## 3 Thermography Data Collection and Preparation
### Transformation Process for Aligning Real and Synthetic Thermographic Image Datasets
Unlike the real specimen thermographic image \(RI\), the synthetic specimen thermographic image \(SI\) is further processed through a transformation module, where it undergoes the product layer and noise layer stages. Figure 5: Comparison between real specimen (RD60-35) and corresponding synthetic specimen (SD60-35). The synthetic specimen thermographic image input into the product layer of the transformation module is a grayscale image, represented by the \(z\) value \(z_{i,j}\) corresponding to the pixel location \(SI_{i,j}\), as shown in Equation (1). The \(SI\) input into the transformation module is reconstructed into a symmetric surface shape, retaining only the \(z\) values \(z_{i,j}\) greater than the mean \(z\). This reconstruction occurs within the range from the \(\overline{z}\) to the \(z_{max}\), symmetrically along the y-axis, with respect to the center of the data. \(H\) is the height of the image and \(W\) is the width of the image. \[SI= \begin{bmatrix}SI_{1,1}&SI_{1,2}&\cdots&SI_{1,W}\\ SI_{2,1}&SI_{2,2}&\cdots&SI_{2,W}\\ \vdots&\vdots&\ddots&\vdots\\ SI_{H,1}&SI_{H,2}&\cdots&SI_{H,W}\end{bmatrix} = \begin{bmatrix}z_{1,1}&z_{1,2}& \cdots&z_{1,W}\\ z_{2,1}&z_{2,2}&\cdots&z_{2,W}\\ \vdots&\vdots&\ddots&\vdots\\ z_{H,1}&z_{H,2}&\cdots&z_{H,W}\end{bmatrix}  \tag{1}\]  
The reason for reconstructing only those \(z_{i,j}\) greater than the \(\overline{z}\) is to preserve the characteristics of the \(z\) values corresponding to low-temperature data in the regions where \(z_{i,j}\) is smaller than the \(\overline{z}\), given that \(SI\) has a standard deviation close to zero. The output \(pz_{i,j}\) generated by inputting \(z_{i,j}\) into the multiplication layer is expressed as shown in Equation (2). \[pz_{i,j}=\left\{ \begin{array}{cc}\frac{1}{(H/2)^{2}}\times(j-(H/2))^{2},&if \ z_{i,j}>\overline{z}\\ z_{i,j}&,\ if\ z_{i,j}\ \leq\overline{z}\end{array} \right. \tag{2}\]  
The synthetic specimen thermographic image \(SI\) is reconstructed into the \(SI^{pz}\) matrix, consisting of the \(pz\) values output from the computational process in the product layer, resulting in a surface shape similar to \(RI\), as shown in the 3D surface graph in Figure 7a. In Figure 7a the maximum and minimum \(z\) values in the \(SI^{pz}\) histogram remain unchanged from the maximum and minimum values of \(SI\), but the mean is 49 and the median is 37. This indicates that the data has become more dispersed around the mean, leading to an increase in variance. Figure 6: Preprocessing Procedure for Synthetic Specim Thermographic Image. However, even though the distribution of \(pz\) values in \(SI^{pz}\) was reconstructed into a surface shape similar to \(RI\), it displays a smooth distribution that does not capture the nonlinear characteristics caused by the noise in the real specimen thermographic data of \(RI\). Therefore, \(SI^{pz}\) was input into the noise layer to modify the data distribution. Figure 7b shows the 3D surface graph and histogram of \(SI^{pz}\), obtained by inputting \(SI^{pz}\) into the noise layer. Style transfer is a technique that modifies the style of one image to match that of another, commonly used to apply the style of artworks to photographs or to alter textures [25]. In the noise layer, the style transfer matrix \(STM\), generated through style transfer, and a random variable matrix \(RM\) with values ranging from 0.9 to 1.1, are used to introduce nonlinear characteristics to the input \(SI^{pz}\). One of the non-defect thermographic images from the real specimen dataset was used as the style image for the style transfer model, while the synthetic specimen thermographic image \(SI\), prior to its reconstruction into \(pz\) values, served as the target image. The style transfer matrix \(STM\), as expressed in Equation (3), was constructed accordingly. \[STM= \begin{bmatrix}STM_{1,1}&STM_{1,2}&\cdots&STM_{1,W}\\ STM_{2,1}&STM_{2,1}&\cdots&STM_{2,W}\\ \vdots&\vdots&\ddots&\vdots\\ STM_{H,1}&STM_{H,2}&\cdots&STM_{H,W}\end{bmatrix}