# ReBiDet: An Enhanced Ship Detection Model Utilizing ReDet and Bi-Directional Feature Fusion
## 2 The Proposed Method
### Rotation-Equivariant Bidirectional FPN  
In the feature extraction network, lower-level features contain more detailed and positional information but have lower resolution. On the other hand, higher-level features have higher resolution and more semantic information but lack detail. In ReDet's ReFPN module, inspired by the traditional FPN [27], a top-down feature fusion approach is adopted as shown in Figure 3. However, the traditional FPN has a relatively simple feature fusion method, performing simple feature upsampling from high to low levels. To provide a more intuitive understanding, we simplify the convolution layer and upsampling layer, representing them with Equation (1):  
\[P_{i}=\sum_{n=i}^{l_{max}}C_{n}(i=2,3,4,5), \tag{1}\]  
here, \(C_{n}\) denotes the feature map extracted by the backbone network, \(P_{i}\) represents the feature map output by the FPN module, and \(i_{max}\) is the total number of layers inputted into FPN from the backbone network. The output \(P_{i}\) fuses only the feature maps from layer \(i\) to \(i_{max}\), ignoring the importance of feature maps below layer \(i\) and not fully utilizing the feature information from different levels, which may lead to information loss. Typically, top-level feature maps with large strides are used to detect large objects, while bottom-level feature maps with small strides are used to detect small objects [28]. However, in the case of \(P_{3}\), if only the features of \(C_{5}\), \(C_{4}\), and \(C_{3}\) from top to bottom are fused, the importance of \(C_{2}\), dedicated to detecting small objects, is ignored. Additionally, both \(P_{5}\) and \(P_{6}\) are extracted from the \(C_{5}\) layer inputted into the backbone network, but \(P_{6}\) only uses \(1\times 1\) convolution downsampling with stride 2, which may result in the loss of significant feature information. In summary, the FPN design in the ReDet model suffers from unbalanced feature fusion, which may affect the detection performance of small objects in the overall model. To address these issues, we introduce the rotation-equivariant bidirectional feature fusion feature pyramid network module, named ReBiFPN, based on the idea of PaNet [29]. Figure 4 illustrates the ReBiFPN module. ReBiFPN balances the output levels by integrating the feature maps of each resolution. It combines the high-resolution of the high-level features with the high-detail information of the low-level features, enhancing the network's ability to extract and integrate multi-scale features through bidirectional path feature fusion. This approach captures richer multi-scale features and improves the detection performance of small objects. For simplicity, we represent the core idea of ReBiFPN with Equation (2):  
\[P_{i}=\sum_{n=l_{min}}^{l_{max}}C_{n}(i=2,3,4,5), \tag{2}\]  
where \(C_{n}\) represents the \(n_{th}\) feature map extracted by ReResNet, \(P_{i}\) denotes the feature map output by the ReBiFPN module, \(l_{max}\) is the total number of layers inputted into ReBiFPN from ReResNet, and \(l_{min}\) is the number of the lowest layer inputted into ReBiFPN from ReResNet. Each level of the output \(P_{i}\) balances the features fused from \(\{C_{2},C_{3},C_{4},C_{5}\}\). The \(P_{6}\) layer is excluded from the feature fusion because experimental results indicate that downsampling directly from the \(C_{5}\) layer to obtain \(P_{6}\) improves the detection accuracy slightly compared to downsampling from the \(P_{5}\) layer. This improvement may be due to  
Figure 2: Difference between the feature maps extracted by ReResNet and ResNet networks. (**a**) Feature maps extracted by the ReResNet network, denoted as (K, N, H, W), where N is an additional dimension compared to traditional ResNet feature maps shown in (**b**). Here, N = 8 indicates that discrete rotation group convolution can extract feature maps at 8 different rotation angles. the weakening of object features after multiple convolution operations.