## 3 Results
### Evaluation Metrics
To calculate SSIMand RMSE for the generated signatures, we used the original signature from each class that had the highest SSIM in the original-forged pairs as the reference sample. The All Classes Case shows the maximum, minimum, and average SSIM and RMSE values across all classes, and the Highest Class Case presents the measurements only for the class with the highest SSIM. In the model with the auxiliary classification process, the highest SSIM was observed in Class 41, while in the model without it, the highest SSIM was observed in Class 46. Analyses of the measurement results revealed that the highest SSIM in the Highest Class Case for the model with the auxiliary classification process was 0.9999, with an average RMSE of 0.1219, indicating an increase of 0.0023 in SSIM and a decrease of 0.0208 in RMSE compared to the highest values in the original-forged signature pairs. These findings suggest that the generated signatures produced by the proposed method successfully capture the structural and visual characteristics of the original signatures. To provide an example of selecting the highest SSIM pair in the original-forged image pairs for each class and comparing it to the generated signature, we selected the original sample 02 and forged sample 18 from Class 46, which had the highest SSIM in the CEDAR dataset. Using sample 02 from Class 46 as the reference, we calculated the SSIM between the forged sample and the generated signature sample produced by the proposed model, with the results summarized in Table 3.  
For the reference sample and the forged samples, the SSIM values ranged from a maximum of 0.9976 to a minimum of 0.9900, with an average of 0.9955. In comparison, when calculating the SSIM between the reference sample and generated signatures, the sample generated by the model with the auxiliary classification process recorded a maximum SSIM of 0.9980, showing higher similarity than the highest SSIM of the forged samples. However, the average and minimum SSIM values were lower than those of the forged samples. This suggests that while the signatures generated by the proposed method may sometimes exhibit less structural similarity than signatures forged by an imitator, the overall range of SSIM values remains quite consistent, indicating that the generated signatures still capture key characteristics of the original signatures. Additionally, the model incorporating the auxiliary classification process achieved a relatively higher SSIM compared to the model without it, demonstrating that the auxiliary classification process significantly contributes to the generation of images with structures that are more similar to the original signatures. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Model** & **Cases** & **Max** & **Min** & **Avg.** & **RMSE** \\ \hline Org-Forg & Train Set & 0.9976 & 0.9749 & 0.9915 & 0.1658 \\ Org-Forg & Highest Class (46) & 0.9976 & 0.9900 & 0.9955 & 0.1427 \\ Aux & All Classes & 0.9999 & 0.8486 & 0.9806 & 0.1819 \\ Aux & Highest Class (41) & 0.9999 & 0.9899 & 0.9965 & 0.1219 \\ Non-Aux & All Classes & 0.9967 & 0.8459 & 0.9722 & 0.2059 \\ Non-Aux & Highest Class (46) & 0.9967 & 0.9839 & 0.9921 & 0.1563 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The maximum, minimum, and average SSIM values and the average RMSE results for the original–forged signature pairs from the CEDAR dataset and the original–generated signature pairs created using the proposed method. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model** & **Cases** & **Max** & **Min** & **Avg.** \\ \hline - & Signatures included in Class 46 of forgery & 0.9976 & 0.9900 & 0.9955 \\ Aux & Including the auxiliary classification & 0.9980 & 0.9676 & 0.9870 \\ Non-Aux & Not including the auxiliary classification & 0.9967 & 0.9839 & 0.9921 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: SSIM comparison for sample 02 in Class 46 of the CEDAR dataset.