## 4 Experimental Evaluation
### Comparison between Different Objectives  
Considering that in the application of VSNs, there may be different actual requirements for different application scenarios corresponding to different optimization objectives, this section assumes some possible real scenarios and conducts simulation experiments to verify the correctness of the perceptual coverage model and the optimization algorithm. There are three different scenario models, i.e., maximum 1-coverage, maximum 2-coverage, and maximum both 2-coverage and reconstruction quality. We assume that the target space is a 2D plane of \(60\times 60\) m without any obstacle and that the camera type and parameters are the same. In this experiment, the sampling and camera parameters are set as \(\Delta_{b}=5\) m, \(\Delta_{m}=5\) m, \(s_{\varphi}=4\), \(for=37^{\circ}\), \(dof=65\) m.  
The first objective is a simple situation where only a simple monitoring is needed, that is, each point in the target area only needs to be covered by at least one sensor, and no constraints on the reconstruction accuracy are required. Figure 6a shows the effect of using four cameras to achieve the maximum 1-coverage objective, and it can be observed that full coverage is achieved with nearly no overlapping area, avoiding the waste of resources.  
Figure 6: Comparisons of optimal camera placements under different objectives. (**a**) Maximized 1-coverage with four cameras; (**b**) maximized 2-coverage with six cameras; (**c**) maximized 2-coverage and reconstruction quality with four cameras; (**d**) maximize the 2-coverage and reconstruction quality with six cameras. We note that the red, black and blue star symbols represent the space points which are simultaneously covered by no, one and two camera sensors, respectively. Solid blue dots represent cameras, and the blue sector represents the coverage area of the cameras.  
The second objective considers the situation where a larger portion of the target space needs to be covered by at least two sensors while no constraints on the reconstruction accuracy are imposed. The effect of four cameras to achieve 2-coverage was tested, and it was found that the coverage to satisfy 2-coverage could only rise up to 50% at most. Therefore, it was necessary to increase the number of cameras to achieve the 2-coverage objective. Figure 6b shows the effect of using six cameras to achieve the maximum 2-coverage objective. It can be seen that the coverage of the whole target area is good (81% network coverage) and mainly in the middle activity area; however, some sensors are close to each other (e.g., 1 and 6), which may lead to larger reconstruction error in the overlapping areas of their coverage. Since no evaluation metrics for reconstruction error were included, this result is as expected.  
Since the position of a space point can be reconstructed only when at least two camera sensors observe it using the triangulation method, we select the maximum 2-coverage as the third objective because we want to discuss reconstruction quality. Figure 6c,d show the effects of using four and six cameras to achieve the third objective, i.e., maximizing the 2-coverage and reconstruction quality, respectively. As can be seen, the sensor layouts are reasonable, and there are no instances of two cameras in close proximity. Furthermore, it is clear that the coverage with six cameras is superior to the coverage with four cameras. The results of the experiment show that the coverage with four cameras is 48%, while with six cameras it is 75%.