# Method for Generating Panoramic Textures for 3D Face Reconstruction Based on the 3D Morphable Model
## 4 Experiments and Analysis
### Panoramic Texture Generation Result for 3 DMM-Based 3D Face Reconstruction
#### 4.3.2 Quantitative Evaluation  
Using the texture quality metrics, the peak signal-to-noise ratio (PSNR) and structural similarity (SSIM), we validated the texture quality of the generated textures on the test dataset of the synthetic face dataset. We determined the average difference between the created and actual textures in the dataset. The metrics can be described as follows: PSNR was used to determine the image quality.  
\[\text{PSNR}=10\cdot log_{10}\left(\frac{MAX_{L}^{2}}{MSE}\right) \tag{5}\]  
Here, MAX is the maximum pixel value of an image and MSE is the mean square error. SSIM compares two inputs based on their brightness, contrast and structure.  
\[\text{SSIM}(\text{x},\text{y})=\frac{\left(2\mu_{x}\mu_{y}+c_{1}\right)\left( 2\sigma_{xy}+c_{2}\right)}{\left(\mu_{x}^{2}+\mu_{y}^{2}+c_{2}\right)\left( \sigma_{x}^{2}+\sigma_{y}^{2}+c_{2}\right)} \tag{6}\]  
Here, \(\mu_{x}\) and \(\mu_{y}\) are the means of images X and Y, respectively; \(\sigma_{x}\) and \(\sigma_{y}\) are the standard deviations of images X and Y, respectively; and \(\sigma_{xy}\) is the covariance of image X and Y. \(c_{1}\) and \(c_{2}\) are constants, given as:  
\[c_{1}=\left(K_{1}L\right)^{2}c_{2}=\left(K_{2}L\right)^{2} \tag{7}\]  
where L is the value of the pixel range; \(K_{1}\) = 0.01 and \(K_{2}\) = 0.03.  
Tables 2 and 3 summarize the PSNR and SSIM results, respectively. PSNR is often used to quantify the quality of image reconstruction. The range of PSNR typically ranges from 20-40, with higher values indicating less visual distortion. In addition, SSIM was used to measure the image quality by considering the perceptual qualities of human visual recognition to accurately capture the subjective perception of human eyes compared to PSNR. The SSIM values ranged from 0 to 1; the greater the value, the higher the quality of the photograph. The textures produced by the proposed method appeared to be of greater quality. We evaluated this strategy using a test batch of 5 K facial texture data. In this section, we present the 2D texture production results and 3D face visual effects from various angles. To demonstrate the efficacy of our method, we validated our texture generation results using the Celeb-A dataset, which comprised 202 K photos of celebrity faces captured in the wild. The Chinese University of Hong Kong received all photos from the internet for the Celeb-A dataset. The photographs in this dataset depict a wide range of poses and backgrounds.  
Figure 14 shows the results of 2D texture translation. These findings indicate that our method works well on the Celeb-A dataset. The texture artifact regions caused by self-occlusion in an input single image can be generated by the texture translator to normal face regions, while preserving the same facial features as the input image in the other sections.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**PSNR** & **DECA** & **PRNet** & **3 DDFA\_v2** \\ \hline Original & 31.4363 & 30.2933 & 30.1772 \\ With our module & 31.7625 & 30.7893 & 30.6663 \\ \hline \hline \end{tabular}
\end{table}
Table 2: PSNR comparison result.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**SSIM** & **DECA** & **PRNet** & **3 DDFA\_v2** \\ \hline Original & 0.8495 & 0.7354 & 0.6703 \\ With our Module & 0.8862 & 0.7827 & 0.7612 \\ \hline \hline \end{tabular}
\end{table}
Table 3: SSIM comparison result.  
Figure 15 shows the results of the textured 3D face mesh analysis. The results could successfully maintain high-quality face representation data even when viewed from a perspective different from the input face; thereby indicating that the proposed method is effective for various facial input images captured in natural environments.  
Figure 14: Texture generation result in Celeb-A dataset.  
Figure 15: Texture generation result in Celeb-A dataset.