# BFE-Net: Bidirectional Multi-Scale Feature Enhancement for Small Object Detection
## 3 Method
### Dilated Feature Enhancement  
The standard RetinaNet discards use the high-resolution pyramid level P2 computed from the output of the corresponding ResNet residual stage C2. The shallow feature C2 in the backbone network contains rich feature location information with higher resolution, which will be beneficial to the localization of small targets. We can employ effective strategies to make full use of the high-resolution features from C2. In this paper, we present the Dilated Feature Enhancement (Figure 4a), which combines the feature enhanced high-resolution feature C2 with P3 in the top-down path to obtain P2 as the input of the enhanced bottom-up structure. The structure consists of Dilated block (Figure 4b) and a lateral connection by \(1\times 1\) conv just as in [16]. The dilated convolution is used to increase the receptive field size of the convolution kernel,  
Figure 3: Illustration of feature layer fusion: (**a**) C6; (**b**) N6. Figure 2: Comparisons of different backbone: (**a**) PANet; (**b**) RetinaNet; (**c**) BFE-Net (our model). extract richer context information, and obtain richer low-level localization features without significantly increasing the computational load. This operation can be constructed as:  
\[\text{P2}=F_{concat}(Conv_{1\times 1}(\text{C2}),D(\text{C2}),Conv_{3\times 3}( \text{P3})), \tag{1}\]  
\[\text{N2}=Conv_{1\times 1}(\text{P2}), \tag{2}\]  
where \(D(\cdot)\) is the Dilated block operation, which is described in detail below, and the detailed description is given in Equation (4). N2 represents the input of the bottom-up augmentation path. \(F_{concat}\) represents the features that are fused in the concatenate method. **Dilated Block:** In most network structures with FPN, feature maps corresponding to different receptive fields are simply merged by element-wise addition in the top-down path. Merging the feature maps corresponding to different receptive fields through element addition cannot make the information captured by different receptive fields interact effectively, resulting in limited utilization of extracted information. As shown in Figure 4, to merge multi-scale information with different receptive fields elaborately, this paper employs residual connection in the Dilated block, where the output of each dilated layer is concatenated with the original input feature maps and then fed into the next dilated layer. At the same time, each dilated layer is given a separate output feature as a part of the output of the Dilated block. Finally, in order to maintain the coarse-grained information of the initial inputs, this paper concatenates the outputs of all dilated layers and feeds them into a \(1\times 1\) convolutional layer to fuse the coarse-and-fine grained features. In this model, we have designed two other feature extraction methods. As shown in Figure 5, Dilated block A (Figure 5a) uses the parallel method in Inception to extract features on the input feature map using dilated convolutions with different expansion rates. Finally, the extracted features are fused in a concatenated manner. Dilated block B (Figure 5b) uses the general feature extraction method to extract features in series and finally obtains only one feature layer. We analyze the effects of different structures in the experimental results in Section 4.4. \[F_{dilated}(i)=\left\{ \begin{array}{ll}Conv_{1\times 1}(\text{C2})\oplus Conv _{3\times 3}(\text{C2})&i=0\\ F_{dilated}(i-1)\oplus Conv_{1\times 1}(\text{C2})&i>0\end{array} \right., \tag{3}\]  
where \(F_{dilated}(i)\) represents the dilated convolution operation function with residual structure. The symbol \(\oplus\) denotes feature fusion by addition. \(Dconv_{3\times 3}(\cdot)\) represents a dilated convolution with a convolution kernel of \(3\times 3\) and expansion rates of \(3\), \(6\), and \(12\), respectively. Then, the three output feature maps containing multi-scale context information are fused in using the concatenate method.