## 4 Experiments
### Datasets and Evaluation Criteria
The formula is as shown in Equation (13), where \(MAX\) is the maximum possible pixel value in the image (typically 255 for 8-bit images), and \(MSE\) is the mean square error. \[PSNR=10\text{log}_{10}\frac{MAX^{2}}{MSE} \tag{13}\]  
The Percentage of Error Pixels (\(pEPs\)) is an indicator of the quality of image reconstruction or processing, which calculates the proportion of pixels in the image that are deemed erroneous. Specifically, \(pEPs\) determines the quality of the image by counting the percentage of pixels in the processed image that differ substantially from the reference image among the total number of pixels. A lower \(pEPs\) value indicates higher image quality, meaning fewer erroneous pixels. The formulas are as shown in Equations (14) and (15). \[pEPs=\frac{1}{H\times W}\sum_{h,w}\left\{E_{r}(D(h,w))\right\} \tag{14}\]  
Figure 6: Examples from the CTW1500 dataset. Figure 7: Examples from the SCUT-Syn dataset. \[E_{r}(x)=\left\{ \begin{array}{ll}0&x<20\\ 1&x\geq 20\end{array} \right. \tag{15}\]  
The percentage of clustered error pixels (\(pCEPs\)) measures the extent of locally clustered errors in an image, specifically expressing the proportion of erroneous pixels in all error pixels where neighboring pixels also contain errors. A lower \(pCEPs\) value indicates a lesser degree of clustering for misclassified pixels in the image, suggesting that the synthesized image's structure and detail more closely resemble reality. Therefore, \(pCEPs\) can effectively evaluate the authenticity and quality of generated images. The formulas are as shown in Equations (16) and (17). Equation (18) represents the absolute difference between the pixel values of two grayscale images, and \(g(. )\) denotes the process of converting an image into grayscale. \[pCEPs=\frac{1}{H\times W}\sum_{h,w}\frac{\{E_{c}(D(h+1,w),D(h,w-1), \tag{16}\] \[D(h-1,w),D(h,w+1))\}}{\]  
\[E_{c}(x_{1},x_{2},x_{3},x_{4})=\left\{ \begin{array}{ll}0&others\\ 1&x_{i}\geq 20\ for\ i\in[1,4]\end{array} \right. \tag{17}\]  
\[D(h,w)=|g(X_{h,w})-g(Y_{h,w}) \tag{18}\]  
_Precision_ measures the proportion of the detected text regions that are actually text regions. High precision means there are relatively few false detections among the detected text regions. For text detection tasks, higher precision indicates that the model has a lower rate of misjudgment within the detected text regions. _Precision_ is defined in Equation (19). \[\Pr\textit{ecision}=\frac{\textit{TruePositives}(TP)}{\textit{TruePositives }(TP)+\textit{FalsePositives}(FP)} \tag{19}\]  
_Recall_ measures the proportion of all actual text regions that are correctly detected via the model. A high recall rate indicates that the model has a strong ability to detect text regions with few omissions. The higher the _recall_ rate, the greater the proportion of actual text regions successfully detected via the model. _Recall_ is defined in Equation (20). \[\textit{Recall}=\frac{\textit{TruePositives}(TP)}{\textit{TruePositives}( TP)+\textit{FalseNegatives}(FN)} \tag{20}\]  
The F-score, also known as the \(F1\) score, is the harmonic mean of precision and recall, and it is used to balance these two metrics, particularly when there is a need to weigh false positives against false negatives. The \(F1\) score is calculated as the geometric mean of precision and recall, which gives a single value that combines the two metrics. The formula for the \(F1\) score is as shown in Equation (21). \[\textit{F-score}=2\times\frac{\Pr\textit{ecision}\times\textit{Recall}}{ \Pr\textit{ecision}+\textit{Recall}} \tag{21}\]