## 2 Methods
### Lightweight Network Design
#### 2.1.3 C2f Module Improvement  
The YOLOv8 network architecture contains a large number of C2f modules, whose main function is feature extraction. The performance of the network is closely related to the feature learning of the C2f module. C2f modules typically employ conventional convolutions, leading to computational redundancy and increasing the model's computational and parameter size. To address this issue, this paper designs a brand-new module based on the Partial Convolution (PConv) from FasterNet [42]--Faster-C2f (F-C2f) module, which simultaneously reduces computational redundancy and memory access. Figure 4b illustrates the working principle of PConv. It applies conventional convolution to only a part of the input channels for spatial feature extraction while keeping the remaining channels unchanged. For continuous or regular memory access, PConv considers the first or last \(c_{p}\) continuous channels as a representative of the entire feature map for computation [42]. The input and output feature maps generally have the same number of channels, so the computational cost of PConv is:  
\[h\times w\times k^{2}\times c_{p}^{2} \tag{1}\]  
The memory access amount for PConv is:  
\[h\times w\times 2c_{p}+k^{2}\times c_{p}^{2}\approx h\times w\times 2c_{p} \tag{2}\]  
In this case, \(h\) and \(w\) represent the width and height of the feature map, respectively, \(k\) represents the size of the convolutional kernel, c represents the number of input channels, and \(c_{p}\) represents the number of channels involved in the convolution. Generally, it is often the case that \(r=c_{p}/c=1/4\) (for example, selecting the first 25% of the channels); thus, the computational load of PConv is only \(1/16\) of that of conventional convolution, and the number of memory accesses is only \(1/4\) of that involved in conventional convolution operations.  
The structural schematic of the F-C2f module is shown in Figure 5. Its main advantages include: (1) by adopting partial convolution technology, it achieves efficient feature extraction, significantly reducing the model's computational complexity and memory access. (2) The F-C2f module inherits the multi-branch design of the C2f module, where the input data are split into two branches for processing. One branch is passed directly to the output, while the other branch is processed through n Bottleneck modules before being merged with the directly transmitted part. This design helps reduce redundant computations while enhancing the diversity of feature representations. Here, n represents the number of Bottleneck modules (default value is 1), and it can be adjusted based on specific requirements. Although each Bottleneck module has the same structure, the features extracted and processed by each module vary depending on their position in the network and the input they receive. For instance, the first Bottleneck module receives feature maps processed by the Conv layer, which are relatively close to the original features of the input image. Therefore, the first Bottleneck module processes more basic features. The subsequent Bottleneck modules receive the output from the previous Bottleneck module, and as each Bottleneck module further processes the input features, the later modules handle more complex and abstract feature information. Finally, these different levels of features are fused together  
Figure 4: The working principles of (**a**) the Conv and (**b**) the PConv.  
to form an output feature map rich in information. This design significantly enhances the model's ability to extract features, enabling the network to effectively capture various important details in the image. By maintaining a lightweight design, the F-C2f module successfully balances performance and speed, ensuring efficient operation of the model. (3) As a replacement for the C2f module, the F-C2f module can be seamlessly integrated into existing model architectures, allowing the model to be lightweight without needing major adjustments to the overall structure.