## 4 Discussion  
In this study, we proposed a signature data generation method using the DDPM and a classifier, and we evaluated its performance using the CEDAR signature dataset. The proposed method aims to generate signatures that are similar to the originals based on existing signature images, thereby addressing data shortages and enhancing the performance of signature recognition systems. The signature generation model using DDPM has demonstrated its ability to learn detailed features such as curves, line flow, and style from only the digital signature images, \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Train Set** & **Precision** & **Recall** & **Acc. (\%)** & **ERR** \\ \hline Original train data & 0.9615 & 0.9220 & 94.26 & 0.0570 \\ Included generated signatures & 0.9554 & 0.9414 & 94.87 & 0.0518 \\ Included generated signatures & 0.9308 & 0.9118 & 92.20 & 0.0749 \\ (not using the classifier) & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of signature verification performance via training data composition. enabling the creation of signatures that closely resemble the originals. It successfully generated new signature images that reflect characteristics observed in multiple original signatures. Moreover, a classifier was employed alongside the signature generation model during the training process to differentiate between forged and original signatures. This approach helped produce generated signatures that are more similar to the originals, thereby reducing the likelihood of misidentification as forged signatures. To quantitatively evaluate the signatures generated by the proposed method, we calculated the SSIM and RMSE for the reference samples in each class and tracked the performance changes in the signature verification model when the generated signatures were added to the training data. Experimental results showed that the proposed model achieved an average SSIM of 0.9806 and an RMSE of 0.1819, indicating that it can produce images with characteristics that are very similar to the original signatures. When the generated signatures were added to the training data in the verification model learning process, the verification model achieved an accuracy of 94.87% and an equal error rate (EER) of 0.0518, marking a 0.61 percentage point increase in accuracy and a decrease of 0.0052 in EER compared to the model without the generated signatures. These results demonstrate that the signatures generated by the proposed method capture a variety of characteristics that original signatures can exhibit, contributing to improvements in the verification system's performance. We expect this approach to be applicable not only to handwritten signatures but also to other biometric fields where data collection is challenging. In this study, we used only the CEDAR dataset as the experimental data. As an initial study on handwritten signature image generation, we focused on generating alphabetic handwritten signatures, which are widely used and accessible, and therefore employed the CEDAR dataset. However, since the signatures included in the CEDAR dataset do not reflect the characteristics of all alphabetic handwritten signatures, improvement in verification performance is not guaranteed across all datasets. This is a limitation of our study. Future research will aim to extend the model to generate signatures in various languages, and we intend to collaborate with other research groups to validate our model across multiple signature image databases. Another limitation is the large number of signature images required to train the generation model. To address the challenge of collecting a substantial number of user signatures in real applications, we intentionally used only half of the CEDAR dataset for training. Nevertheless, 12 original and 12 forged signatures per class were used, which may still be too many for practical applications. In future studies, we plan to address this issue by improving our model based on well-established few-shot learning algorithms. Conceptualization, D.-J.H.