# PSDFH: A Phase-Space-Based Depth from Hologram Extraction Method
## 4 Experimental Results
### Phase Space Segmentation  
In the following, we analyze the binary phase masks extracted in the second step of our method. The Dice and Jaccard metrics [17] are used to evaluate the quality of the overlap between the predicted binary mask and the ground truth. Table 2 gives the results obtained for the test and validation set.  
From the obtained results, we can see that for the test part, the network has an overall accuracy of 95%. This performance drops by 5% on the validation set, but the general performance remains high enough to hope for good results in the next steps of the algorithm. The low difference in segmentation performance between the validation and test set suggests that the network is not subject to overfitting, which can occur when the network is over-parameterized and the amount of data is not sufficient.  
A bad segmentation performance leads to a bad estimation of the phase space representation. Therefore, fewer candidate points can be extracted during the back projection  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Object 1** & **Object 2** & **Object 3** & **Object 4** & **Object 5** \\ \hline Piano & 0.044/0.054/0.052 & 0.023/0.017/0.01 & & & \\ \hline Table & 0.039/0.026/0.038 & 0.018/0.037/0.016 & 0.016/0.037/0.018 & 0.018/0.037/0.016 & 0.016/0.037/0.018 \\ \hline Woods & 0.03/0.045/0.03 & 0.021/0.046/0.023 & 0.034/0.032/0.028 & 0.025/0.042/0.025 & 0.031/0.042/0.022 \\ \hline Dice & 0.02/0.017/0.021 & 0.028/0.029/0.034 & 0.023/0.025/0.028 & 0.0512/0.0512 & \\ \hline Cars & 0.085/0.014/0.052 & 0.082/0.016/0.052 & 0.049/0.025/0.082 & 0.046/0.03/0.073 & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Scene object sizes along the X/Y/Z, in centimeters.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Piano** & **Table** & **Woods** & **Cars** & **Dice** \\ \hline Dice & 0.97 & 0.97 & 0.98 & 0.94 & 0.94 \\ \hline Jaccard & 0.94 & 0.94 & 0.96 & 0.89 & 0.88 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Segmentation metric for the test (piano, table, woods) and validation set (cars, dice).  
operation, and some scene points may not be included in the extracted ROIs as shown in Figure 8. By using multiple color channels those areas that are missing on one color channel can be filled in on another channel. It is therefore important but not mandatory when processing RGB holograms to merge the extracted ROIs. The merged ROIs can be projected back into a selected color channel phase space representation and used as a target for the iterative algorithm. More formally,  
\[R_{b}=\mathcal{G}_{\theta}\{(\mathbb{R}e\{L_{R}\},\mathbb{I}m\{L_{R}\})\}, \tag{28}\]  
\[G_{b}=\mathcal{G}_{\theta}\{(\mathbb{R}e\{L_{G}\},\mathbb{I}m\{L_{G}\})\}, \tag{29}\]  
\[B_{b}=\mathcal{G}_{\theta}\{(\mathbb{R}e\{L_{B}\},\mathbb{I}m\{L_{B}\})\}, \tag{30}\]  
\[\hat{\mathcal{P}}=\bigcup_{M\in\{R_{b},G_{b},B_{b}\}}ROI(M), \tag{31}\]  
\[\hat{M}_{b}=\Omega(\hat{\mathcal{P}}), \tag{32}\]  
where \(R_{b},G_{b}\), and \(B_{b}\) are the estimated phase space representation for each color channel. Their mappings in the 2D space are unified by selecting all the points that fall in at least one of the three mappings and projected back into phase space using a single color channel. The set of candidate points \(\hat{\mathcal{P}}\) and its projection \(\hat{M}_{b}\) are used as input to the iterative algorithm.