## 3 Definitions and Basic Concepts
### Quality of Monitoring  
Quality of Monitoring is a generic term used to refer to the congruence between the expected and performed monitoring functions over a region of interest. In the case of a WVSN, QoM can be related to how good are the visual data definition and sharpness provided by a set of cameras for a region located on a certain distance \(dov\) (distance of view). The farther is the monitored region from the camera, the lower is the level of details related to that region in captured images, and consequently, the lower should be the amount of visual information extracted from that region. The QoM modeling used as reference in this article was initially proposed in Reference [5], being summarized next. A sensor node \(vs\in VS\) has its FoV divided into several disjoint sub-regions. In this article it is considered only three sub-regions (\(FoV_{vs}^{H}\), \(FoV_{vs}^{M}\) and \(FoV_{vs}^{L}\)), which determine the visual levels with  
Figure 2: Monitoring area being covered by visual sensor nodes \(vs_{i},i=1,\dots,7\)[5]. high, medium_ and _low_ quality, respectively. The first level is defined by an isosceles triangle \(\triangle\)_AFG_ with its high \(\mathit{dov}_{H}\) defined as the distance from vertex \(A\) to the end of \(FoV_{\text{vs}}^{H}\). The second and third levels are defined by isosceles trapezoids \(\circ\)_DEGF_ and \(\circ\)_BCED_ with highs equal to \((\mathit{dov}_{M}-\mathit{dov}_{H})\) and \((\mathit{dov}_{L}-\mathit{dov}_{M})\), respectively, as depicted in Figure 3. It is important to notice that the sensor FoV is not modified. It is only re-interpreted, being \(FoV_{\text{vs}}~{}=~{}FoV_{\text{vs}}^{H}\cup FoV_{\text{vs}}^{M}\cup FoV_{ \text{vs}}^{L}\) and \(FoV_{\text{vs}}^{H}\cap FoV_{\text{vs}}^{M}\cap FoV_{\text{vs}}^{L}~{}=~{}\emptyset\). The distances \(\mathit{dov}_{H}\), \(\mathit{dov}_{M}\) and \(\mathit{dov}_{L}\) can be computed according to Equation (6) and the proportion of \(\mathit{dov}_{H}\) and \(\mathit{dov}_{M}\) with respect to \(\mathit{dov}_{L}\) can be defined freely, considering the application requirements and camera's constraints. The coordinates of vertices \(D\), \(E\), \(F\) and \(G\) can be computed similarly to Equation (1). \[ \begin{array}{l}\mathit{dov}_{L}~{}=~{}R_{s}.\cos\left(\theta_{\text{vs}}/2 \right)\\ \mathit{dov}_{M}~{}=~{}\left(3/4\right)\mathit{dov}_{L}\\ \mathit{dov}_{H}~{}=~{}\left(2/4\right)\mathit{dov}_{L}.\end{array}  \tag{6}\]  
The QoM can be assessed by the Area Quality Metric (AQM), which is computed considering that each monitoring block \(\mathit{mb}\in FoV_{\text{vs}}\) receives a weight \(w_{l}\) which is the weight of the FoV sub-region of \(\mathit{vs}\) where \(\mathit{mb}\) can be viewed, as expressed in Equation (7). The weight values for each visual level are assigned as \(w_{1}~{}=~{}1\) for \(FoV_{\text{vs}}^{H}\), \(w_{2}~{}=~{}0.5\) for \(FoV_{\text{vs}}^{M}\) and \(w_{3}~{}=~{}0.25\) for \(FoV_{\text{vs}}^{L}\). \[ \begin{array}{l}w_{l}\left(\mathit{mb},\mathit{vs}\right)~{}=~{}\left\{ \begin{array}{ll}w_{1},&\text{if }\mathit{mb}\in FoV_{\text{vs}}^{H}\\ w_{2},&\text{if }\mathit{mb}\in FoV_{\text{vs}}^{M}\\ w_{3},&\text{if }\mathit{mb}\in FoV_{\text{vs}}^{L}\end{array}\right.\end{array}  \tag{7}\]  
If a monitoring block \(\mathit{mb}\) is redundantly covered by a visual sensor set \(\mathit{VS}\), then the weight of \(\mathit{mb}\) is the maximum weight among the associated sensor, as expressed in Equation (8). \[ \begin{array}{l}w_{\max}\left(\mathit{mb},\mathit{VS}\right)~{}=~{}\max \left(\mathit{wl}\left(\mathit{mb},\mathit{vs}\right)\right|_{\text{vs}\in \mathit{VS}}\right).\end{array}  \tag{8}\]  
Figure 4 illustrates the mapping of monitoring quality of the \(\mathit{MB}\) covered by three visual sensors, including the overlapping considerations. The visual sensor \(\mathit{vs}_{1}\) performs a normal monitoring, while the sensors \(\mathit{vs}_{2}\) ans \(\mathit{vs}_{3}\) have their FoV occluded by an obstacle. The occlusion scenario is addressed in Section 3.3.