## 2 Methodology
### SynthSecureNet Architecture Network Development  
The input to the SynthSecureNet model is a video, which undergoes further preprocessing and is converted into a sequence of frames. The input video is denoted by V, whereas N represents the number of frames in it; refer to the following Equation (5):  
\[V=\{f_{1},\ f_{2},\ldots,\ f_{N}\} \tag{6}\]  
where \(f_{i}\) is an image (each frame). In a preprocessing phase, before exposure to the model, the frame (or stack of frames) goes through data augmentation processing that increases training sample diversity and improves generalization. Some of these techniques that were used in augmentation include the following [18]:  
1. Random flipping;
2. Random zooming;
3. Random brightness adjustment;
4. Random rotation. For better explanation purposes, we denote an augmented frame as \(f_{i}^{aug}\). In the feature extraction phase of the proposed system, the augmented frames were then passed through MobileNetV2 and ResNet50V2 to extract the features. These models were initialized with pre-trained weights of what is commonly known as ImageNet dataset [29]. MobileNetV2 is made up of a series of depthwise separable convolutions and inverted residual blocks. The output of the MobileNetV2 model for the frame \(f_{i}^{aug}\) is denoted as follows:  
\[f_{m}\left(f_{i}^{aug}\right)=MobileNetV2\left(f_{i}^{aug}\right) \tag{7}\]  
where the feature map \(f_{m}(f_{i}^{aug})\) has the shape of \((l_{m},\ w_{m},\ c_{m})\), where \(h_{m}\), \(w_{m}\), and \(c_{m}\) are the height, width, and number of channels, respectively. Given that the ResNet50V2 model is made up of a sequence of residual blocks, each block learns a residual function. The output of this ResNet50V2 model for the frame \(f_{i}^{aug}\) can be written as follows:  
\[f_{r}\left(f_{i}^{aug}\right)=ResNet50V2\left(f_{i}^{aug}\right) \tag{8}\]  
where the feature map \(f_{r}(f_{i}^{aug})\) has the shape of \((h_{r},\ w_{r},\ c_{r})\), where \(h_{r}\), \(w_{r}\), and \(c_{r}\) are the height, width, and number of channels, respectively. The final feature map is acquired by concatenating feature maps from MobileNetV2 and ResNet50V2 along the channel dimension. The concatenation operation can be represented as follows:  
\[f_{c}\left(f_{i}^{aug}\right)=concat\left(f_{m}\left(f_{i}^{aug}\right),\ f_{r}\left(f_{i}^{aug}\right)\right) \tag{9}\]  
The resulting feature map \(f_{c}(f_{i}^{aug})\) has the shape of \((h_{c},\ w_{c},\ c_{c})\), where \(h_{c}=min(h_{m},\ h_{r})\), \(w_{c}=min(w_{m},\ w_{r})\), and \(c_{c}=c_{m}+c_{r}\). The concatenated feature map \(f_{c}(f_{i}^{aug})\) is passed through additional layers to learn higher-level representations and perform classification [34]. Then the flattened layer con verts the spatial feature map into a 1D vector. The output of the flattened layer can be represented as follows:  
\[v_{i}=flatten\Big{(}f_{c}\Big{(}f_{i}^{aug}\Big{)}\Big{)} \tag{10}\]  
where the flattened vector \(v_{i}\) has the shape of \((c_{c}\times h_{c}\times w_{c})\). In dense layers for the proposed model, the flattened vector \(v_{i}\) is passed through a series of dense (fully connected) layers. Each dense layer applies a linear transformation followed by a non-linear activation function like ReLU. The output of the \(j\)-th dense layer can be represented as follows:  
\[d_{j}(v_{i})=ReLU\big{(}W_{j}\bullet v_{i}+b_{j}\big{)} \tag{11}\]  
Here, \(W_{j}\) and \(b_{j}\) are the learnable weights and biases of the \(j\)-th dense layer, respectively. Dropout is implemented for regularization where some of the neurons/synapses are omitted randomly during the training process in a given iteration to overcome overfitting. The output of the dropout layer can be represented as follows:  
\[d_{j}^{drop}(v_{i})=dropout\big{(}d_{j}(v_{i}),\ rate\big{)} \tag{12}\]  
where rate is the dropout rate, specifying the fraction of units to be dropped.