## 3 Methodology  
### Improved Coordinate Attention Mechanism  
The CA mechanism is added to 3D U-Net to achieve high segmentation accuracy in this work. A diagram of the CA is displayed in Figure 1. First, the input images are divided into a one-dimensional aggregated feature on the width dimension and a one-dimensional aggregated feature on the height dimension by the average pooling method. Then, the two aggregated features are concatenated together and processed by a 1 \(\times\) 1 convolution block to fully learn channel-domain information. Next, the concatenated features are split into two one-dimensional features followed by a 1 \(\times\) 1 convolution block to learn the weight of each pixel of the two aggregated features. Then, the two aggregatedfeatures are multiplied by one another to obtain the final attention weight. Finally, to assign each input element a different weight value, the attention weight element is multiplied by the correlating input element.  
Many datasets for medical image segmentation tasks comprise 3D data, providing additional depth-dimension information compared to 2D medical images. The depth dimension can capture contextual information about the segmentation target along the depth direction, which is crucial for accurately locating and segmenting targets, as it provides the relative position and relationship between targets and surrounding structures [32]. However, the CA mechanism is designed for 2D data [29]. Therefore, 3D images must be sliced into 2D images before being processed by the CA mechanism. Thus, an additional depth dimension structure is added to the CA structure, and the original 2D convolution operations are replaced by 3D convolution operations in the CA structure to process 3D images. Furthermore, convolution operations with a kernel size of \(1\times 1\) can only extract channel-domain information and ignore adjacent features in the spatial domain. Therefore, convolution operations with kernel sizes of \(1\times 1\times 3\), \(1\times 3\times 1\), and \(3\times 1\times 1\) are substitutes for the \(1\times 1\) convolution layers to extract spatial domain features and channel features simultaneously. The average pooling operation also loses important texture features. Inspired by the structure of CBAM [28], the combination of average pooling and max pooling operations is used to preserve important texture features. Figure 2 shows the framework of the improved CA mechanism.  
As shown in Figure 2, the input images are pooled into six aggregated features: three different dimensions of aggregated features by the average pooling method and three different dimensions of aggregated features by the max pooling method. Similar to CA, the two aggregated features from the same dimension are concatenated together. Then, channel- and spatial-domain features are extracted using convolutional operations with kernel sizes of \(1\times 1\times 3\), \(1\times 3\times 1\), and \(3\times 1\times 1\). Finally, to adaptively refine features, these aggregated characteristics are multiplied by the input data. In the structure of the improved CA, the combination of average pooling operations and max pooling operations can reduce the loss of important texture features and background information. The larger kernel of the convolution can extract more adjacent features of the spatial domain than convolution operations with a kernel size of 1. The improved CA mechanism is introduced in the skip connection of 3D U-Net to improve segmentation accuracy in this research.  
Figure 1: Coordinate attention [29].