## 3 Sensor Coverage/Deployment in WVSNs
However, in most of the cases, the view angle of the camera is less than 360 \({}^{\circ}\)(e.g., 120 ) and sensing range of the sensor is limited. This makes the sensor coverage problem in WVSN more challenging than the art gallery problem. In [2], we consider a WVSN deployment algorithm with consideration of the sensing range coverage and angle coverage constraints. Optimization-based heuristics are proposed to tackle this problem. From the computational experiments, fewer sensors will be needed in a smaller grid size when in fixed sensing range and span angle. In [17], the angle coverage problem in WVSNs is assessed. When sensors are deployed, the objective is to identify a minimum set of sensors that can capture all the angles of view of the object while fulfilling the image resolution requirements. This paper is about an object tracking system capturing the images of moving targets from all angles. In [18], a visual sensor deployment algorithm, which minimizes the total deployment cost while guaranteeing full multi-perspective (or multi-angle) coverage of the area (i.e., the coverage needed for video panorama generation) and the minimum required resolution is discussed. This multi-angle coverage problem is the same as the all angle coverage problem described in [17]. In both of these works, the occlusion problem is not considered. References [19, 20, 21] discuss the sensor deployment problem with consideration of occlusion. In [19], by assuming the shape of obstacle to be square block, they derive the expected coverage area of the camera sensors. The mathematical derivation of the coverage area starts from one camera sensor and then generalizes to the multiple sensors. The assumption of square shape obstacle helps to derive the coverage mathematical model but it is not applicable to real WVSNs. This mathematical coverage  
Figure 2: Sensor coverage in WSN and WVSN. model is a lower bound on the coverage areas because it fails to consider the possible cooperation between camera sensors to reduce the uncovered areas caused by the obstacle. The method to calculate the \"_certainty map_\" that are the non-occluded areas for target localization and counting applications is found in [20, 22]. By cooperatively fusing the certainty map from neighboring sensors, the occluded areas beside the objects and obstacles could be minimized. In [21], based on the idea of certainty map, the authors derive a close form visual coverage mathematical formulation that considers visual occlusions. Then, the minimum sensor density that suffices to ensure a visual K-coverage in a crowded sensing field is estimated. In [23], the two-tier deployment problem in WVSN is considered. Tier-1 consists of visual sensor nodes that can capture the image data and tier-2 consists of relay nodes that can relay the image data back to the sink node. The goal is to minimize the deployment cost and at the same time to prolong the lifetime of the WVSN. However, without considering the FoV angle coverage and visual occlusion makes this work is not applicable to real WVSN networks. In [24], a decentralized control strategy is proposed to position and orient the cameras placed on flying robots so as to cover the targeted area with minimum deployment cost. The control strategy considers heterogeneous degrees of mobility, where some cameras can translate and some cameras can only rotate. They propose an interesting performance metric, \"minimum information per pixel\", to minimize the aggregate information per camera pixel over the environment. With this minimum information per pixel performance metric, the cameras' overlapped FoV could be minimized. This performance metric also minimizes the number of camera sensors that needs to be deployed. In [25], they consider the mobile camera sensor coverage optimization problem as a repeated multi-player game. They propose distributed camera sensor coverage learning algorithms based on game theory to maximize the coverage and in the same time minimize the processing/energy cost. In