# WDS-YOLO: A Marine Benthos Detection Model Fusing Wavelet Convolution and Deformable Attention
## 3 Methods
### Feature Extraction Module: C2f-WTConv  
Owing to underwater light scattering and attenuation, captured images often suffer from color distortion and reduced contrast, which complicates the process of feature identification and introduces additional challenges for marine bentnos feature extraction. Additionally, due to the habitat characteristics of marine bentnos, their distribution is often concealed with protective coloration, making boundary information more critical than surface color for feature extraction. This necessitates a feature extraction network with an expanded receptive field. The C2f structure in YOLOv8's backbone network employs fixed-size convolutional kernels for feature extraction, limiting its ability to effectively capture the boundary information of marine bentnos objects. To address this issue, we introduced the Wavelet Convolution (WTConv) module [51], a convolutional structure based on the Wavelet Transform (WT). This module aims to expand the receptive field through hierarchical frequency decomposition while avoiding the issue of excessive parameters. The core idea of WTConv is to apply the cascade WT to recursively decompose the input signal into different frequency components, perform small-kernel convolution operations on each frequency component, and finally merge the results through Inverse Wavelet Transform (IWT). Specifically, the WTConv employs 2D Haar WT, which performs depth-wise convolution on the input using four distinct filters: a low-pass filter (f\({}_{\text{LL}}\)) to capture the global low-frequency information of the image, while horizontal high-pass  
Figure 2: WDS-YOLO network structure. (f\({}_{\rm LH}\)), vertical high-pass (f\({}_{\rm HL}\)), and diagonal high-pass (f\({}_{\rm HH}\)) filters are utilized to preserve the local high-frequency details of the image. By cascading the application of WT, the WTConv module can generate frequency components at multiple scales. Specifically, at each level of the wavelet decomposition, the low-frequency component from the previous level (\(X_{LL}^{(i-1)}\)) is further decomposed, yielding a new low-frequency component (\(X_{LL}^{(i)}\)) and corresponding high-frequency components (\(X_{H}^{(i)}\)). This hierarchical decomposition effectively emphasizes low-frequency information, thereby enhancing the model's responsiveness to such features. Then, at each level of frequency components, the WTConv module performs a small-kernel depth-wise convolution. The process is expressed as follows:  
\[X_{LL}^{(i)},X_{H}^{(i)}=\text{WT}(X_{LL}^{(i-1)}) \tag{1}\]  
\[Y_{LL}^{(i)},Y_{H}^{(i)}=\text{Conv}(W^{(i)},(X_{LL}^{(i)},X_{H}^{(i)})) \tag{2}\]  
where \(W^{(i)}\) represents the weights of the depth-wise convolution kernel at level \(i\), while \(Y_{LL}^{(i)}\) and \(Y_{H}^{(i)}\) represent the low-frequency and high-frequency outputs, respectively, after the convolution operation. Since WT reduces the spatial resolution of each sub-band, small convolutional kernels can cover larger regions of the image, thereby significantly expanding the receptive field without a substantial increase in the number of parameters. After the convolution operation, the WTConv module reconstructs the convolution results of each frequency component into the original spatial domain using the IWT. Leveraging the linear properties of the IWT, it efficiently integrates information from multi-level convolutions, preserving multi-frequency features while achieving convolution operations with large receptive fields. The equation is as follows:  
\[Z^{(i)}=\text{IWT}(Y_{LL}^{(i)}+Z^{(i+1)},Y_{H}^{(i)}) \tag{3}\]  
where \(Z^{(i)}\) represents the aggregated output from level \(i\) and above. Figure 3 illustrates an example of the WTConv module employing a 2-level WT and a \(3\times 3\) convolutional kernel. The 2-level wavelet decomposition can provide a sufficiently large receptive field without excessively increasing computational complexity, while the \(3\times 3\) convolutional kernel effectively captures local features across each frequency component.