# Identifying Synthetic Faces through GAN Inversion and Biometric Traits Analysis
## 4 Experimental Setup and Analysis of Results
### Classification Results
Figure 10: Visualization of \(FN_{512}\) and \(LM_{68}\) differential feature vectors through the UMAP dimensionality reduction. Figure 9: Plots above visualize the histograms of the distributions of the landmarks of different areas of the face for the different datasets. The full set of landmarks shows better discrimination capability. The results obtained with different types of differential vectors are reported in the following Table 2a-d. We first tested the datasets of real images individually against the _SG2_ data (indicated as * vs. _SG2_), as well as their union (indicated as _All_ vs. _SG2_), yielding six different settings reported row-wise in the tables. We observe that the SVM provides, on average, better results, and also in front of limited computational complexity. In addition, we verified that the Radial Basis Function (RBF) kernel with hyperparameter \(C=1\) consistently yields the best performance; thus, we select it as the reference model for the following experimental analyses. In terms of computational efficiency, the training time of SVM models is in the order of milliseconds, thus, it is negligible with respect to the inversion time. Interestingly, the landmark-based differential analysis yields substantially higher discrimination capabilities with respect to the FaceNet-based one, despite their generally lower dimensionality. In particular, they perform exceptionally well on the _LFW_ pairs, which are the more critical case for the FaceNet representations. For a better understanding, we report in Figure 11 a comparative visualization of the landmarks detected in the input and reconstructed faces, and we plot them together to visualize the misalignment. It can be seen that the synthetic StyleGAN2 image pairs present almost overlapping landmarks, while the real ones show irregular displacements of individual landmarks. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline  & **SVM** & **RF** & **LR** & **MLP** & **FNN** \\ \hline _FFHQ_ vs. _SG2_ & 80.63 & 76.88 & 70.63 & 70.63 & 79.38 \\ _CelebA_ vs. _SG2_ & 82.28 & 82.91 & 69.62 & 69.62 & 82.91 \\ _CelebHQ_ vs. _SG2_ & 88.05 & 86.16 & 77.99 & 77.99 & 86.79 \\ _LFW_ vs. _SG2_ & 76.88 & 74.38 & 71.25 & 73.13 & 75.63 \\ _Caltech_ vs. _SG2_ & 89.38 & 81.88 & 81.25 & 81.25 & 83.13 \\ _All_ vs. _SG2_ & 78.13 & 75.00 & 71.88 & 73.13 & 77.50 \\ \hline \hline  & **SVM** & **RF** & **LR** & **MLP** & **FNN** \\ \hline _FFHQ_ vs. _SG2_ & 81.88 & 78.75 & 73.75 & 73.13 & 80.00 \\ _CelebA_ vs. _SG2_ & 88.61 & 84.81 & 83.54 & 81.01 & 88.61 \\ _CelebHQ_ vs. _SG2_ & 86.79 & 84.91 & 81.13 & 79.25 & 86.16 \\ _LFW_ vs. _SG2_ & 79.38 & 78.13 & 77.50 & 72.50 & 81.25 \\ _Caltech_ vs. _SG2_ & 85.63 & 83.75 & 85.00 & 86.25 & 86.25 \\ _All_ vs. _SG2_ & 78.13 & 78.75 & 76.88 & 76.25 & 78.75 \\ \hline \hline  & **(b)**_FN\({}_{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{ \text{\text{\text{\text  
In general, the \(FFHQ\) pairs seem to be the harder ones to distinguish from \(SG2\) pairs also for landmark-based features, possibly because the former were employed for training the StyleGAN2 generator. This is also observed in Figures 12 and 13, where the ROC curves of the different classification scenarios and feature representations are reported. Even if the results are very good in all cases, Table 3 shows that AUC values for the \(LM_{68}\) and \(LM_{136}\) case remain lower for the \(FFHQ\) data with respect to other real images. Figure 11: Visualization of the landmarks detected on the input and the reconstructed images from different datasets. In each case, the left image is the input one with the detected landmarks marked in blue, and the central one is the corresponding reconstruction with the detected landmarks marked in red. On the right, the two sets of landmarks are reported on the same spatial grid, so that their displacement can be visualized.