## 3 Wireless Sensor Network and Wireless Sensor Node Deployment
### Analytical Network Model for Node Placement
Any point placed in the sensing radius of the sensor could be sensed. So, any stem, grape or leaf will be covered if is closer than the maximal sensing distance (\(d_{max}\)). When the camera only covers a region (not the whole circle), the target must be located inside the angle of the rotatory movement of the camera. Based on the perspective projection model of a camera sensor, we propose a partial circle model. The area inside a partial circle bounded by a radius \(r\) and an arc \(\alpha\) is provided by Equation (4):  
\[Area=\frac{1}{2}{d_{max}}^{2}\cdot(\pi\cdot\frac{\alpha}{180}-sin\alpha) \tag{4}\]  
Here r is the circle radius and \(\alpha\) is the angle (in degrees). We also define a minimal sensing distance because the focal length of the camera could be very small, so d\({}_{\min}\) will be the minimal distance of effective imaging. Figure 3 shows the partial circle area covered by a wireless sensor camera. \(r\) is the distance between the camera and the target. The field of view (FoV) of a camera (if the image system is rectilinear) depends on the collimator focal length and the target size (assuming the sensed image includes the whole target). It can be estimated by Equation (5):  
\[FoV=2\cdot\frac{D}{d}arctan(\frac{d}{2\cdot f_{c}}) \tag{4}\]  
where \(D\) is the dimension of the full image, \(d\) is the dimension of the target and \(f_{c}\) is the focal length of collimator. Let us assume that all nodes have same radio coverage radio (thus the same radio coverage area) and the same sensing area, but the radio coverage area and the sensing areas are different. Moreover, we assume that all nodes have the same computation capabilities. Let a network of wireless sensor nodes be \(G=(V,E)\), here \(V\) is the set of wireless sensors and \(E\) is the set of connections between them. Let us suppose \(n=|V|\) (the number of sensors of \(V\)) to cover a field, which we refer to as the sensing field. The sensing coverage area of a wireless sensor is denoted by \(S\) while the radio coverage area is denoted by \(C\). The sensing area is different to the radio coverage area (\(S\
eq C\)). For simplicity, we assume a sensing area of a node \(i\) being a disk centered at sensor \(i\) with  
Figure 3: Sensing coverage of a wireless sensor camera. radius \(s\). Likewise, a sensor \(i\) covers a target \(q\) if and only if target \(q\) is in the sensing disk of \(i\). That is, if \(d_{min}\leq d(Lc\), \(Lq)\leq d_{max}\), here \(d(Lc\), \(Lt)\) is the Euclidean distance between \(Lc\) (camera location) and \(Lq\) (target location), \(d_{max}\) the maximal sensing distance and \(d_{min}\) the minimal sensing distance. It is desired a non-overlapping sensing areas in order to maximize the performance of the network. Two sensors can communicate directly with each other if and only if each sensor is inside the radio coverage area of the other. That is, if \(d(Lc_{I}\), \(Lc_{2})\leq C\), here \(d(Lc_{I}\), \(Lc_{2})\) is the Euclidean distance between the camera 1 and the camera 2 and \(C\) is the radio coverage radius of the wireless sensors (we have assumed that all wireless sensors have the same radio coverage radio). A node that can directly send messages to its neighbors, we call it 1-hop communication. The position of the wireless sensors on the network coverage area (also called as Region Of Interest, ROI), should be those ones whose coverage percentage is maximized and coverage holes is minimized. There are three main strategies for this:  
* Visual forced algorithm [36]: the sensors and the objects to be sensed in the ROI make the placement of sensors away from the objects and also from each other, so that their sensing areas are not overlapping and a full coverage is achieved. * Grid based sensor networks divide the ROI into square grids and the sensors are placed at the center of each square [37]. Generally, the bigger the grid size with respect to the sensing range the higher accuracy sensing the ROI or the higher probability to object tracking.