# High-Precision Depth Map Estimation from Missing Viewpoints for 360-Degree Digital Holography
## 4 Experiment Results and Discussion
### Quantitative Results  
Figure 2(a) shows the loss curve averaged over four objects (torus, cube, cone, and sphere) during training for the HDD model. Then, Figure 2(b) shows the typical trends of _PSNR_ (peak signal-to-noise) of HDD and CDD for the torus, where the \(x\)-axis represents the step number over 90 epochs. In the case of the torus, Figure 2(c) shows the distribution of _ACC_ (accuracy) [28], indicating the similarity between the ground truth depth map and the depth map estimated from HDD and from CDD, where the \(x\)-axis represents the angular degree corresponding to viewpoints (see Figure 1). In addition, Figure 2(d) shows the comparison between _RMSE_ from the HDD and _RMSE_ from CDD for each object. Table 4 shows the performance comparison between HDD and CDD by using various quantitative metrics, for each one that is defined and explained in Equations (S1)-(S9).  
\begin{table}
\begin{tabular}{c c c} \hline Bottleneck & 1 × 1 convolution & [ch = 1104, shape = 20 × 11] \\ \hline \multirow{4}{*}{Decoder (Dense Depth)} & Up-sampling layer & [ch = 552, shape = 40 × 22] \\ \cline{2-3}  & Up-sampling layer & [ch = 276, shape = 80 × 45] \\ \cline{2-3}  & Up-sampling layer & [ch = 138, shape = 160 × 90] \\ \cline{2-3}  & Up-sampling layer & [ch = 69, shape = 320 × 180] \\ \hline Convolution & 3 × 3 convolution & [ch = 1, shape = 320 × 180] \\ \hline Output & Bilinear interpolation & [ch = 1, shape = 640 × 360] \\ \hline
**Dense layer** & **Transition layer** & **Up sampling layer** \\ \hline Batch normalization & Batch normalization & Bilinear interpolation \\ \hline ReLu & ReLu & Skip connection \\ \hline
1 × 1 convolution & 1 × 1 convolution & 3 × 3 convolution \\ \hline Batch normalization & 2 × 2 max pooling & Batch normalization \\ \hline ReLu & - & ReLu \\ \hline
3 × 3 convolution & - & 3 × 3 convolution \\ \hline - & - & Batch normalization \\ \hline - & - & ReLu \\ \hline \end{tabular}
\end{table}
Table 3: _Cont._  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{Models} & \multicolumn{6}{c}{**(a) _SSIM_} & \multicolumn{6}{c}{**(b) _PSNR_ (dB)} \\ \cline{2-9}  & Torus & Cube & Cone & Sphere & Torus & Cube & Cone & Sphere \\ \hline HDD & 0.9999 & 0.9999 & 0.9999 & 0.9999 & 84.95 & 84.42 & 84.90 & 85.03 \\ \hline CDD & 0.9999 & 0.9999 & 0.9999 & 0.9999 & 84.64 & 83.94 & 84.68 & 84.62 \\ \hline \multirow{2}{*}{Models} & \multicolumn{6}{c}{**(c) _ACC_**} & \multicolumn{6}{c}{**(d) _Abs rel_**} \\ \cline{2-9}  & Torus & Cube & Cone & Sphere & Torus & Cube & Cone & Sphere \\ \hline HDD & 0.9933 & 0.9933 & 0.9928 & 0.9965 & 0.022 & 0.018 & 0.022 & 0.017 \\ \hline \multirow{2}{*}{CDD} & 0.9925 & 0.9934 & 0.9926 & 0.9959 & \multirow{2}{*}{0.019} & \multirow{2}{*}{0.017} & \multirow{2}{*}{0.016} & \multirow{2}{*}{0.017} \\  & \(\pm\) 0.0039 & \(\pm\) 0.0027 & \(\pm\) 0.0036 & \(\pm\) 0.0013 & & & \\ \hline \multirow{2}{*}{Models} & \multicolumn{6}{c}{**(e) _Sq rel_**} & \multicolumn{6}{c}{**(f) _RMSE_**} \\ \cline{2-9}  & Torus & Cube & Cone & Sphere & Torus & Cube & Cone & Sphere \\ \hline HDD & 0.0058 & 0.0046 & 0.0058 & 0.0043 & 0.0009 & 0.0007 & 0.0006 & 0.0005 \\ \hline CDD & 0.0062 & 0.0052 & 0.0061 & 0.0047 & 0.0012 & 0.0013 & 0.0008 & 0.0013 \\ \hline \multirow{2}{*}{Models} & \multicolumn{6}{c}{**(g) _LRMSE_**} \\ \cline{2-9}  & Torus & Cube & Cone & Sphere & & & \\ \hline HDD & 0.0114 & 0.0117 & 0.0111 & 0.0110 & & & \\ \hline CDD & 0.0116 & 0.0122 & 0.0113 & 0.0112 & & & \\ \hline \hline \end{tabular}
\end{table}
Table 4: Quantitative comparison of HDD (proposed model) and CDD (reference model). (**a–c**): The higher is better; (**d–g**): The lower is better.  
Figure 3: (**a**) Curve of the loss _MSE_ averaged over all objects during training for the HDD model; (**b–d**) comparison of HDD and CDD using _PSNR_ trend, _ACC_ distribution with ground truth depth map for torus, _RMSE_ difference for all objects after training.