## 4 Results
### Data Augmentation  
Before performing the YOLOv4 algorithm, data augmentation was performed to secure big data for transfer learning [22; 23; 24]. Virtual data for the moving speeds of the specimen were acquired at 3 and 17 mm/s. Regression analysis was performed based on the maximum temperature value for each image in Figure 5. Table 4 shows the maximum temperature values and residual values for each moving speed. Figure 7 shows a graph analyzing the residual plot by performing regression analysis.  
In Figure 7a, to obtain the data for 3 and 17 mm/s, the correlation equation was obtained as follows.  
\[y=-1.559\text{ln}(x)+32.612 \tag{7}\]  
When 3 and 17 mm/s were substituted into Equation (7), the values were calculated as 30.485 \({}^{\circ}\)C and 27.394 \({}^{\circ}\)C, respectively. In order to obtain reference data for substituting the predicted values that came out later, the residuals for each moving speed were analyzed. The smallest residual value of 0.05 \({}^{\circ}\)C was confirmed at 13 mm/s, and the differences with 3 and 17 mm/s were calculated as 2.209 \({}^{\circ}\)C and \(-0.495 ^{\circ}\)C, respectively. After that, 2.209 \({}^{\circ}\)C and \(-0.495 ^{\circ}\)C were input to all frames of 13 mm/s to obtain virtual big data for 3 and 17 mm/s.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Moving Speed** & **Max. Temperature** & **Residual Values** \\ \hline
5 mm/s & 30.286 \({}^{\circ}\)C & 0.358 \\ \hline
7 mm/s & 29.527 \({}^{\circ}\)C & \(-0.079\) \\ \hline
9 mm/s & 28.905 \({}^{\circ}\)C & \(-0.379\) \\ \hline
11 mm/s & 28.771 \({}^{\circ}\)C & \(-0.192\) \\ \hline
13 mm/s & 28.692 \({}^{\circ}\)C & 0.05 \\ \hline
15 mm/s & 28.564 \({}^{\circ}\)C & 0.242 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Maximum temperature and residual values for each moving speed.  
Figure 6: Sequence image with FFT algorithm applied according to Gaussian standard deviation to remove foreign substances around Line 1 for each moving speed.  
The videoLabeler application of MATLAB S/W (R2023a) was used for labeling the augmented data. Since labeling 2602 images took a lot of time, the temporal interpolator algorithm was used. The temporal interpolator algorithm interpolates the ROI of the crack for each frame to predict the axis-aligned or projected ROI between frames, and the process is shown in Figure 8. Assuming that the total length of the video is 80 s, cracks are labeled for images corresponding to sections 30, 40, 50, and 60 s. After that, the ROI points set at 30, 40, 50, and 60 s are interpolated. For example, the ROI is automatically interpolated between 30 and 40 s, so the ROI set on the crack moves accordingly. In this way, the ROI area between 30 and 60 s is labeled along the crack. However, since the size of the labeling may be enlarged or reduced in a specific section, refinement is required.  
Figure 8: Process of temporal interpolator algorithm using videoLabeler of MATLAB S/W.  
Figure 7: Regression analysis and residual comparative graphs for each moving speed.  
In this study, when conducting experiments to acquire data, the algorithm is highly optimized because the specimen moves at a constant speed for the LS, enabling efficient labeling in a very short time. The data with applied labeling were saved in the form of groundTruth to prepare for transfer learning [25].