## 3 Results
### Objective Quality Comparison  
In order to objectively evaluate the quality of the generated virtual viewpoint images in Figure 12, the Structural Similarity Index (SSIM) and the Peak Signal to Noise Ratio (PSNR) were adopted. The SSIM measures the similarity between the ground truth image and the virtual viewpoint image from brightness, contrast and structure, respectively. Its value range is  
Figure 11: Different types of virtual viewpoint images rendered by the method in this paper. Figure 12: Rendered virtual viewpoint images. (**a**) Input images; (**b**) The partial enlarged images of the contents in red boxes in (**a**); (**c**) The true images of virtual viewpoint images (**d**,**e**); (**d**) Virtual viewpoint images generated by the method of [58]; (**e**) Virtual viewpoint images generated by the method in this paper. [0, 1], and the larger the value is, the smaller the image distortion is. The expression is as follows:  
\[SSIM(X,Y)=l(X,Y)\times c(X,Y)\times s(X,Y) \tag{15}\]  
where \(X\) is the virtual viewpoint image, \(Y\) is the ground truth image. \(l(X,Y)\), \(c(X,Y)\) and \(s(X,Y)\) are the brightness similarity, contrast similarity and structure similarity of the image, respectively, and the expressions are as follows:  
\[l(X,Y)=\frac{2\mu_{X}\mu_{Y}+C_{1}}{\mu_{X}^{2}+\mu_{Y}^{2}+C_{1}} \tag{16}\]  
\[c(X,Y)=\frac{2\sigma_{X}\sigma_{Y}+C_{2}}{\sigma_{X}^{2}+\sigma_{Y}^{2}+C_{2}} \tag{17}\]  
\[s(X,Y)=\frac{\sigma_{XY}+C_{3}}{\sigma_{X}\sigma_{Y}+C_{3}} \tag{18}\]  
where \(\mu_{X}\) and \(\mu_{Y}\) are the mean value of \(X\) and \(Y\), respectively, \(\sigma_{X}\) and \(\sigma_{Y}\) are the variances of \(X\) and \(Y\), respectively, and \(\sigma_{X}\sigma_{Y}\) are the covariances of \(X\) and \(Y\). The _PSNR_ is the inter-pixel error, and the larger the value is, the smaller the image distortion is. The expression is as follows:  
\[PSNR=10\log_{10}\left(\frac{(2^{n}-1)^{2}}{MSE}\right) \tag{19}\]  
where \(n\) is the number of bits per pixel, which is generally set as 8; \(H\) and \(W\) are the height and width of the image, respectively; \(MSE\) is the mean square error of virtual view image \(X\) and ground truth image \(Y\), and the expression is as follows:  
\[MSE=\frac{1}{H\times W}\sum_{i=1}^{H}\sum_{j=1}^{W}\left(X(i,j)-Y(i,j)\right)^ {2} \tag{20}\]  
The SSIM values and _PSNR_ values of true images and virtual viewpoint images generated by different methods in Figure 12 are calculated, respectively, as shown in Table 1. It can be seen from the values in Table 1 that the virtual viewpoint images rendered by the method in this paper are of high similarity and with small inter-pixel error. To prove that the proposed method can be used to generate high-quality virtual view images and is suitable for various scenarios, 3D image sequences of ballet and breakdancers provided by Microsoft Research Asia were used to evaluate the proposed method. In the experiment, the proposed method was compared with other excellent methods, and the Root Mean Squared Error (RMSE), SSIM and PSNR were selected as evaluation indexes. The results are shown in Tables 2 and 3. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Virtual Viewpoint Images** & **Method** & **SSIM** & **PSNR** \\ \hline Image1 & [58] & 0.8319 & 26.54 \\  & Ours & 0.8742 & 30.45 \\  & [58] & 0.8517 & 27.10 \\  & Ours & 0.8933 & 30.79 \\  & [58] & 0.8378 & 26.85 \\  & Ours & 0.8825 & 29.87 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: SSIM and PSNR of true images and virtual viewpoint images generated by different methods. As can be seen from Tables 2 and 3, the performance of the proposed method in the three evaluation indexes was outstanding. The error was lower than other algorithms, and the accuracy was higher than most other algorithms. In [7], the binocular view image was used to generate the virtual view image, and the occluded area was inpainted by the fusion of left and right view images.