## 2 Background and Basic Principle
### Detectability Assessment  
In order to assess the detectability of the target, this section will discuss the performance of three aspects of the target's own feature assessment, the background's own feature assessment, and the background element confusion assessment in a comprehensive manner and study the quantitative assessment techniques of the detectability of the weak target. The contrast between the target and background directly affects the performance of the detection algorithm. In order to improve the tracker's ability to recognize targets in the local background region, a number of methods have been proposed to assess the degree of fluctuation of the augmented response map and the confidence level of the detected targets. The Target Saliency Degree (TSD) is used to measure the difficulty of recognizing targets in local and global background regions and is defined as follows:  
\[\text{TSD}=\text{TSR}\times\text{SCR}\times\text{LSCR} \tag{24}\]  
\[\text{TSD}=\frac{1}{1+\text{TSD}} \tag{25}\]  
where SCR and LSCR are the results after normalization by the Norm function. The Norm function maps the values of \(x\) to between 0 and 1, and the distribution density of the values can be adjusted by the tuning parameter \(k\)[22]. The selection of \(k\) affects the smoothness and the trend of the values of \(x\), and it can be applied to contrast enhancement and feature scaling in image processing:  
\[Norm(x,k)=\frac{x}{x+k} \tag{26}\]  
The value of \(k\) can be determined with reference to actual SCR and LSCR usage experience; \(k\) is set to one for SCR and three for LSCR. In a single-frame image, the background is the main factor affecting the target-recognition accuracy. Complex edges and texture elements in the background can cause significant interference in target detection and recognition. The Background Complexity Degree (BCD) is defined as follows and combines global and local measures of background complexity:  
\[\text{BCD}=\frac{\text{RDR}+\text{R}+\text{E}+\text{CON}}{\text{U}+\text{ASM }+\text{IDM}+\text{COR}} \tag{27}\]  
where E, U, and CON are normalized using \(Norm(\cdot,1)\) for normalization. In addition, beyond the characteristics of the target and the background itself, it is necessary to evaluate the target-like elements in the background scene. In this paper, we propose the target intra-frame confusion degree to reflect the evaluation of the intra-frame \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & **HPR** & \(R_{\text{cf}}\) & \(E_{\text{cf}}\) & \(U_{\text{cf}}\) & \(CON_{\text{cf}}\) & \(ASM_{\text{cf}}\) & \(IDM_{\text{cf}}\) & \(COR_{\text{cf}}\) \\ \hline (a) & 0.0019 & 0.4677 & 1.4847 & 0.4330 & 0.2737 & 0.5653 & 0.4060 & 0.8675 \\ (b) & 3.81 \(\times\) 10\({}^{-6}\) & 0.7733 & 2.7218 & 0.1737 & 0.2856 & 0.8575 & 0.1764 & 0.8683 \\ (c) & 0.2610 & 0.8991 & 3.0797 & 0.1653 & 0.5424 & 0.8800 & 0.1959 & 0.8127 \\ (d) & 0.0652 & 0.9836 & 4.7025 & 0.0487 & 4.8836 & 0.8385 & 0.0177 & 0.5227 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Analysis results of background confusion characteristics in typical scene images. confusion degree caused by the similarity between the target and the global background, and the Target Confusion Degree (TCD) is defined as follows:  
\[\text{TCD}=\frac{\text{HPR}+\text{R}_{\text{cf}}+\text{E}_{\text{cf}}+\text{ CON}_{\text{cf}}}{\text{U}_{\text{cf}}+\text{ASM}_{\text{cf}}+\text{ID}_{\text{ cf}}+\text{COR}_{\text{cf}}} \tag{28}\]  
where \(\text{E}_{\text{cf}},\text{U}_{\text{cf}}\), and \(\text{CON}_{\text{cf}}\) are normalized using \(Norm(\cdot,1)\) for normalization. On the basis of the above analysis, this paper integrates the three partial parameters--target characteristics, background characteristics, and background element confusion--to construct the feature matrix.