## 5 Results  
The data are made of 98% randomly sampled data (1253) from a normal specimen and 2% randomly sampled data (23) from a specimen with voids in the duct. All of these data are converted into a scalogram image and used to train and test the CNN auto-encoder. When the image data of the PSC specimen's internal duct are put into the CNN AE, the results show the normal and void distribution as the histogram similarity of the input and output, as shown in Table 1. Figure 11 shows the visual plot. The boundaries of the similarity  
Figure 10: Example of histogram distributions of input image and reconstructed image. Similarity is obtained using Open CV. Figure 9: The architecture of the auto-encoder. The output data are the restructured input data. distribution are Average, Avg-Std (\(-\sigma\)), and Avg-2*Std (\(-2\sigma\)). As a result, we compare the distribution of data with high similarity and low similarity to the boundary line. First, we examine the distribution with the mean as the boundary. The proportion of data with a histogram similarity higher than the mean is 17.3% for void data and 55.3% for normal data. In comparison to the normal data, where the ratio of the data less than the mean is 44.6%, the void data occupies most, at 82.6%. When comparing data distributions based on mean-standard deviation--that is, \(-\sigma\)--data distributions higher than the boundary are 86.9% normal. In the case of data that have a lower similarity than the boundary, the normal data have a distribution with a ratio of 13%, but the void data have a distribution with a ratio of 47.8%. Finally, when comparing data on the mean-2\(\times\)standard deviation boundary--that is, \(-2\sigma\)--data over the boundary have a normal ratio of 95.9%. Furthermore, for data with a histogram similarity lower than the boundary, it is confirmed that the normal data have a ratio of 4% and the void data ratio is 34.7%. The normal ratio is much larger than the void ratio for data above the boundary, whereas the void ratio is much larger than the normal ratio for data below the boundary. As a conclusion, the overall distribution indicates that the histogram similarity of normal data is mainly high, whereas that of void data is mostly lower than that of the boundary. Additional experiments, on the other hand, were carried out using the GAF and MTF methods, which are the image transformation methods mentioned in Section 3.2. Other Image Transform Methods. The Compare_ssim() function of scikit-image was used to calculate the similarity between input and output images. Figure 12 shows the similarity \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{1}{c}{**Boundary**} & \multicolumn{1}{c}{**Higher/Lower**} & \multicolumn{1}{c}{**Normal**} & \multicolumn{1}{c}{**Void**} \\  & & **Num (Ratio)** & **Num (Ratio)** \\ \hline \multirow{2}{*}{Mean} & Higher & 693/1253 (55.3\%) & 4/23 (17.3\%) \\  & Lower & 560/1253 (44.6\%) & 19/23 (82.6\%) \\ \hline \multirow{2}{*}{Mean–Standard deviation} & Higher & 1089/1253 (86.9\%) & 12/23 (52.1\%) \\  & Lower & 164/1253 (13\%) & 11/23 (47.8\%) \\ \hline \multirow{2}{*}{Mean–2\(\times\)Standard deviation} & Higher & 1202/1253 (95.9\%) & 15/23 (65.2\%) \\  & Lower & 51/1253 (4\%) & 8/23 (34.7\%) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Distribution of normal and void data in the duct. In the histogram similarity distribution, the boundaries are set as mean, mean–standard deviation (\(-\sigma\)), and mean–2 \(\times\) standard deviation (\(-2\sigma\)). Figure 11: Histogram similarity distribution plot. It shows where the 2% void data appear for the boundary. It helps in assessing the performance of the CNN auto-encoder model. distribution plot for the experimental results. The performance of anomaly detection was examined using the \(-2\sigma\) boundary. First, in the GAF experiment, the data with a lower similarity to the \(-2\sigma\) boundary have a distribution of normal 5% and void 17.3%.