv module. Index \(i\) represents the position of each encoder layer. We define the convolution kernels according to the different positions of the layer as follows:  
Layer 1: Kernel Size is \(3\times 3\times 3\to UI\to f_{sl1}\in R^{C\times H\times W\times D}\)  
Layer 2: Kernel Size is \(5\times 5\times 5\times 5\to U2\to f_{sl2}\in R^{2C\times\frac{1}{2}H\times\frac{1}{2}W\times\frac{1}{ 2}D}\)  
Layer 3: Kernel Size is \(7\times 7\times 7\to U3\to f_{sl3}\in R^{4C\times\frac{1}{2}H\times\frac{1}{2}W\times\frac{1}{ 2}D}\)  
Layer 4: Kernel Size is \(7\times 7\times 7\to U4\to f_{sl4}\in R^{8C\times\frac{1}{2}H\times\frac{1}{2}W\times\frac{1}{ 2}D}\)  
After SL\({}_{i}\)Conv, group convolution with the same number of groups as the number of input channels is used to quickly capture features with receptive fields. The specific expression is as follows:  
\[GU_{i}=ReLU(BN(GConv_{3\times 3\times 3}(U_{i}))) \tag{2}\]  
where \(GConv_{3\times 3\times 3}\) denotes Group Convolution with \(3\times 3\times 3\) kernel, with the number of groups the same as the number of input channels. \(BN\) represents batch normalization; \(ReLU\) is Rectified Linear Unit. The top part in Figure 3 is the channel attention weight section, which captures the weights of the channel features.