# Hole Concealment Algorithm Using Camera Parameters in Stereo 360 Virtual Reality System
## 4 Simulation Results
### Objective Performance  
The objective performances of the concealment algorithms were evaluated with common measures like the structural similarity (SSIM) [35], peak-to-peak signal-to-noise ratio (PSNR) [36], and consumed CPU time. All experiments are run on the CPU based on AMD Ryzen 3.40 GHz and 32-GB RAM. The SSIM and PSNR are the average values of the SSIM and PSNR values for the red, green, and blue components. SSIM is in the range of 0-1. As the values of SSIM and PSNR increase, the quality of the resulting image increases. Note that SSIM and PSNR can be evaluated when the reference pictures are given, as in Figures 10 and 11 and Figures 12 and 13. On the other hand, the CPU times consumed by the methods were checked using a personal computer. The CPU time was measured with the resolution of a second. As the CPU time depended on the complexity of the algorithm, the technique consuming the smallest CPU time was considered the simplest method. The outdoor pictures (Mozart Hall) shown in Figures 10 and 11 are evaluated in Tables 1 and 2, where the best and 2 nd best results are represented with red and blue numbers, respectively. As seen in Table 1, the proposed algorithm produced the best quality from the viewpoints of both the SSIM and PSNR. Theipaint [34] had the 2 nd best quality for both SSIM and PSNR. The \"simple copy\" required the smallest CPU time, because it filled the hole just by copying the same size block of the other view. The proposed algorithm is one of the simplest algorithms in the consumed time. When the method of [PERSON] [19] was used, the consumed CPU time could not be measured because the training time was huge and depended on the quantity of the training data. Table 2 shows the performances of the proposed algorithm for a variety of sizes of neighboring blocks \(\{B_{R}^{l},\ B_{R}^{r},\ B_{L}^{l},\ B_{L}^{r}\}\), where the numbers in the first column denote the ratio between the widths of neighboring block \(B_{L}^{l}\) and block \(B_{L}^{c}\) that includes the hole. As observed in this table, the best performance is found when the ratio is 1.5 (i.e., the width of \(B_{L}^{l}\) is 50% wider than that of \(B_{L}^{c}\)). When the size of the neighboring blocks is small (the ratio is under 1.5), the performance of the proposed algorithm increases with the size, because the accuracy of \(H(B_{L}^{c}\to B_{R}^{c})\) increases as the number of pixels utilized to derive it increases. However, when the size is large (the ratio is over 1.5), the neighboring blocks include fractions of multiple pictures, which degrades the accuracy of \(H(B_{L}^{c}\to B_{R}^{c})\). In this table, the complex \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Method** & **SSIM** & **PSNR (dB)** & **Time (s)** \\ \hline Bertalmio [16] & 0.6483 & 19.6982 & 12.9177 \\ [PERSON] [17] & 0.6320 & 16.5155 & 13.1796 \\ [PERSON] [18] & 0.4406 & 17.0804 & 30346 \\ [PERSON] [19] & 0.2381 & 17.3725 & N/A \\ Glisoft [33] & 0.7427 & 24.6347 & 2.1600 \\ Theinpaint [34] & 0.7701 & 25.0058 & 28.1900 \\ Simple copy & 0.6196 & 21.1793 & 0.0160 \\ Proposed algorithm & 0.7954 & 25.4479 & 7.3261 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison between performances of various methods for outdoor pictures (Mozart Hall). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Width Ratio** & **SSIM** & **PSNR (dB)** & **Time (s)** \\ \hline
1.0 & 0.7491 & 24.1525 & 5.4439 \\
1.2 & 0.7585 & 24.4355 & 6.3663 \\
1.5 & 0.7954 & 25.4479 & 7.3261 \\
1.75 & 0.7614 & 24.6553 & 8.0263 \\
2.0 & 0.5986 & 19.8681 & 8.8201 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Performances of proposed method according to the size of the neighboring blocks for outdoor pictures (Mozart Hall). ity increases with the width of the neighboring blocks, because the number of pixels to be considered in making \(H(B_{L}^{I}\to B_{R}^{I})\) and \(H(B_{L}^{r}\to B_{R}^{r})\) increases. Tables 3 and 4 show the simulation results for the indoor pictures (Hallway) shown in Figures 12 and 13.