## 3 Overview of Proposed Method
### Evaluation Method  
This study evaluates the distance image data obtained by super-resolving the test data and the correct distance image data by calculating the root mean squared error (RMSE) value per pixel. The lower the RMSE calculation result, the smaller the error in the distance information. In our study, the fine-tuned Read-ESRGAN model received test images 200 \(\times\) 1250 pixels in size and output same-sized distance images.  
Figure 4: Image of the test specimen.  
Figure 5: The results of converting RGB images into distance images.  
Figure 6: The results of splitting the image dataset into a test image (**upper**) and a training image (**lower**).  
The result of super-resolving the input image, which was 0.5 times the size of the original evaluation image, two times using Real-ESRGAN was Real - ESRGAN\({}_{\times 2}\), and the result of super-resolving the input image, which was 0.25 times the size of the original evaluation image, four times was Real - ESRGAN\({}_{\times 4}\). As the baseline, the results of the bilinear interpolation method were denoted as Baseline\({}_{\times 2}\) and Baseline\({}_{\times 4}\), respectively, for the distance image generated in the same way using the enlarged result. Table 1 shows the results of calculating the RMSE values using the values for each pixel of each image. The images are also shown in Figure 7, in which the pixels which matched the correct distance to the generated distance image are painted in green, those which matched only the results generated by Real-ESRGAN are painted in blue, those which matched only the baseline results are painted in yellow, and those which did not match the results of both methods are painted in gray. Figure 7 also shows an image in which the tones of the distance image are changed with emphasis.  
The results in Table 1 show that the distance image super-resolved using Real-ESRGAN has a larger error than the magnified image using the conventional method. For both the super-resolution and conventional methods, the RMSE value increases with the magnification factor, and the accuracy of the generated distance image decreases. The results in Figure 7 show scattered gray pixels, indicating that the baseline method makes errors at boundaries with varying distances. On the other hand, blue pixels are more prevalent at the boundaries of the distance change, and the distance image generated by Real-ESRGAN is more accurate than the baseline at the boundary pixels where the distance changes. This tendency becomes stronger as the magnification factor increases. The Real-ESRGAN results also show results that are correct for a coherent range of the same distance, failing to generate certain distances. This may be due to a bias in the number of training data per distance in the model's training data. These results suggest that the super-resolution of  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \(\mathbf{Baseline}_{\times 2}\) & \(\mathbf{Baseline}_{\times 4}\) & \(\mathbf{Real-ESRGAN}_{\times 2}\) & \(\mathbf{Real-ESRGAN}_{\times 4}\) \\ \hline RMSE & 0.215 & 0.263 & 2.085 & 2.651 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Comparison of the delamination detection results.  
Figure 7: Images of the evaluation. (**a**) Input color image; (**b**) input distance image; (**c**) result of \(\times 2\); and (**d**) result of \(\times 4\).  
distance images using Real-ESRGAN can obtain more accurate distances at the boundaries than conventional methods of enlargement. Even if the model is trained with a small number of training data (about 100 original images), it is possible to obtain a specific distance, suggesting the possibility of highly accurate image generation by expanding the training data.