## 3 Method
### Enhanced Feature Pyramid Network
Convolutional operations are executed across four residual convolutional modules (referred to as layer_1 to layer_4), generating feature maps at corresponding scales: \(256\times H\times W,512\times H/2\times W/2,1024\times H/4\times W/4\), and \(2048\times H\times W\). This design allows the feature extraction network to progressively gather insights from both diminutive-scaleand substantial-scale features spanning diverse scales. Notably, subsequent to each residual convolutional module, the feature map is proportionally downsampled by factors of 0.5, 0.25, and 0.125, respectively. Within the FPN network of Sparse R-CNN, subsequent to the extraction of feature maps at the four distinct scales, a process of reversed feature fusion is initiated. To facilitate this fusion, a \(1\times 1\) convolutional operation is applied to the feature map of each layer. This operation ensures uniformity in output channel dimensions across layers, thus simplifying the ensuing feature fusion process. Typically, fusion is executed through element-wise addition. In the ultimate top-level feature map at the 0.125\(\times\) scale (depicted in Figure 2), a module for top-level feature enhancement is incorporated. The module's output undergoes fusion with the original top-level features, thereby generating enhanced top-level features. This augmentation effectively counteracts the loss of top-level feature data that can arise during the ensuing process of reversed multi-scale feature fusion. Consequently, this addresses the constraint attributed to the absence of higher-level features available for fusion with the top-level counterparts. Figure 1: Feature extraction network. Figure 2: Top-level feature fusion module. To be more precise, the top-level feature enhancement module incorporates an adaptive pooling mechanism. In this process, the aspect ratio of the feature map remains constant, while the pooling ratio can be altered. This permits the execution of adaptive pooling using multiple pooling ratios. Consequently, the model operates at diverse scales, generating target features of varying scales based on the original top-level input features. This approach enables progressive feature fusion across distinct channels, and the resultant feature scale \(\varsigma\) after extraction can be expressed as shown in Equation (1). \[\varsigma=(a_{1}\times S,a_{2}\times S,\ldots,a_{n}\times S) \tag{1}\]  
where \(S\) represents the initial feature scale, corresponding to the scale of the top-level feature. The symbols \(a_{i}\), where \(i=1,2,\ldots,n\), signify the designated pooling ratios. Following this, a \(3\times 3\) convolutional kernel is applied to condense the multi-channel features to 256. Subsequently, an upsampling procedure is engaged to restore the dimensions to the original scale \(S\) in preparation for subsequent fusion. The technique of bilinear interpolation is harnessed in the upsampling phase to compute new pixel values. For given coordinates of four points, \((x_{1},y_{1}),(x_{2},y_{2}),(x_{3},y_{3})\), and \((x_{4},y_{4})\), the interpolation formula employed to ascertain the value at a novel coordinate \((x,y)\) is as follows:  
\[f(x,y_{1})\approx\frac{x_{2}-x}{x_{2}-x_{1}}f(Q_{11})+\frac{x-x_{1}}{x_{2}-x_{ 1}}f(Q_{21}) \tag{2}\]  
\[f(x,y_{2})\approx\frac{x_{2}-x}{x_{2}-x_{1}}f(Q_{12})+\frac{x-x_{1}}{x_{2}-x_{ 1}}f(Q_{22}) \tag{3}\]  
\[f(x,y)\approx\frac{y_{2}-y}{y_{2}-y_{1}}f(x,y_{1})+\frac{y-y_{1}}{y_{2}-y_{1}} f(x,y_{2}) \tag{4}\]  
where \(Q_{11}=(x_{1},y_{1})\), \(Q_{12}=(x_{1},y_{2})\), \(Q_{21}=(x_{2},y_{1})\), \(Q_{22}=(x_{2},y_{2})\). In this process, following the upsampling step, the feature maps that underwent pooling with varying ratios in the preceding stage have their scales equalized. These feature maps are subsequently concatenated. Recognizing the semantic disparity among these feature maps with distinct original ratios, each of them undergoes a sequence consisting of a \(1\times 1\) convolutional layer, an ReLU layer, and a \(3\times 3\) convolutional layer.