# PSDFH: A Phase-Space-Based Depth from Hologram Extraction Method
## 4 Experimental Results
### Depth Estimation Results  
To evaluate the depth estimation performance of our proposed method, three experiments illustrated in Figure 9 are conducted:  
* Without ROI: in this experiment, the depth extent in Equation (25) spans the interval \([0,z]\), where \(z\) is the maximum possible depth value set to 0.20 cm in the experiment. * With ROI: in this second experiment, the depth extent in Equation (25) is reduced to the interval \([z_{\min},z_{\max}]\) where \(z_{\min},z_{\max}\) are the maximum and minimum depth values present in the extracted ROI. * With refined ROI: in this third experiment, the depth extent in Equation (25) is reduced to a fixed-size interval of size \(N_{z}+1\) centered on the minimal representation lines extracted from the initial ROI using the iterative method. Figure 8: An illustrative example of the importance of color blending. The segmentation masks made for each color channel contain small defects, which lead to a bad extraction of the regions of interest because the points that are defined on the segmentation defects will not be selected. By unifying the results produced by the different color channels, imperfections related to segmentation performance can be bridged, and a greater number of points are included in the extracted regions of interest. Those experiments have two objectives: (1) to assess the quality of the extracted regions of interest (ROIs), as any degradation of the ROI can negatively impact the DFF method, especially if a few scene points fall within it, and (2) to evaluate the efficiency of the iterative method by aiming to produce an estimate that is as close as possible to the ground truth. This is crucial in order to minimize the number of reconstruction planes required for the DFF, specified by \(N_{z}\). In our experiments, the DFF method was performed using the six most performing focus measures in [8] and detailed in Table 3. The operators used are highly parallelizable and offer a good compromise between performance and speed.We evaluated the performance of each focus measure using the \(\ell_{1}\) norm between the predicted and ground truth depth maps used by the layer-based method. Table 4 gives the obtained results with and without the proposed ROI approach, Figure 10 gives the obtained results with an additional ROI refinement step using the iterative method with different \(N_{z}\) values, and Figure 11 gives some visual results. First, we can observe that the WAVR, WAVV, and GLVA operators are the best focus measure operators for the without ROI case. The FM performance varies depending on the processed scene, with a mean \(\ell_{1}\) norm of roughly 15 reconstruction planes. Performance may be lower if the scene contains many flat areas with no texture variation. The focus operators generally work best on regions with high texture variances such as edges and corners. Second, using extracted regions of interest results in improved performance, with gray-level variance-based operators being the most optimal. This is because the depth extent used in Equation (25) is reduced, providing a more accurate estimate of the depth of each pixel. The performance variance between the first and second cases may be due to the quality of the extracted ROI or to multiple extremum values present in the focus curve. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Focus Operator** & **Abbr.** & **Focus Operator** & **Abbr.** \\ \hline Variance of & & & \\ Laplacian [18] & LAPV & Image contrast [19] & CONT \\ Variance of wavelet & & & \\ coefficients [20] & WAVV & Ratio of the wavelet & \\ Gray level variance [21] & GLVA & & \\  & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Abbreviations of focus measure operators used in the experiments.