# Research on the Intelligent Modeling Design of a Truck Front Face Driven by User Imagery
## 3 Methods
### Imagery Product Generative Adversarial Network
#### 3.4.3 Overview of the StyleGAN2 Principle and the Interpretation of Equations  
StyleGAN2 is a high-resolution image synthesis model based on generative adversarial networks, which includes multiple generator and discriminator networks. The generator network learns the features and distributions in the dataset, operates on potential vectors, and gradually converts low-resolution images into high-resolution images, ultimately obtaining realistic and high-quality image output. Specifically, the generator network of the StyleGAN2 network adopts a progressive approach for training, which gradually increases resolution from lower-resolution images until the target resolution is reached. In addition, StyleGAN2 also introduces orthogonal regularization technology to constrain the parameters of the generator network to reduce the correlation between parameters, increase the diversity and controllability of the model, and generate images with more diverse features. Therefore, StyleGAN2 is a widely recognized and used efficient and high-quality image synthesis network. It is worth noting that the term \"Style\" in StyleGAN2 does not refer to the artistic style of the dataset image but rather to the characteristic attributes of the dataset image.  
Figure 13: Comparison of the generative effects of two generative networks.  
The overall formula of the StyleGAN2 network is shown in Equation (1):  
\[\underset{\text{G}}{\text{minmax}}\text{V}(\text{G},\text{D})=\text{E}_{\text{x} \sim\text{P}_{\text{data}}}[\text{logD}(\text{X})]+\text{E}_{\text{x}\sim\text {P}_{\text{G}}}[\text{logD}(1-\text{G}(\text{Z}))] \tag{1}\]  
The parameters of the equation are introduced as follows:  
V is the letter specified in the original GAN paper to represent the cross entropy;  
G is a network that generates images and receives random noise Z;  
D is a binary discriminant network that distinguishes between true and false for a given image;  
V(G,D) is the degree of difference between the real sample and the generated image;  
x is a parameter that represents x sample images;  
P\({}_{\text{data}}\) is the distribution interval of real data for all samples;  
log is a logarithm with a natural base e;  
X is a real image, and the corresponding label is 1;  
D(X) represents the probability that x is a real image;  
P\({}_{\text{G}}\) is the distribution interval of all noise-generated data;  
Z is random noise;  
G(Z) is the image generated by a given noise Z, with a corresponding label of 0;  
D(1-G(Z)) is the probability that the D network determines whether the image generated by G is true.  
The loss function formula for generator G is shown in Equation (2):  
\[\widetilde{\text{J}}=-\frac{1}{\text{m}}\sum_{i=1}^{\text{m}}\text{log}\Big{(} \text{D}\Big{(}\text{G}\Big{(}\text{z}^{i}\Big{)}\Big{)}\Big{)} \tag{2}\]  
The loss function formula of discriminator D is shown in Equation (3):  
\[\widetilde{\text{J}}=-\frac{1}{\text{m}}\sum_{i=1}^{\text{m}}\text{log}\text{ D}\Big{(}\text{x}^{i}\Big{)}-\frac{1}{\text{m}}\sum_{i=1}^{\text{m}}\text{log} \Big{(}1-\text{D}\Big{(}\text{G}\Big{(}\text{z}^{i}\Big{)}\Big{)}\Big{)} \tag{3}\]  
The parameters in the equation are introduced as follows:  
m represents a total of m samples;  
i represents the number of iterations of training;  
log is a logarithm with a natural base e;  
x\({}^{i}\) represents any real data;  
D(x\({}^{i}\)) represents the result determined by the discriminator on real data x\({}^{i}\);  
z\({}^{i}\) represents any random data with the same structure as real data;  
G(z\({}^{i}\)) represents false data generated in the generator based on z\({}^{i}\);  
D(G(z\({}^{i}\))) represents the result determined by the discriminator on false data G(z\({}^{i}\));  
D(x\({}^{i}\)) and D(G(z\({}^{i}\))) are both probabilities of the sample being 'true'.