# Face De-Identification Using Convolutional Neural Network (CNN) Models for Visual-Copy Detection
## 3 Proposed Methods
### Face-De-Identification Model using D2 GAN  
This section describes the de-identification model that employs the D2 GAN model proposed in this study, as illustrated in Figure 3. In contrast to the feature-inversion model, which requires two sets of data--images and corresponding bounding-box labels--for training, face de-identification using the D2 GAN model requires three components: the original image, the bounding-box labels, and images with the face regions blurred using a Gaussian filter. The original images are represented by \(x_{orin}\), serving as a basis for learning how to generate de-identified versions and ensuring the model accurately captures and retains the essential visual information of each face. The generator \(G\) utilizes an input vector, which is denoted by \(z\), from the latent space, to produce de-identified facial images. This allows for a diverse range of outputs from a single-input image through the manipulation of \(z\). The D2 GAN model is designed to mitigate mode collapse by using two discriminators. The first discriminator discerns whether the image is real or synthetic, whereas the second distinguishes between the original and the de-identified image, similar to a conventional GAN. The generator used in this context is the renowned ResNet generator network. The ResNet-based generator network is structured to transform input images into de-identifiedversions while preserving essential features of the original image. It employs a series of downsampling, residual blocks, and upsampling layers. This architecture ensures the preservation of crucial visual information and maintains the integrity of the original image during the de-identification process. Equation (4) represents the loss function of the discriminator \(D_{RF}\) that determines whether an input image is real or fake. In this equation, \(G\) denotes a generator that creates de-identified face images, while \(D_{RF}\) signifies a discriminator that discerns whether an image is real or fake. The loss is updated by computing the operation as outlined in Equation (4):  
\[L_{D_{RF}}=-(\mathbf{E}_{x_{min}}[\log D_{RF}(x)+\mathbf{E}_{z}\log(1-D_{RF}(G (z)))]) \tag{4}\]  
Equation (5) depicts the loss function of the discriminator \(D_{OD}\) that distinguishes between the original and de-identified images. In this equation, similar to Equation (4), \(G\) denotes a generator that creates de-identified face images, while \(D_{OD}\) signifies a discriminator that discerns whether an image is original or de-identified. The de-identified images produced by the generator \(G\) are represented by \(z\), and are used alongside original images to train \(D_{OD}\) in distinguishing between original and altered facial features. The loss is updated by computing the operation as outlined in Equation (5):  
\[L_{D_{OD}}=-\big{(}\mathbf{E}_{x_{did}}[\log D_{OD}(x)+\mathbf{E}_{z}\log(1-D_ {OD}(G(z)))]\big{)} \tag{5}\]  
The Real vs. Fake Discriminator (\(D_{RF}\)) is tasked with differentiating between real face images and those generated by the generator. It plays a crucial role in assessing  
Figure 3: Model structure of face de-identification using D2 GAN. This structure illustrates the stages of detecting and cropping faces from the original image, followed by a de-identification process that generates transformed facial images. The generated de-identified facial images are then overlaid onto the original full image to create the final de-identified image. The de-identification process utilizes two discriminators to distinguish between real and fake images and to assess the authenticity of the face region de-identification. The model is optimized to minimize a comprehensive loss function, which includes the losses from the two discriminators, the feature similarity between the original and de-identified full images, and the generator’s loss. the authenticity of the images produced during the training process.