# Crack Defect Detection Method for Plunge Pool Corridor Based on the Improved U-Net Network
## 2 Methods
### Cross-Dimensional Interaction Attention Module  
The attention module [30] primarily enhances the model's detection performance of target features through spatial information, channel information of the feature data, and their combination. Currently, the widely acknowledged attention modules that effectively enhance feature detection capabilities mainly consist of CBAM [31], SE [32], ECA [33], and CA [34]. In the crack segmentation task, the channel or spatial attention mechanism has been demonstrated to be highly effective in extracting crack features. Nevertheless, when handling cross-dimensional information, the approach of channel dimensionality reduction may result in information loss during the extraction of higher-dimensional features. To address this issue, this paper, based on the existing research of the attention mechanism, puts forward a cross-dimensional interaction attention module (CDIAM). This attention module reminds part of the channel information into the batch-processing dimension, divides the channel dimension into multiple sub-feature groups, and guarantees the even distribution of spatial semantic features. Meanwhile, this module utilizes global information to calibrate the weights of the channel dimension, integrates the features output from parallel branches, captures pixel-level relationships, and enhances the model's crack feature extraction capacity and crack recognition precision. The architecture of the cross-dimensional interaction attention module is shown in Figure 5.  
To enable the model to better differentiate between foreground and background pixels, the input feature map is subjected to cross-dimensional division, splitting it into N sub-feature groups. Suppose the input feature map is X \(\in\mathbb{R}^{\text{C}\times\text{H}\times\text{W}}\). Following cross  
Figure 4: Comparison of FOV between traditional convolution and morphological irregular dynamic convolution methods: (**a**) FOV of traditional convolution; (**b**) FOV of MIDConv. Figure 5: Cross-dimensional interaction attention module structure. dimensional division, the feature map can be denoted as \(\mathrm{X}=[\mathrm{X}_{0},\mathrm{X}_{1},\mathrm{X}_{2}\cdots\mathrm{X}_{\mathrm{ N}}]\), of which \(\mathrm{X}_{i}\mathrm{e}\mathbb{R}^{C/IN\times\mathrm{H}\times\mathrm{W}}\), typically \(\mathrm{N}\ll C\). Meanwhile, it is hypothesized that the learned attention weight descriptor will be employed to enhance the feature representation of the regions of interest within each sub-feature. This implies that the model can concentrate its attention on specific areas, thus enhancing the quality and significance of the feature representation in those areas. By this means, the network can capture the crucial information in the input data more efficiently, thereby enhancing the performance and expressivity of the task. The attention module consists of three parallel branches, which are the H-direction feature map-processing branch (the first branch), the W-direction feature map-processing branch (the second branch), and the input sub-feature-group-processing branch (the third branch). After the features of average pooling and convolution in the first and second branches are concatenated, weight redistribution is carried out with the input sub-feature group, thus obtaining the output features. Subsequently, the output features are interactively integrated across dimensions with the feature map of the third branch that has undergone \(3\times 3\) convolution processing, and ultimately, the output feature map is acquired. To realize diverse cross-channel feature interactions between the first and second branches, the product operation is utilized to aggregate the channel features of these two branches. Meanwhile, to capture local cross-channel interactions and broaden the feature space, the third branch conducts processing on the input features with a \(3\times 3\) convolution.