# Use of Generative Adversarial Networks (GAN) for
## 2 Methods and Samples
### Phase 2: GAN-Augmented Sampling and Model Testing  
Subsequently to the parameter and model testing, the most successful combinations of model-function-optimizer were selected and used as the protocol for the complete model analysis with image augmentation. For this last stage, the original highly unbalanced sample was augmented with GAN. Given that, originally, they were between five and eight times smaller than the cut mark subsample, we artificially augmented only the tooth mark and trampling mark datasets by adding 500 images for each category. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Model** & **Function** & **Optimizer** & **Accuracy** & **Loss** & **F1-Score** \\ \hline \hline \multicolumn{2}{c}{VGG16} & & & & \\  & relu & SGD & 95.83 & 0.214 & 0.73 \\  & swish & SGD & 95.83 & 0.286 & 0.67 \\  & mish & SGD & 95.31 & 0.245 & 0.67 \\  & relu & [PERSON] & 96.35 & 0.247 & 0.65 \\  & swish & [PERSON] & 95.31 & 0.246 & 0.77 \\  & mish & [PERSON] & 96.35 & 0.258 & 0.69 \\ \hline \multicolumn{2}{c}{Densenet 201} & & & & \\  & relu & SGD & 94.27 & 0.2 & 0.67 \\  & swish & SGD & 93.75 & 0.206 & 0.63 \\  & mish & SGD & 95.31 & 0.185 & 0.67 \\  & relu & [PERSON] & 95.31 & 0.162 & 0.71 \\  & swish & [PERSON] & 93.75 & 0.224 & 0.64 \\  & mish & [PERSON] & 89.06 & 0.395 & 0.65 \\ \hline \multicolumn{2}{c}{Jason2} & & & & \\  & relu & SGD & 96.35 & 0.133 & 0.69 \\  & swish & SGD & 95.38 & 0.16 & 0.7 \\  & mish & SGD & 96.35 & 0.126 & 0.68 \\  & relu & [PERSON] & 94.79 & 0.194 & 0.76 \\  & swish & [PERSON] & 93.75 & 0.224 & 0.69 \\  & mish & [PERSON] & 95.83 & 0.212 & 0.71 \\ \hline \multicolumn{2}{c}{Resnet 50} & & & & \\  & relu & SGD & 97.92 & 0.112 & 0.8 \\  & swish & SGD & 98.44 & 0.058 & 0.77 \\  & mish & SGD & 97.92 & 0.104 & 0.69 \\  & relu & [PERSON] & 95.83 & 0.124 & 0.76 \\  & swish & [PERSON] & 97.4 & 0.074 & 0.71 \\  & mish & [PERSON] & 97.92 & 0.147 & 0.67 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Accuracy and loss of the four selected sequential and parallel models, according to combination of activation function and optimizer. In order to generate images for each class, two main requirements were to be fulfilled. First, the generated images should be large enough to be fed to the discriminator. On the other hand, in order to train the algorithm, few images were made available. Despite that modern image generation models complying with these two requisites do exist, as the recently published F2 GAN [27], technical constraints made this and other approaches, such as DAGAN [28] non-viable. As a result, in order to tackle the problem, a divide and conquer strategy was adopted: a simple GAN for creating high-fidelity low-resolution images and a super resolution GAN (SRGAN) that would upscale the generated images into a resolution optimum to train the model. Regarding the GAN, a simple approach was taken, using a simple GAN [11], but with small modifications. In the case of the generator, the initialization of the input vector followed a standard normal distribution. This vector was convolved into a squared array with 128 channels and width 64. After a LeakyReLU activation, the data were convolved and upsampled using a Conv2 DTranspose layer, normalized using batch normalization, and then activated with a LeakyReLU. This process was done twice, using a momentum of 0.8 in batch normalization and an alpha of 0.2 in LeakyReLU in both cases. As a result, the generation returned 64 \(\times\) 64 grayscale images (Figure 1). In order to train the discriminator, both real and fake images were used, applying a sequence of convolution, LeakyReLU, and a dropout at a rate of 0.5. This process was done four times. Including the dropout layer is a small change from the original implementation, which avoided the discriminator to learn the images and create overfitting or chances of collapse mode, improving the model's performance. For the generation of trampling and tooth marks, the GAN was run through 7000 epochs of training. After this, the model ended up generating realistic images (Figure 2).