**3. The surveillance mechanism**

### **3.1 Preliminary**

We assume wireless sensor nodes with fixed lenses providing a θ angle FoV, densely deployed in a random manner. The assumption of fixed lenses is based on the current WMSN platforms (Tavli et al, 2011). Almost all of them (SensEye, MicrelEye, CITRIC, Panoptes, Meerkats) (Kulkarni et al., 2005; Kerhat et al., 2007; Chen et al., 2008; Feng et al., 2005; Margi et al., 2006) have fixed lenses and only high powered PTZ cameras have movement capabilities. We consider a monitor area with N wireless multimedia sensors, represented by the set S = {S1,S2,...,SN} randomly deployed. Each sensor node is equipped to learn its location coordinates and orientation information via any lightweight localization technique for wireless sensor networks. It is not the purpose of this chapter to define mechanisms to find this location. Without loss of generality, let us assume that nodes in the set S belong to a single-tier network or the same tier of a multitier architecture.

Our policy in order to applying collaboration among multimedia sensor nodes in the surveillance mechanism is clustering the network nodes based on their similarity in sensing the environment. The criterion applied in this purpose is the clustering scale of FoVs of nodes. The nodes having a large region of common area in their FoV, have a similar view of the sensing area then can cooperate in a established group, (Alaei & Barcelo, 2010).

#### **3.2 Cluster formation and cluster membership**

Now, let us consider the set S = {S1,S2,...,SN} of wireless multimedia nodes belonging to the same tier of a network randomly deployed. The cluster formation algorithm is executed in

the best trade-offs between these two aspects of visual sensor networks. Additional work is needed to compare the performance of different camera node scheduling sensor policies, including asynchronous (where every camera follows its own on-off schedule) and synchronous (where cameras are divided into different sets, so that in each moment one set of cameras is active) policies. From an application perspective, it would be interesting to explore sensor management policies for supporting multiple applications utilizing a single

The presented mechanism in the following section groups multimedia nodes in clusters based on their common sensing region of the whole deployment region. The clusters monitor the environment independently but in each cluster the members collaborate in data acquisition in an intermittent manner. The scheduling and activity times in each cluster are determined based on the cluster population and the scale of overlapping between FoV of cluster members. So, the data transmissions are not limited in this kind of sensor management but the volume of sensed data is reduced by management in only sensing subsystem and applying coordination among cluster members to optimize capturing image times and to avoid redundant sensing of the same data in the overlapped FoVs. On the other hand, the sensing region is divided between clusters and each cluster monitors its domain with its exclusive frequency and member scheduling. Thus, clusters are not synchronized for sensing the region whiles each point of the sensing region is monitored frequently

according to the number of nodes that cover that point by their sensing subsystem.

set S belong to a single-tier network or the same tier of a multitier architecture.

the sensing area then can cooperate in a established group, (Alaei & Barcelo, 2010).

**3.2 Cluster formation and cluster membership** 

We assume wireless sensor nodes with fixed lenses providing a θ angle FoV, densely deployed in a random manner. The assumption of fixed lenses is based on the current WMSN platforms (Tavli et al, 2011). Almost all of them (SensEye, MicrelEye, CITRIC, Panoptes, Meerkats) (Kulkarni et al., 2005; Kerhat et al., 2007; Chen et al., 2008; Feng et al., 2005; Margi et al., 2006) have fixed lenses and only high powered PTZ cameras have movement capabilities. We consider a monitor area with N wireless multimedia sensors, represented by the set S = {S1,S2,...,SN} randomly deployed. Each sensor node is equipped to learn its location coordinates and orientation information via any lightweight localization technique for wireless sensor networks. It is not the purpose of this chapter to define mechanisms to find this location. Without loss of generality, let us assume that nodes in the

Our policy in order to applying collaboration among multimedia sensor nodes in the surveillance mechanism is clustering the network nodes based on their similarity in sensing the environment. The criterion applied in this purpose is the clustering scale of FoVs of nodes. The nodes having a large region of common area in their FoV, have a similar view of

Now, let us consider the set S = {S1,S2,...,SN} of wireless multimedia nodes belonging to the same tier of a network randomly deployed. The cluster formation algorithm is executed in

visual sensor network.

**3. The surveillance mechanism** 

**3.1 Preliminary** 

a centralized manner by the sink after deploying the network. The main reasons in choosing a central architecture are the following: (i) for a distributed architecture, each node should notify to the rest of the nodes about its location Ai and its orientation αi (i = 1,…,N). In a centralized architecture the nodes should notify to the sink their location and orientation. Note that this notification can be done using any energy efficient sensor routing protocol and only is necessary at bootstrap phase. All phases of the clustering algorithm are executed only one time, right after node deployment. (ii) In many WSN applications, the sink has ample resources (storage, power supply, communication and computation) availability and capacity which make it suitable to play such a role. (iii) Collecting information by a sink node is more power efficient compared to spreading this information to each and every other node within the network. (iv) Having the global view of the network at the sink node facilitates provision algorithms for closer-to-optimal cluster determination; the global knowledge can be updated at the sink when new nodes are added or some nodes die. Such maintenance tasks can be regarded as a normal routine for the sink. (v) Finally, using a centralized scheme can relieve processing load from the sensors in the field and help in extending the overall network lifetime by reducing energy consumption at individual nodes. The following phases are performed to establish and form clusters, (Figure 2):


Fig. 2. Clustering Procedure.

The algorithm is executed by the sink once upon deployment and thus all nodes will become clustered. If a node joins to the network hereinafter, it has to send its position and orientation to the sink for announcing itself as a new node. The sink computes the FoV of the new node and finds the first cluster that can accept it as a new member. For this purpose, the sink computes the overlapping regions between FoV of the new node and the CH of each cluster and checks whether he is satisfying the cluster membership test. Then, the sink sends a message to the CH in order that this node re-organizes the cluster with the new member. Depending on the application, this notification may suppose a new reconfiguration in the monitoring task (*i.e.*, a new duty-cycle period). On the other hand, each node periodically sends a Hello message to the CH notifying its current residual energy. When a node dies, the CH will notify the rest of the members about the new cluster set and will reconfigure any parameter related to the cluster. The CH also periodically compares the residual energy of cluster members and its residual energy to select the new CH with the maximum residual energy in the cluster. If the CH decides to entrust CH role to another cluster member, notifies to the cluster members about the new CH. Note that the beaconing among cluster members implies low overhead since clusters have few nodes and hello periods can be on the order of duty-cycle sensing periods.

#### **3.2.1 Intra-cluster collaboration**

Let us see the potential of cooperative node monitoring in clusters in terms of sensor area coverage. We define the Maximum Cluster Coverage Domain (MCCD) parameter for a cluster as the maximum monitoring area which is covered by that cluster. Since each cluster is established considering the clustering scale equal to γ, the MCCD can be computed as follows (Csize is the size of the cluster):

$$\text{MCCD} = \chi \cdot A\_{FoV} + (1 - \chi) \cdot A\_{FoV} \cdot C\_{size} = (\mathbf{C}\_{size} - \chi \cdot (\mathbf{C}\_{size} - 1)) \cdot A\_{FoV} = \mathcal{J} \cdot A\_{FoV} \tag{1}$$

where:

556 Wireless Communications and Networks – Recent Advances

Node Deployment

Bootstrap

Cluster Formation

Creation a cluster

Calculation of intersection area between unclustered nodes FoV and the CH

> Selection of cluster members based on intersection area

> > Is there any unclustered node?

> > > No

Yes

and Scheduling

Membership Notification

The algorithm is executed by the sink once upon deployment and thus all nodes will become clustered. If a node joins to the network hereinafter, it has to send its position and orientation to the sink for announcing itself as a new node. The sink computes the FoV of the new node and finds the first cluster that can accept it as a new member. For this purpose, the sink computes the overlapping regions between FoV of the new node and the CH of each cluster and checks whether he is satisfying the cluster membership test. Then, the sink sends a message to the CH in order that this node re-organizes the cluster with the new member. Depending on the application, this notification may suppose a new reconfiguration in the monitoring task (*i.e.*, a new duty-cycle period). On the other hand, each node periodically sends a Hello message to the CH notifying its current residual

Cluster Management Cluster Maintenance

Fig. 2. Clustering Procedure.

$$\mathbf{1} \le \beta = \mathbf{C}\_{size} - \boldsymbol{\chi} \cdot (\mathbf{C}\_{size} - \mathbf{1}) \tag{2}$$

The effective cluster covering domain can be inferior to the MCCD calculated by Equation (1) since some nodes can overlap more than the region determined by γ. Since MCCD gives us an upper bound on the area covered by the cluster, using MCCD will allow us worst-case dimensioning. Factor β represents the increment of area that the cluster senses with respect to an individual sensor. When each node of a cluster obtains an image from its FoV, a part of the related MCCD with a ratio at least equal to 1/β respect to the MCCD is captured whereas this part includes overlapped areas of other nodes in the cluster. Sensing the environment by each member delivers information not only from the FoV of the active node but also from some overlapped parts of other nodes in the same cluster: at least γAFoV of the area is common to the first-member and more than 1/β of the MCCD is monitored. For example, in a cluster consisting of just 2 members, assuming a clustering scale of γ = 0.5, the MCCD is 1.5AFoV. Thus, when each of the two members of the cluster is activated and monitors the environment, an area of one FoV is captured that is at least 2/3 of the whole MCCD of the cluster. Consequently, scheduling and coordination among members in order to sense the field in a collaborative manner may yield a gain in energy saving and performance efficiency even with a low number of members in the cluster.

#### **3.2.2 Cluster formation evaluation**

All sensor nodes have been configured with a FoV vertex angle of θ = 60º and RS of 20 m. A sensing field spanning an area of 120m × 120m has been used. Sensor densities were varied to study the cluster formation from sparse to dense random deployments. Figures illustrate the average results of 50 independent running tests whereas each test corresponds to a different random deployment. Once a random deployment is defined, cluster formation is obtained from node location, angle of orientation and FoVs of nodes, using the described method whose complexity is O(N.logN). Furthermore, as it was mentioned before, each node sends a packet to the sink in the bootstrap phase, then the sink notifies each CH via one packet his membership set for that cluster (phase 3) and then the CHs notify cluster nodes about their cluster membership and any related parameter. Thus, the average overhead of the algorithm is forwarding N packets from the nodes to the sink and forwarding NC packets from the sink to first-members and forwarding NC(μCsize–1) packets from CHs to cluster nodes; where N is the number of nodes, NC is the average number of clusters and μCsize is the average cluster size. So the total overhead will be: N + NC + NC(μCsize–1) packets. The maintenance overhead is NC(μCsize–1) beacons every keep-alive period, where the keep-alive period can be a multiple of the sensing duty-cycle period.

#### **3.2.2.1 Number of clusters and cluster-size**

The average number of clusters, μNC, and the average cluster-size (μCsize) in a tier/network for different node densities with several clustering scales are shown in Figures 3 and 4. Increasing the node density does not only cause an increment in the number of clusters but also yields more overlapping areas among FoVs and thus raises the cluster-size. However, the clustering scale (γ) also impacts in the cluster membership selection process. The clustering scale determines the minimum region that is required to be overlapped between the FoV of each node belonging to a given cluster and the FoV of the CH of that cluster. So, γ determines the minimum intersection part of FoV of each member with the CH of an established cluster. Lower clustering scales obligate less overlapping areas for cluster membership and increase the domain covered by a given cluster since more nodes will be conforming to the membership rule. Increasing the clustering scale restricts node membership because of higher required overlapping areas between FoVs of nodes. Thus, higher clustering scales result in lower cluster-sizes, less MCCD and thus higher number of clusters.

Fig. 3. Average number of established clusters.

Sparse networks have low average cluster-size, μCsize, because sparse deployments result in low overlapping areas. Moreover, high values of γ also will produce low μCsize. The result will be lower potential for node coordination. On the other hand, dense wireless multimedia sensor networks can particularly benefit from higher cluster sizes and thus more potential for node coordination.

Fig. 4. Average size of established clusters.

558 Wireless Communications and Networks – Recent Advances

node sends a packet to the sink in the bootstrap phase, then the sink notifies each CH via one packet his membership set for that cluster (phase 3) and then the CHs notify cluster nodes about their cluster membership and any related parameter. Thus, the average overhead of the algorithm is forwarding N packets from the nodes to the sink and forwarding NC packets from the sink to first-members and forwarding NC(μCsize–1) packets from CHs to cluster nodes; where N is the number of nodes, NC is the average number of clusters and μCsize is the average cluster size. So the total overhead will be: N + NC + NC(μCsize–1) packets. The maintenance overhead is NC(μCsize–1) beacons every keep-alive period, where the keep-alive period can be a multiple of the sensing duty-cycle period.

The average number of clusters, μNC, and the average cluster-size (μCsize) in a tier/network for different node densities with several clustering scales are shown in Figures 3 and 4. Increasing the node density does not only cause an increment in the number of clusters but also yields more overlapping areas among FoVs and thus raises the cluster-size. However, the clustering scale (γ) also impacts in the cluster membership selection process. The clustering scale determines the minimum region that is required to be overlapped between the FoV of each node belonging to a given cluster and the FoV of the CH of that cluster. So, γ determines the minimum intersection part of FoV of each member with the CH of an established cluster. Lower clustering scales obligate less overlapping areas for cluster membership and increase the domain covered by a given cluster since more nodes will be conforming to the membership rule. Increasing the clustering scale restricts node membership because of higher required overlapping areas between FoVs of nodes. Thus, higher clustering scales result in lower cluster-sizes, less MCCD and thus higher number of

Sparse networks have low average cluster-size, μCsize, because sparse deployments result in low overlapping areas. Moreover, high values of γ also will produce low μCsize. The result

50 100 150 200 250 300

**Node density**

**3.2.2.1 Number of clusters and cluster-size** 

Fig. 3. Average number of established clusters.

**γ=0.7 γ=0.65 γ=0.6 γ=0.55 γ=0.5**

0

50

100

150

**µNC**

200

250

clusters.

Finally, Figure 5 shows the cumulative probability function for the cluster-size in the network for different node densities assuming a clustering scale of γ = 0.5. For example, in a network consisting of 250 nodes, 28% of clusters have a single member which does not have enough overlapping with others to satisfy the clustering scale, 32% of clusters have a cluster size of 2, 21% of 3, 12% of 4 and 7% of them consisting of more than four members.

Fig. 5. The cluster size cumulative distribution function (γ = 0.5).

#### **3.2.2.2 Coverage**

Figure 6 illustrates the percentage of area that is covered by the random deployment in terms of node density. As it is shown in the figure, for covering 95% of the area, a dense deployment of 300 nodes is required. As the figure shows, the rate of increment of the covered area for low node densities is faster than for high node densities. This indicates that after a new node is added in a dense deployment, low new coverage area is obtained.

For example, the first 100 nodes cover 75% of the field, but the next 100 nodes will only cover 15% of new area. The conclusion is that dense networks are able to cover high areas at the cost of high overlapping and sensing redundancy, but this overlapping can be used for improving reliability if nodes belonging to the same cluster work in a coordinated manner. Furthermore, the existence of obstacles produces a reduction of the sensing area because of FoV occlusion effect, (Tezcan & Wang, 2008). So, employing dense networks of low-cost, low-resolution and low-power multimedia sensor nodes instead of sparse networks of highpower, high-resolution sensors (*e.g*., PTZ) will be more beneficial.

Applications that are interested in multiple views will also benefit from this situation, since there will be several nodes monitoring the same area from several perspectives. Applications that are interested in detecting objects and are not interested in having an instantaneous multiple-view of the object may benefit from collaborative node processing in terms of energy savings. For the first set of applications clustering of nodes may serves as an indicator of triggering simultaneous multi-perspective pictures. For the second set of applications, clustering may serve as a baseline framework for collaborative node scheduling avoiding redundant sensing and processing and thus increasing network lifetime. Other applications that are interested in correlated data (*e.g*., Distributed Video Coding, DVC) may use clustering in order to exploit multi-view correlations to build joint encoders (Pereira et al., 2008).

#### **3.3 Cooperative node selection and scheduling**

560 Wireless Communications and Networks – Recent Advances

Figure 6 illustrates the percentage of area that is covered by the random deployment in terms of node density. As it is shown in the figure, for covering 95% of the area, a dense deployment of 300 nodes is required. As the figure shows, the rate of increment of the covered area for low node densities is faster than for high node densities. This indicates that after a new node is added in a dense deployment, low new coverage area is obtained.

For example, the first 100 nodes cover 75% of the field, but the next 100 nodes will only cover 15% of new area. The conclusion is that dense networks are able to cover high areas at the cost of high overlapping and sensing redundancy, but this overlapping can be used for improving reliability if nodes belonging to the same cluster work in a coordinated manner. Furthermore, the existence of obstacles produces a reduction of the sensing area because of FoV occlusion effect, (Tezcan & Wang, 2008). So, employing dense networks of low-cost, low-resolution and low-power multimedia sensor nodes instead of sparse networks of high-

85

<sup>90</sup> <sup>93</sup> <sup>95</sup>

**Node density** 

50 100 150 200 250 300

Applications that are interested in multiple views will also benefit from this situation, since there will be several nodes monitoring the same area from several perspectives. Applications that are interested in detecting objects and are not interested in having an instantaneous multiple-view of the object may benefit from collaborative node processing in terms of energy savings. For the first set of applications clustering of nodes may serves as an indicator of triggering simultaneous multi-perspective pictures. For the second set of applications, clustering may serve as a baseline framework for collaborative node scheduling avoiding redundant sensing and processing and thus increasing network lifetime. Other applications that are interested in correlated data (*e.g*., Distributed Video Coding, DVC) may use clustering in order to exploit multi-view correlations to build joint

Fig. 6. Percentage of the covered area with respect to the whole deployment area.

encoders (Pereira et al., 2008).

54

power, high-resolution sensors (*e.g*., PTZ) will be more beneficial.

75

**3.2.2.2 Coverage** 

In monitoring mechanisms, usually cameras should perform duty-cycled monitoring over the area that they sense. That means that every T (Figure 7.a) seconds the sensors in the monitored area will awake and monitor the area. This is the situation for a planned network in which every sensor is placed in such a position that there is no overlapping among sensors. Nevertheless, this duty-cycle scheduling will produce high power consumption in those situations in which there are overlapping sensors, since camera nodes with overlapping areas do not cooperate to sense the area and thus they redundantly monitor the area.

In this section, we explain a cooperative mechanism based on the clustering method that coordinates nodes belonging to the same cluster to work in a collaborative manner to monitor the sensing area. The objective of this mechanism is to increase power conservation by avoiding similar sensing and redundant processing at the same time. Also, collaborative sensing by nodes that have FoVs intersecting each other yields to more reliability: cluster members will monitor the region sequentially and if a moving object is not detected in one image capturing, it will be in the vicinal FoVs at the next capturing times. Thus, the other members in the same cluster may detect the object.

Let us divide the environment in domains covered by clusters of nodes (MCCD, Section 3.2). All clusters concurrently sense their domains. In each cluster, members are awakened sequentially in an intermittent manner by the CH with a time interval related to the clustersize and the scale of clustering (see Figure 7.b); (*i.e.*, Tinterval is the time between awakening two consecutive members of a cluster). In this way, each node of a given cluster periodically participates in capturing an image from its unique perspective and surveillance the environment and finally sleeps again with a cluster-based period called Tp. Formulas for these periods are derived in Section 3.3.1.

Fig. 7. (a) Period of awakening a given node in the un-cooperative scheduling. (b) Scheduling for a cluster consisting of three members (S1, S2, S3).

#### **3.3.1 Cluster-based TP and Tinterval computation**

Let us consider as baseline mechanism a non-collaborative duty-cycled scheme in which every node awakes with an interval period of time T and monitor the area (i.e., takes a picture and performs object detection) as tier 1 in (Kulkarni et al., 2005). The objective of the collaborative mechanism is to produce a cluster-based duty-cycled scheduler in which: (i) Each node is awakened and senses the area with a reliable period of Tp>T taking advantage of the overlapping among nodes in the cluster, thus, saving energy and increasing network lifetime. Each cluster will have its own TP interval, determined according to the cluster-size and the clustering scale. (ii) During the sleeping period of each member of a given cluster, other nodes belonging to the cluster are awakened with intervals of Tinterval < T (that is equal to: Tp /Csize) in a sequential manner.

The area sensed by each cluster is related to the MCCD area. In order to compute Tp we will consider the MCCD area. By awaking each member of a given cluster, in average, a part of the related MCCD with a ratio equal to 1/β is captured (Equation (2)). Note that the MCCD is an area of β.AFoV and is sensed by Csize overlapping members, thus sensing the environment by each node delivers information not only from the FoV of the awakened node but also from some overlapped parts of the FoV of other nodes in the same cluster. Then, we may define the node interval duty-cycle period as:

$$T\_P = T \cdot \frac{\mathbf{C}\_{size}}{\beta} = T \cdot \frac{\mathbf{C}\_{size}}{\mathbf{C}\_{size} - \chi \cdot (\mathbf{C}\_{size} - 1)}\tag{3}$$

Note that the TP is proprietary for each cluster in terms of its cluster-size and clustering scale. As it was mentioned before, the MCCD calculated by Equation (1) is the maximum covering domain of a cluster while the effective cluster covering domain may be less than MCCD since some members of a given cluster may overlap more than the region determined by γ. Consequently, a given cluster can cover an area less than βAFoV. Thus, using β gives us the lowest interval Tp and thus the most reliable one since lower values of β would increase the interval TP. On the other hand, members of a cluster are awakened sequentially to sense their environment in an intermittent way with time intervals equal to Tinterval:

$$T\_{interol} = \frac{T\_P}{\mathbb{C}\_{size}} = \frac{T}{\mathbb{C}\_{size} - \chi \cdot (\mathbb{C}\_{size} - 1)} \le T \tag{4}$$

Let us consider Figure 6.b and for example a cluster with three members, C = {S1, S2, S3}, cluster-head S1 and γ = 0.5. Every node will be awakened every TP = 1.5T seconds and the area will be monitored every Tinterval = 0.5T seconds. As can be observed, every sensor is awakened with a period higher than the non-collaborative scheme but the area is monitored more times. Then, the area duty-cycled frequency is increased while the sensor duty-cycled frequency is reduced.

Table 2 shows the evolution respects of Tp and Tinterval to T as a function of γ for several Csize. We first have to notice that for a clustering scale factor γ =1, Tp = T, while for γ < 1, T ≤ Tp ≤ T/(1–γ). Then, the duty-cycle frequency at which a specific node is awakened is decreased by a factor that at least is (1–γ) times the frequency of the non-collaborative scheme. On the other hand some sensor of the cluster will be on duty every Tinterval seconds. Note that Tinterval will be lower than T and will be smaller as Csize increases. This means that the area is monitored more frequently although every specific sensor monitors with less frequency. The reason is justified in how clusters are formed. Any sensor of the cluster overlaps with the first-member by at least an area of γAFoV. Thus, when a sensor enters in duty, he will monitor an area equal to γAFoV overlapped with the first-member and an area equal to (1–γ)AFoV that in the worst case does not overlap with any other member of the cluster. Sensing the whole cluster area with Tinterval equal to T would result in that an area equivalent

lifetime. Each cluster will have its own TP interval, determined according to the cluster-size and the clustering scale. (ii) During the sleeping period of each member of a given cluster, other nodes belonging to the cluster are awakened with intervals of Tinterval < T (that is equal

The area sensed by each cluster is related to the MCCD area. In order to compute Tp we will consider the MCCD area. By awaking each member of a given cluster, in average, a part of the related MCCD with a ratio equal to 1/β is captured (Equation (2)). Note that the MCCD is an area of β.AFoV and is sensed by Csize overlapping members, thus sensing the environment by each node delivers information not only from the FoV of the awakened node but also from some overlapped parts of the FoV of other nodes in the same cluster.

*size size*

Note that the TP is proprietary for each cluster in terms of its cluster-size and clustering scale. As it was mentioned before, the MCCD calculated by Equation (1) is the maximum covering domain of a cluster while the effective cluster covering domain may be less than MCCD since some members of a given cluster may overlap more than the region determined by γ. Consequently, a given cluster can cover an area less than βAFoV. Thus, using β gives us the lowest interval Tp and thus the most reliable one since lower values of β would increase the interval TP. On the other hand, members of a cluster are awakened sequentially to sense their environment in an intermittent way with time intervals equal

> *size size size T T T T*

Let us consider Figure 6.b and for example a cluster with three members, C = {S1, S2, S3}, cluster-head S1 and γ = 0.5. Every node will be awakened every TP = 1.5T seconds and the area will be monitored every Tinterval = 0.5T seconds. As can be observed, every sensor is awakened with a period higher than the non-collaborative scheme but the area is monitored more times. Then, the area duty-cycled frequency is increased while the sensor duty-cycled

Table 2 shows the evolution respects of Tp and Tinterval to T as a function of γ for several Csize. We first have to notice that for a clustering scale factor γ =1, Tp = T, while for γ < 1, T ≤ Tp ≤ T/(1–γ). Then, the duty-cycle frequency at which a specific node is awakened is decreased by a factor that at least is (1–γ) times the frequency of the non-collaborative scheme. On the other hand some sensor of the cluster will be on duty every Tinterval seconds. Note that Tinterval will be lower than T and will be smaller as Csize increases. This means that the area is monitored more frequently although every specific sensor monitors with less frequency. The reason is justified in how clusters are formed. Any sensor of the cluster overlaps with the first-member by at least an area of γAFoV. Thus, when a sensor enters in duty, he will monitor an area equal to γAFoV overlapped with the first-member and an area equal to (1–γ)AFoV that in the worst case does not overlap with any other member of the cluster. Sensing the whole cluster area with Tinterval equal to T would result in that an area equivalent

*C C TT T*

*P*

*interval*

*size size*

*<sup>β</sup> <sup>C</sup> <sup>γ</sup> (C 1)* (3)

*C C <sup>γ</sup> (C 1)* (4)

to: Tp /Csize) in a sequential manner.

to Tinterval:

frequency is reduced.

Then, we may define the node interval duty-cycle period as:

*P*

to (1–γ)AFoV would be monitored every CsizeT, a value that can be very high. However, using Equation (3), monitoring of the area equivalent to (1–γ)AFoV is guaranteed by a monitoring interval that is not superior to T/(1–γ), that is much lower than CsizeT.




(b)

Table 2. (a) Tp/T , (b) Tinterval/T for different cluster sizes and clustering scales.

Sleep/wake up protocols has extensively been studied in the area of wireless sensor networks, mainly for the radio subsystem, (Anastasi et al., 2009). Our clustering algorithm works on the sensing subsystem. It is important to notice that executing object detection does not imply sending packets to the sink. Thus, the sleep/wake up algorithm can be decoupled with the radio subsystem. Sleep/wake up can be based on periodic duty-cycle synchronized by the first-member: every Tp period, the sensing subsystem wakes up and performs object detection. However, clock drifts can cause cluster de-synchronization. To handle resynchronization, the system makes use of the beaconing scheme for cluster maintenance: nodes receive periodical beacons from the first-member and vice versa in order to detect new members or to detect members that have died. Beaconing duty-cycling belongs to the radio subsystem and it is independent of the sensing subsystem. That means that waking up the sensor to send a beacon is independent of waking up the sensor to take a picture and perform object detection. Thus, the cluster-head may resynchronize cluster members without need of waking up the sensing subsystem.
