## 2 Materials and Methods
### YOLOv8 Network Improvement
#### 2.3.2 Spatial and Channel Reconstruction Convolution for Feature Redundancy  
In the pursuit of augmenting the operational efficiency of the YOLOv8n network, the present investigation introduces SCConv (Spatial and Channel Reconstruction Convolution for feature redundancy). This strategic insertion precedes the SPPF module within the pre-existing Backbone architecture, effectively mitigating the propagation of redundant information throughout the feature extraction phase and concurrently attenuating the computational expenditure. The enhancement, which is not a substitution but rather an augmentation of the original framework, maintains the streamlined profile of the model, thereby preserving its lightweight characteristic [45]. The core principle of the module is illustrated in Figure 7, where SCConv consists of two modules, namely the SRU (Spatial Reconstruction Unit) and CRU (Channel Reconstruction Unit), connected in sequential order. These modules aim to reduce the spatial and channel feature redundancy found in the standard convolutional operations. The core step of the SRU is the separate-reconstruct process, which aims to suppress spatial redundancy in the feature maps. The schematic diagram is depicted in Figure 8. The separation operation in the SRU primarily employs GN (Group Normalization) to evaluate the information content of the feature maps and obtain the feature \(X_{out}\). \(\mu\) and \(\sigma\) represent the mean and standard deviation of the input feature maps, respectively, while \(\epsilon\) is a small positive constant added for stable division. \(\gamma\) and \(\beta\) denote trainable affine transformations. \[X_{out}=GN(X)=\gamma\frac{x-\mu}{\sqrt{\sigma^{2}}+\epsilon}+\beta \tag{6}\]  
Figure 7: Diagram of SCConv’s overall structure. The channel weights \(W_{\gamma}\) are obtained by normalizing randomly initialized parameters. Here, \(W_{\gamma}\) represents the set of weights assigned to each channel, where C denotes the total number of channels. \[W_{\gamma}=\{w_{i}\}=\frac{\gamma_{i}}{\sum_{j=1}^{\zeta}\gamma_{j}},(i,j=C) \tag{7}\]  
The product of \(W_{\gamma}\) and \(X_{out}\) is mapped to the range (0, 1) through the Sigmoid function. A threshold gate is used to assign a weight of \(W_{1}\) to high-information expression features with \(W_{\gamma}\) values above the threshold and a weight of \(W_{2}\) to irrelevant features with \(W_{\gamma}\) values below the threshold. \[W_{n}=Gate\big{(}Sigmoid\big{(}W_{y}(X_{out})\big{)}\big{)} \tag{8}\]  
\[ \begin{cases}W_{1},W_{\gamma}>\textit{threshold}\\ W_{2},W_{\gamma}<\textit{threshold}\end{cases}  \tag{9}\]  
The reconstruct operation combines the information-rich feature \(X_{1}^{w}\) and the information-poor feature \(X_{2}^{w}\) in a cross-reconstruction manner, enhancing the information flow between them. This process aims to generate more informative features while suppressing redundant ones, resulting in a spatially enriched feature map \(X^{w}\). \[ \begin{cases}\begin{array}{c}X_{1}^{w}=W_{1}\otimes X,\\ X_{2}^{w}=W_{2}\otimes X,\\ X_{11}^{w}\oplus X_{22}^{w}=X^{w1},\\ X_{21}^{w2}\oplus X_{12}^{w2}=X^{w2},\\ \par[X^{w1},X^{w2}]=X^{w}.\end{array}\end{cases}  \tag{10}\]  
Figure 8: SRU schematic diagram. \"\(\otimes\)\" represents element-wise multiplication, which is used to apply a weight matrix to the original feature map \(X\). \"\(\oplus\)\" represents a fusion concatenation operation, which is used to merge feature vectors along the spatial dimension into a new feature vector. The use of square brackets signifies the concatenation operation, where two feature vectors are concatenated along the channel dimension. The core steps of the CRU involve segmentation, transformation, and fusion, aiming to reduce channel redundancy in the feature maps. The schematic diagram is illustrated in Figure 9.  
The segmentation operation splits the feature map \(X^{w}\) into two channel dimensions, \(\alpha C\) and \((1-\alpha)C\).