## 6 Conclusions, Limitations and Future Research  
In this research, we addressed the limitation of annotated forged data for training models, compared to other computational approaches that rely on annotated or large datasets. The high cost and significant effort required to create and annotate forged data, which demands expert knowledge, have hindered the performance of supervised learning models. We contributed to the literature by training adversarial models using RTI data to capture an artist's unique brushstroke style. Our results demonstrated the potential of adversarial networks leveraging in-depth information to detect forgeries at an early stage. We proposed an oil painting brushstroke forgery detection method by simultaneously training a conditional generator and discriminator model on the original artist's brushstroke style's depth information. We analyzed the differences between the frequencies of the generated 3D representation of the brushstroke image patches based on RTI technique and their corresponding GT RTI on unseen oil paintings. The presented approach enabled patch-level brushstroke counterfeit identification based on the trained discriminator model. Results illustrated the capability of our approach to discriminate the forged sample from the original one, as well as detecting the novel forged painting which had no original sample and was created based on the artist's original brushstroke style with imaginary novel content. Both approaches including dissimilarity frequency analysis and trained discriminator models evaluated authentication of the paintings that were used neither during the training nor validation. Hence, our approaches were able to detect unknown contemporary counterfeit oil paintings of the aimed artist which was claimed to be original. Moreover, in contrast to previous applications of the GANs, the positive potential of GANs was demonstrated in this context as an artificial artist that learned depth information of the artist's unique brushstroke style. This study is presumably the first to use conditional GANs trained on brushstroke depth information for oil painting forgery detection. Although quantitative evaluation of the model demonstrated promising results, further improvements could be achieved by finding the best match between RTI modes and different \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Models’ Name** & **Accuracy** & \begin{tabular}{c} **Average** \\ **Precision** \\ \end{tabular} & \begin{tabular}{c} **Macro Average** \\ **Precision** \\ \end{tabular} & \
\begin{tabular}{c} **Macro Average** \\ **Recall** \\ \end{tabular} &
\begin{tabular}{c} **Macro Average** \\ **F1-Score** \\ \end{tabular} \\ \hline PatchGAN & 0.82 & 0.72 & 0.86 & 0.82 & 0.82 \\ \hline ImageGAN & 0.77 & 0.69 & 0.85 & 0.78 & 0.77 \\ \hline PixelGAN & 0.50 & 0.50 & 0.54 & 0.50 & 0.33 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Models’ performances evaluation for identification of counterfeit artist’s unique brushstroke style at the scale of patches. Figure 6: Comparison of various discriminator models’ performances based on ROC curve. The red dashed line serves as a baseline reference for evaluating the performance of the discriminator model. networks' architectures. Additionally, for future studies, enhancing discriminator models could significantly improve the overall approach, from generating depth information to detecting painting forgeries. Conceptualization, E.A., A.A. and J.A. ; methodology, E.A. ; validation, E.A. and A.A.; investigation, E.A. ; resources, E.A. ; data curation, E.A. ; writing--original draft preparation, E.A. ; writing--review and editing, E.A. and J.A. ; supervision, A.A. and J.A. All authors have read and agreed to the published version of the manuscript. This research was funded by the Ministry of Culture, Sports, and Tourism (MCST) and the Korea Creative Content Agency (KOCCA) through the Culture Technology (CT) Research Development Program for the year 2021.