# Spatial Small Target Detection Method Based on Multi-Scale Feature Fusion Pyramid
## 4 Experimental Results and Discussion
### Experimental Setup  
In this paper, in order to verify the performance of different feature pyramids, we used CSPNet [42] as the backbone algorithm and constructed a target detection algorithm using PANet, BiFPN, and MFFPN proposed in this paper for the experiments. The migration learning strategy was used in the experimental process. First, the constructed algorithm was pre-trained on the COCO dataset and the pre-trained weight parameters were obtained. Then, the weights of the algorithm were initialized using the pre-training file and trained on the constructed spatial small target dataset, i.e., the idea of migration learning was used to accelerate the training speed of the model. (1) Experimental details  
During the experiment, the batch size (the number of data samples during batch training) was determined to be 128 using automatic optimization, the image size was 640 \(\times\) 640, the number of epochs was 500, the initial learning rate was 0.001, the momentum factor was 0.937, and the weight decay rate was 0.0005. In order to speed up the training of the model, we used the migration learning strategy. At the same time, we used the warm-up strategy to use a smaller learning rate at the beginning of training to ensure the \begin{table}
\begin{tabular}{c c} \hline \hline
**Category Name** & **Detail** \\ \hline Operating system & Windows10 \\ CPU & Intel i7-12700 (Sanata Clara, CA, USA) \\ GPU & NVIDIA RTX A6000 \\ (Santa Clara, CA, USA) \\ Cuda with Cudnn & v.11.7 \\ Python & v.3.8 \\ Pytorch & v.2.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters related to the experimental environment. Figure 5: Improved spatial pyramid pooling module. (**a**) is a structural diagram of a kind of spatial pyramid pooling. (**b**) is the structure of the improved spatial pyramid pooling module. stability of the model and increase the learning rate to improve the convergence speed of model training after the model was stabilized. In this study, we used a variety of data enhancement methods to enhance the detection accuracy of the model in the presence of external disturbances. In addition to the commonly used image brightness, saturation, and noise enhancement methods, we also used geometric variation methods such as random scaling, cropping, panning, shearing, and rotation. In addition to individual image data enhancement methods, we also used mosaic data enhancement methods, where multiple images are spliced after data enhancement and the corresponding bounding boxes are changed correspondingly to obtain new images and bounding boxes. Considering the strong similarity of the star background, we used copy-pasting to enhance the data to increase the number of targets in the image and strengthen the detection performance of the model. Data enhancement can effectively extend the dataset to make the model have stronger detection performance for targets in different scenes and increase the generalization of the model for image detection in different scenes. Evaluation indicators  
The performance of a model is usually evaluated using precision (P), recall (R), and mean average precision (mAP). Precision refers to the proportion of true positive samples among all samples predicted by the classifier, which can be expressed as:  
\[Precision=\frac{TP}{TP+FP}=\frac{TP}{num_{pred}} \tag{4}\]  
where \(TP\) denotes the number of samples that were true positive examples, \(FP\) denotes the number of samples that were incorrectly predicted to be positive examples, and \(num_{pred}\) denotes the total number of objects recognized. Recall is the percentage of the number of samples that are correctly predicted to be positive out of all the samples that are positive, and can be expressed as:  
\[Recall=\frac{TP}{TP+FN}=\frac{TP}{num_{sample}} \tag{5}\]  
where \(FN\) denotes the number of samples that were incorrectly predicted as negative examples and \(num_{sample}\) denotes the total number of objects to be detected. Mean average precision (mAP) is a metric for evaluating the performance of target detection algorithms.