## 3 Materials and Methods
### TSA Triplet Spatial Reconstruction Attention Mechanism  
The proposed TSA triplet spatial reconstruction attention mechanism adopts horizontal spatial pooling, vertical spatial pooling, and global feature enhancement as a triplet processing strategy, dividing input image features \(X\) into two branches for parallel processing, achieving reduced computational overhead while enhancing recognition effectiveness. The horizontal and vertical pooling operations extract directional spatial dependencies while preserving channel information, and the global enhancement component applies semantic-driven threshold discrimination to distinguish meaningful features from redundant information, enabling adaptive feature reconstruction through cross-reorganization operations.  
The first branch performs horizontal and vertical pooling on input feature values \(X\), retaining channel information while combining the two directional dimensional values for batch normalization, obtaining target feature weight coefficients under the combination of spatial directional feature information and channel dimensions. After multiplying the weights with the feature map values \(X\) themselves, sigmoid activation mapping is performed. Using these values for threshold judgment, features are divided into feature values \(X_{1}^{\omega}\) with higher semantic information and relatively lower feature values \(X_{2}^{\omega}\). The two sets of feature values are then divided separately, with four groups of data undergoing pairwise cross-reorganization and addition to suppress redundant spatial features, finally combining the two sets of features into original-size feature values.  
The other branch performs batch normalization on feature values \(X\), and after activation mapping, adds them to the first branch output feature values with weight coefficient readjustment to ensure output feature values do not overfit, yielding output \(X^{\omega}\). The entire TSA triplet spatial reconstruction attention mechanism is shown in Figure 3.  
Figure 3: TSA Triplet spatial reconstruction attention structure diagram.  
The computational efficiency of TSA stems from its parallel processing architecture and linear complexity design. The horizontal and vertical pooling operations maintain O (C \(\times\) H \(\times\) W) complexity for spatial feature extraction, while the dual-branch structure avoids the quadratic channel dependencies inherent in traditional attention mechanisms. In contrast to SCConv's O (C\({}^{2}\times\) H \(\times\) W) complexity arising from its sequential spatial-channel processing, TSA achieves feature separation and reconstruction through threshold-based operations that scale linearly with input dimensions. Similarly, while CA mechanisms typically require O (C \(\times\) H \(\times\) W + C\({}^{2}\)) operations for coordinate embedding and channel-wise attention computation, TSA's triplet processing strategy eliminates the need for expensive channel-wise matrix operations through its parallel pooling and reconstruction approach. The threshold separation and cross-reorganization operations maintain constant computational overhead regardless of channel depth, contributing to the overall efficiency gain.