# Feature Detection of Focused Plenoptic Camera Based on Central Projection Stereo Focal Stack
## 4 Experiments
### Simulated Experiments
#### 4.1.2 Relation between Layer Distance in CPSFS and Detected Results  
The purpose of the experiment in this part is to verify the relationship between layer distance selected in CPSFS and feature detection results. To simplify the problem, the detection method with two-layer CPSFS is used during the experiment. The simulated parameters of the camera are shown in Table 1 and we use the textured pictures to simulate the plane targets. The evaluated indicators include detection speed, and the number and depth accuracy of detection points. During the experiment, the planar target is placed at a fixed position away from the camera and perpendicular to the optical axis, which will form an imaging plane at the position with plenoptic disc radius \(R_{gt}\). Two refocus planes in the CPSFS are selected at \(R_{gt}+\Delta R/2\) and \(R_{gt}-\Delta R/2\) respectively. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \(f_{L}\) (mm) & \(b\) (mm) & \(B\) (mm) & \(g_{x}\)(\(\mu\)m) & \(s_{y}\)(\(\mu\)m) & \(f_{m1}\)(mm) & \(f_{m2}\)(mm) & \(f_{m3}\)(mm) \\ \hline \(100\) & \(-104.5\) & \(-1.32\) & \(5.5\) & \(5.5\) & \(1.62\) & \(1.92\) & \(2.35\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulated parameters of multi-focus plenoptic camera. \((s_{x},s_{y})\) stands for the physical size of a pixel in raw image. \(f_{m1},f_{m2}\), and \(f_{m3}\) represent the focal lengths of three types of micro-lenses. We change the value of \(\Delta R\) within the range \(\{\Delta R|\Delta R=0.5i,i=1,\dots,12\}\) and observe the change of the detection results. For generality of the results, we carry out 20 independent feature detection experiments on 20 different simulated raw images for each \(\Delta R\). The evaluation indexes include the total number of detected features, the mean errors of the detected features' plenoptic disc radii, the root mean square errors (RMSEs) of the detected features' plenoptic disc radii, and the detection time. Besides, we repeat the above experiment 3 times with the \(R_{gt}\) set to \(-4\), \(-8\), and \(-12\), respectively. The other parameters used are set as \(d=1/2,\theta_{R}=5\). The results are presented in Figure 8.  
Figure 6: Simulated results of refocusing experiment. (**a**) Simulated raw image with vignetting. (**b**) Simulated raw image without vignetting. (**c**) Traditional refocused image at \(v_{F}=-6\). (**d**) Traditional refocused image at \(v_{F}=-12\). (**e**) Our refocused image at \(R_{F}=-5.64\). (**f**) Our refocused image at \(R_{F}=-10.54\). It can be seen that the trends of three curves in Figure 8 are similar, which reflects the general relationship between layer distance of CPSFS and detected results. When the positions of two refocus planes are close to the \(R_{gt}\) (\(\Delta R\) is smaller), both the number of detected feature points and the RMSE of the detected features' plenoptic disc radius are large. This is because the closer the refocusing planes are to \(R_{gt}\), the clearer the refocusing image, which makes it easier to detect more feature points. However, at the same time, the parallax among the central projection stereo refocused image pair is relatively small, which leads to the increase of calculation error in plenoptic disc radius. As can be seen from Figure 8b, the mean error is close to 0, which indicates that the proposed algorithm is unbiased. Figure 8d illustrates that the proposed algorithm is time efficient and the mean detection time of each frame is about 20 s. The example of detection result is illustrated in Figure 9.  
Figure 8: Detected results of proposed algorithm using 2-layer central projection stereo focal stack (CPSFS) on simulated raw images. (**a**) The number of the detected features. (**b**) Mean error of detected features’ plenoptic disc radius (dimensionless). (**c**) Root mean square error (RMSE) of detected features’ plenoptic disc radius (dimensionless). (**d**) Total detection time of 20 independent experiments. Figure 7: Reconstructed results of simulated experiment.