## 4 Experimental Setup and Result Analysis
### Comparative Analysis  
(1) Evaluation of Convolution Kernel Configurations in the TPS Prediction Module  
This experiment analyzes the impact of different convolutional kernel configurations, corresponding to varying numbers of TPS control points, on the rectification performance of the network. Specifically, we examine how the number of control points predicted at each layer of the TPS prediction module affects the output quality. Quantitative metrics, including PSNR and SSIM, are used for evaluation. The experimental results are summarized in Table 3.  
To investigate the impact of TPS control point density on correction performance, this study adjusts the output dimensions of convolutional layers in the TPS module to generate different numbers of control points (e.g., 10 \(\times\) 10, 12 \(\times\) 12, 16 \(\times\) 16) and conducts systematic evaluations on a standard distortion dataset. The results are summarized in Table 4. The experiments reveal that the relationship between the number of control points and correction accuracy is not linearly positive. Specifically, when all four TPS modules output 16 \(\times\) 16 control points, the model--despite its theoretically stronger spatial fitting capacity--shows a notable performance drop in both PSNR and SSIM (16.34 dB, 0.5234), falling behind the medium-scale 12 \(\times\) 12 configuration and even underperforming the initial 10 \(\times\) 10 setting. This phenomenon can be attributed to the following factors:  
(1) Overfitting to local distortions: Excessive control points tend to overfit localized deformation regions, which reduces global correction smoothness and causes geometric inconsistencies across the image. (2) Increased model complexity: A higher number of control points significantly increases the output dimensionality of the network, leading to greater computational overhead and potential training instability or gradient degradation--especially detrimental for embedded deployment. (3) Enhanced noise sensitivity: In regions with blurred edges or weak textures, dense control points often lack sufficient semantic support, resulting in erroneous displacements and degraded correction accuracy. In comparative experiments, certain existing methods (e.g., RecRecNet) exhibit significant performance degradation when applied to irregularly distorted images, with substantial drops in PSNR and SSIM. This is largely due to their limited geometric adaptability and lack of structural guidance. In contrast, the optical flow-guided vector constraint \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Metric** & **10-10-10-10** & **10-12-12-14** & **16-16-16-16** &
\begin{tabular}{c} **Ours** \\ **(10-10-12-14)** \\ \end{tabular} \\ \hline PSNR & 17.29 & 18.36 & 16.34 & 19.97 \\ SSIM & 0.5875 & 0.5769 & 0.5234 & 0.6151 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Performance comparison with different numbers of TPS control points. Figure 17: Rectification result with TPS control point configuration of 10–10–10–10. Figure 18: Rectification results with TPS control point configuration of 16–16–16–16. It is worth noting that methods such as Crop, ROP, and Padding rely on manual parameter adjustments and cannot be executed in an automated inference pipeline. Therefore, inference time is marked as \"-\" in the table to indicate exclusion from speed comparison. In the comparative experiments, the proposed method was evaluated using two widely adopted objective metrics--PSNR and SSIM--for quantitatively assessing the quality of rectified images. Additionally, a qualitative comparison based on subjective visual perception was conducted against existing state-of-the-art algorithms. As illustrated in Figure 19, the proposed method exhibits superior overall performance in correcting wide-angle distortions, with particularly pronounced improvements in regions affected by severe deformation.