Surveillance with wireless sensor networks in obstruction: Breach paths as watershed contours

Computer Networks 54 (2010) 428–441

Contents lists available at ScienceDirect

Computer Networks journal homepage: www.elsevier.com/locate/comnet

Surveillance with wireless sensor networks in obstruction: Breach paths as watershed contours Ertan Onur a,b,*, Cem Ersoy b, Hakan Deliç c, Lale Akarun d a

Wireless and Mobile Communications Group, EEMCS, Delft University of Technology, P.O. Box 5031, 2628 CD Delft, The Netherlands NETLAB, Department of Computer Engineering, Bogaziçi University, Bebek 34342, Istanbul, Turkey c Wireless Communications Laboratory, Department of Electrical and Electronics Engineering, Bogaziçi University, Bebek 34342, Istanbul, Turkey d pLab, Department of Computer Engineering, Bogaziçi University, Bebek 34342, Istanbul, Turkey b

a r t i c l e

i n f o

Article history: Received 2 June 2008 Received in revised form 22 June 2009 Accepted 15 September 2009 Available online 23 September 2009 Responsible Editor: C.J. Sreenan Keywords: Watershed segmentation Wireless sensor networks Sensing coverage Breach path Surveillance

a b s t r a c t For surveillance applications of wireless sensor networks, analysis of sensing coverage and quality of sensing is crucial. For rough terrains where obstacles block the sensing capability, region-based approaches must be employed to determine the sensing quality. In this paper, we present a method to determine the breach paths and the deployment quality defined as the minimum of the maximum detection probabilities on the breach paths in the presence of obstacles. We propose the utilization of watershed segmentation on the iso-sensing map that reveals the equally-sensed regions of the field-of-interest in a surveillance application. Probabilistic sensor models are utilized to produce the iso-sensing map considering the sensing coverage degree and reliability level as the design criteria. The watershed segmentation algorithm is applied on the iso-sensing map to identify the possible breach paths. An algorithm is proposed to convert the watershed segmentation to an auxiliary graph which is then employed to determine the deployment quality measure (DQM). The effects of the sensor count and coverage degree on the DQM are analyzed.  2009 Elsevier B.V. All rights reserved.

1. Introduction Suppose that a rough terrain is to be monitored to detect unauthorized entries as shown in Fig. 1a. This task can be risky for humans. Instead of deploying a wired surveillance system, a wireless sensor network (WSN) is an easy alternative where the sensors can be dropped by an aircraft. As soon as the sensors configure themselves, they can start sensing the environment and communicate the target presence decisions to a sink. Measures must be defined to analyze the sensing quality that signifies how well a surveillance wireless sensor network (SWSN) covers a region and senses the phenomena

* Corresponding author. Address: Wireless and Mobile Communications Group, EEMCS, Delft University of Technology, P.O. Box 5031, 2628 CD Delft, The Netherlands. Tel.: +31 15 278 5201. E-mail addresses: [email protected] (E. Onur), [email protected] (C. Ersoy), [email protected] (H. Deliç), [email protected] (L. Akarun). 1389-1286/$ - see front matter  2009 Elsevier B.V. All rights reserved. doi:10.1016/j.comnet.2009.09.006

of interest such as an intrusion. The sensing quality depends on the characteristics of the sensor, target and environment, as well as the number and the deployment scheme of the sensors. The variety of sensor technologies makes the coverage analysis difficult because the underlying signal processing and detection procedures depend on the physics of the devices. If the target detection probability is well-defined, a quality of sensing measure can be established. The sensing quality can be defined through how well the breach path is covered. Finding breach paths is referred to as the weakest breach path problem [1], or the best coverage problem [2]. Megerian et al. define the worst-and the best-case coverage of a WSN for homogeneous sensors [3]. The target wants to avoid the sensors. Thus, passing far from the sensor is good from the target’s viewpoint. The worst case coverage (maximal breach path) is defined with the quality of sensing measure as the closest distance to the sensors while the target crosses the field [4]. A similar problem derived from the worst case coverage defini-

E. Onur et al. / Computer Networks 54 (2010) 428–441

secure side field of interest

sensor

possible trajectories obstacle sensor

insecure side

secure side

sensor Intruder cannot follow these edges due to obstacle obstacle

429

grid in [5] and the grid size is equal to the product of the target speed and the sensor sampling period. If the sampling periods of sensors are not synchronized, this approach weakens the accuracy. Moreover, signal characteristics and environmental conditions are not taken into account in [3,5]. The main research question addressed in this paper is: How can the sensing quality be measured in the presence of obstacles in a SWSN? We propose a deployment (sensing) quality measure in terms of the detection probability of a target crossing the field on breach paths. This deployment quality measure (DQM) can be used to design the network to provide a required sensing quality and to answer typical questions such as how many sensors or how the sensors should be deployed. If the field of interest is known a priori, and deterministic deployment is possible, the designer may utilize the near optimal sensor placement algorithm proposed by Lin and Chiu [6] to provide a complete sensing coverage. For random deployment, it is concluded that the optimal sensor placement problem is NP-complete [6]. Younis and Akkaya present an extensive survey on the issues for node placement in WSNs in [7]. Therefore, it is practically important to have an accurate DQM because the main functionality of a SWSN is to secure a field-of-interest.

sensor

2. Breach paths

Voronoi edges insecure side

secure side

sensor Obstacle is avoided

obstacle sensor

Watershed contours insecure side

Fig. 1. How Voronoi segmentation fails and watershed segmentation avoids the obstacles in the field.

tion is to find the farthest distance to the sensors when the target wants to stay as close as possible to the sensors. This problem is referred to as the best case coverage (maximal support path) problem. Such worst case measures can be employed in applications with high security requirements such as the surveillance of a mission-critical place. Clouqueur et al. consider the unauthorized traversal problem where the likelihood of detecting the target (referred as path exposure) is studied [5]. The field is modelled as a

Traditionally, Voronoi decomposition is utilized to reveal breach paths based on exposure definitions [8,3,9,10]. Voronoi decomposition of a discrete set of sensors distributed in the Euclidean space is the partition of the plane where each sensor is associated with a region. All of the points in the region of any sensor are closer to that sensor than any other. The borders between the regions, which are equidistant to multiple sensors, are the breach paths. Given a set S of discrete number of generating points (sensors) in the Euclidean space (surveillance field), for any point (x, y) in this space, there is one point from S, say si, to which (x, y) is closer than any other point in S except the equally distant ones. Hence, the set of closest points to si 2 S produces a convex polytope referred to as the Voronoi cell. The set of Voronoi cells tessellates the whole Euclidean space [11]. The major difference of our work from the others is the presence of obstacles. When there are obstacles in the field model, some parts of the field cannot be monitored because sensors may not detect the phenomenon due to the lack of line-of-sight. If there is an obstacle between the sensor and the target, considering only the sensor-totarget distance misleads the calculations. The simple Voronoi decomposition approach considers just the positions of the sensors (in a way just the Euclidean distance), and therefore falls short of finding the breach paths when there are obstacles in the field. Obstacles may also block the trajectory of the target. A simple scenario is depicted in Fig. 1b, where the breach path found through Voronoi segmentation passes over the obstruction, which may be impossible geographically. A generalized weighted Voronoi decomposition approach can be developed to address the line-of-sight

430

E. Onur et al. / Computer Networks 54 (2010) 428–441

problem caused by obstacles. For example, a region growing algorithm can be designed where the generating points of the Voronoi tessellation are the positions of the sensors and the obstacles. Each generating point is marked with an explicit tag. All points covered by the obstacles are tagged. Then, at each stage of the algorithm, the generating points offer their tags to neighboring grid points with a predetermined weight (speed) until all grids are tagged. The region growing weight is the number of the hops to the grid to which the tag is offered. If the region growing speeds of the obstacles and sensors are set to zero and one, respectively, then, the produced contours do not cross the obstacles and pass far from the sensors. Determining the weights is not easy when heterogeneous sensors are used or the geographic characteristics are not uniform throughout the field. Delaunay triangulation, which is the straightline dual of the Voronoi diagram [12], is used in [13] to determine locations in the field for redeployment, where deployment quality is defined as the coverage percentage of the field. An adaptive sensor deployment algorithm that uses Delaunay triangulation and considers the boundaries of the obstacles as virtual sensors in order to avoid them is presented in [14]. Such an approach increases the number of generating points and may not work in a 3-D field model. When there are many obstacles or when the topology of the field is complex, another approach that works using the topology instead of individual sensor and obstacle positions is required. This hints at using the watershed segmentation that considers the topology as a discretized image. Because Voronoi decomposition considers only the sensor (and obstacle) positions, it is not possible to fuse the decisions of the sensors and subsequently determine the breach paths. Morphological segmentation methods can be utilized instead of the generalized weighted Voronoi decomposition approach. In this paper, we employ a well-known morphological segmentation method, namely the watershed segmentation [15] to determine the breach paths in the presence of geographic or manmade obstacles as shown in Fig. 1c. The details of the watershed segmentation are presented in Section 4. Meyer proved that if appropriate distance measures are used, then morphological segmentation produces Voronoi tessellations [16]. When there are no obstacles in the field, the geodesic distance reduces to the Euclidean distance and the geodesic Voronoi decomposition becomes the simple Voronoi decomposition and fails to solve the lineof-sight problem. When the field-of-interest is modeled as a grid, the detection probabilities (or exposure levels) can be calculated for each grid point depending on the positions of the sensors. Adding the detection probability as the third dimension to a 2-D field model, a surface referred as the iso-sensing map is obtained as shown in Fig. 2 where the sensors are deployed randomly. The iso-sensing map resembles the contours that denote the equal-heights in a topographic map. Correspondingly, the contours in the iso-sensing map represent the equally-sensed areas. In the next section, we explain how the watershed segmentation algorithm is applied on the iso-sensing map to identify the possible breach paths.

Fig. 2. A sample iso-sensing surface.

3. Iso-sensing map definition In this section, we define how the iso-sensing map is produced, and present how the watershed algorithm is used to determine the breach paths. 3.1. Field and obstacle models The field is a long narrow strip modeled by an N  M grid as seen in Fig. 2, where N > M. Throughout the paper, we use the term grid points to address the dimensionless intersection points of equally space horizontal and vertical lines. For a grid point (x, y), the 4-connected neighborhood is defined as the set of grid points G4(x, y) = {(x + 1, y), (x  1, y), (x, y + 1), (x, y  1)} and the 8-connected S neighborhood is the set of grid points G8(x, y) = G4 (x, y) {(x + 1, y + 1), (x  1, y  1), (x  1, y + 1), (x + 1, y  1)}. We use the 8-connected neighborhood definition in the field model. The two grid points (x1, y1) and (x2, y2) are assumed to be connected if (x2, y2) 2 G8(x1, y1). We tag one side of the field as insecure and the opposite side as secure as shown in Fig. 1a. The secure and insecure sides represent the destination and the origin of intruder traversals, respectively. We do not address any specific points in either side. The definition of the secure and insecure sides is an engineering decision to be given by the network designer based on the environmental properties such as the topology and the application requirements. To be faithful to the real world, obstacles that disable sensing and physical traversals are incorporated in the field model. The objective of the target is to go through the field-of-interest while simultaneously avoiding the obstacles. A sample field model can be seen in Fig. 2. In this example, the field is modeled by 160  40 grids where each grid is 1  1 m. In this work, sensors are deployed randomly and their locations are assumed to be known as in [8,10,17]. The sensor and obstacle positions are not restrained to the grid points and can be floating numbers. In the simulations, we consider obstacles as isotropic discs where the position and the radii are uniform random variables. The coordinates of the obstacle centers and the perimeters of the obstacles do not need to align with the grid points. The obstacles block both the line-of-sight of sensors and the breach paths. Depending on the operational characteristics of the sensors, the effect of obstacles

431

E. Onur et al. / Computer Networks 54 (2010) 428–441

on the sensing performance may change. For example, if radar operates using radio signals, as the frequency increases, the penetration capability of signals through the obstacle reduces significantly. For infrared and sonar, the effect may be different. The ability to sense through obstacles depends on the size, shape, motion and temporal change of the nature of the obstacle. For the sake of analytical simplicity, we assume that sensing through an obstacle is impossible. Instead of trying to model obstacle effects for all kinds of sensors, in this paper, we present a generic model. For a detailed discussion on the effects of obstacles the reader may refer to [18]. The probability of detecting a target on each grid point can be calculated if there is line-of-sight between the target and the sensor (e.g., no obstacles exist in between). To incorporate the obstacles in the model, we define oijk = 1 if there is line-of-sight between the target at grid point (i, j) and the sensor k, and oijk = 0 otherwise. If obstacles are not modeled, then oijk = 1, "i, j, k. Depending on the type of the sensor, obstacles may not disable sensing functionality completely. For such situations, the designer may assume 0 6 oijk 6 1 as a sensing degradation factor. In this paper, we consider the Boolean approach as Kansal et al. presented in [19], where they analyze the effect of obstacles on the sensing coverage. A similar obstruction approach is presented in [20].

point x, and dijk is the Euclidean distance between the grid point (i, j) and sensor node k, modeling MIR as a Neyman– Pearson detector (NPD) [21,26,27]. Being a generic model, Elfes’s detector [28] can be used for other types of sensors. The detection probability of a target at grid point (i, j) by sensor k is

pijk

8 > > <1 1 b ¼ ekðdijk dt Þ > > : 0

1

if dijk 6 dt ; 1

2

if dt < dijk < dt ; if

2 dt

ð2Þ

6 dijk ;

1 2 dt ; dt ; k

where the parameters and b are adjusted according to the physical properties of the sensor. Both detectors exhibit an exponential behavior, and Elfes’s model can accommodate the Neyman–Pearson detector through proper parameter matching [21]. In this paper, instead of the common binary detection with static [29–31] and adjustable sensing ranges [32,33], we use the Neyman–Pearson and Elfes’s detector in the simulations. The latter models present a particularly suitable formulation for radar sensing, which is pivotal in the surveillance of very large areas. In the following section, we define different approaches to produce the iso-sensing map in obstruction. Since the iso-sensing map definition does not depend on any particular detector model, the readers may consider using other probabilistic sensor models to produce the iso-sensing map.

3.2. Detector models 3.3. Iso-sensing map Binary detector is the most common model in WSN research [21]. The sensing coverage of a sensor is modeled as an isotropic disc with radius dt [22]. If the target trajectory intersects any disc, it is assumed to be detected. As experimented by Cao et al. in [23], the sensing capability of the passive infrared sensors (PIR) is not isotropic and the sensing ranges for any direction can be modeled with normal distribution. However, for PIR sensors, if the sensor-to-target distance exceeds the sensing range by 3–7%, the detection performance deteriorates sharply. This result shows that PIR sensors can be approximated by the binary detection model. Isotropic binary detection assumption is commonly adopted for its analytical simplicity, and it may be acceptable when line-of-sight is ensured, e.g., for indoor deployment. The micropower impulse radar (MIR) [24,25] can be employed outdoors. Current commercial MIR devices have a sensing range around 15 m. The signal path-loss occurs with propagation exponent g. During an observation epoch, the breach decision is made based on L data samples, where the sensor-to-target distance is assumed to remain the same. The detection probability of a target at grid point (i, j) by sensor k in additive white Gaussian noise with zero-mean and variance r2n is

qffiffiffiffiffiffiffiffiffiffiffiffiffi  g pijk ¼ 1  U U1 ð1  aÞ  cLdijk ;

ð1Þ

where the sensor node transmits with power w, A accounts for factors such as the antenna gains and the transmission frequency, c ¼ Aw=r2n controls the signal-to-noise ratio (SNR), U(x) is the cumulative distribution function of the zero-mean, unit-variance Gaussian random variable at

In this section, we present how the iso-sensing map is produced. We assume that a set of sensors is deployed in the 2-D field and there are obstacles in the field. We assume that obstacles block target traversals, as well as all detections and communications. The detector models presented in the previous section define the sensing quality based on the sensor-to-target distance. Using such detector models, the target detection probability for any point in the field can be calculated using the iso-sensing map definitions presented in this section. This calculation produces the iso-sensing map which resembles a topographic map where the detection probability can be deemed as the altitude; i.e., the third dimension. To decrease the computational complexity of the calculation, the field is modelled as a grid and the detection probabilities are calculated only for grid points. The iso-sensing map can also be considered as an image where the detection probabilities are mapped to the intensities of the pixels. In Section 4, we present these issues in detail. In the iso-sensing map definitions, the decisions of a subset of sensors are fused to produce the breach decision which may or may not be the case in an active network. Operationally, all nodes are in sensing mode unless any sleep scheduling for the sensing circuitry is implemented. Therefore, the following iso-sensing map definitions and calculations can be deemed as an off-line process. For grid point (i, j), define the set of sensors in decreasing order of detection probabilities as Sij = {s1, s2, . . . ,s‘, . . . ,sR} where s‘, ‘ = 1, . . . ,R, is the identity of the sensor with pijs1 P pijs2 P    P pijsR , and R is the total number of sensors deployed in the field. Throughout the lifetime of the

432

E. Onur et al. / Computer Networks 54 (2010) 428–441

WSN, sensor nodes do not communicate to sort out their detection probabilities for any grid point; they just function to sense and communicate the phenomenon. 3.3.1. K-degrees of iso-sensing (KIS) In this type of iso-sensing map definition, K 6 R of the closest sensors (first K sensors in Sij) act on the decision for a grid point. Then, the detection probability of a target on grid point (i, j) is

pKIS ¼1 ij

K Y ð1  pijs‘ oijs‘ Þ:

ð3Þ

‘¼1

Kumar et al. propose algorithms in [34] to determine whether a deployment provides K degrees of coverage or not. This type of iso-sensing surface definition is useful when the nodes sleep from time to time for energy conservation. Designing a sleep scheduling algorithm according to the sensing performance is beyond the scope of this paper. But, for example, Lui et al. propose a scheduling algorithm without accurate location information subject to sensing coverage and connectivity requirements [35]. For a given coverage degree, they propose a lower bound on the required number of sensors to provide a coverage intensity level. Coverage intensity is defined as the ratio of active time to the total time where the points in the field is covered by at least one active sensor. For other scheduling algorithms considering sensing coverage and connectivity, the reader may refer to [36,37] and a detailed survey of coverage and connectivity issues can be found in [38]. Other application level motivations for more coverage degrees can be based on accuracy or fault tolerance. For applications such as battlefield surveillance, increasing the degree of sensing coverage, improves the sensing accuracy. In other words, failure of an individual sensor must not block network operation. Hence, fault tolerance can be provided with higher coverage degrees. Another motivation is that when the position of the target is to be estimated, measurements from multiple sensors are required. For triangular positioning algorithms, the degree of coverage may be adjusted accordingly.

Although the pt does not impact the computational complexity, larger values of it impose greater sensor demand. From another viewpoint, the reliability threshold can be mapped to sensing distance. That is, sensor decisions are deemed sufficiently reliable to be incorporated in the calculations only at those dijs‘ distances where pijs‘ > pt . Depending on the application and the false alarm requirement, typically pt P 0.9. Ideally, pt < pijsK ; otherwise, the degree of the coverage is smaller than K. Moreover, in an active network the sensor does not decide if it is reliable or not; it just decides if there is a target according to its functional design. 3.3.3. Reliable subset iso-sensing (RIS) Since only those sensor decisions that are sufficiently reliable are incorporated in KRIS, to alleviate the problem of determining an appropriate value of K, the designer may prefer to set K = R so that

pRIS ij ¼ 1 

R Y

pKRIS ¼1 ij

K Y

ð1  pijs‘ oijs‘ r ijs‘ Þ:

ð4Þ

‘¼1

The threshold probability pt 2 (0.5, 1) represents the confidence level of the sensor and it is an engineering parameter which depends on the application requirements. Large values of it indicate better security since the points in the field with smaller target detection probabilities than the threshold are regarded as sensing holes with zero detection probabilities. Hence, pt sets the requirement for the full coverage of the field with a minimum security level.

ð5Þ

which is referred to as the reliable subset iso-sensing (RIS). Uncorrelated sensor decisions are implicitly assumed here. However, multiple sensors may observe a common volume, and if a sensor detects a target, it is highly probable that there is another sensor seeing the same target. With RIS, the total effect of the sensor correlations is bounded because low probability values are truncated. Hence, the variance is not affected. 3.3.4. Most-dominant-sensor iso-sensing (MDIS) In dense deployment, assuming the same environmental conditions, a target can be detected by several sensors, implying correlations among sensor decisions. Based on this phenomenon, the designer may assume that the sensor with the largest detection probability dominates the grid point. A similar approach is considered in [8] where observability by the closest sensor is dominating. In this case,

pMDIS ¼ max fpijk oijk g: ij 16k6R

3.3.2. Reliable K-degrees iso-sensing (KRIS) In KIS, large values of K increase the variance of sensor decisions. For a more reliable design, Sij can be bounded with a reliability factor such that r ijs‘ ¼ 1, if pijs‘ > pt , and rijs‘ ¼ 0, otherwise, giving rise to the Reliable K-degrees iso-sensing (KRIS) where the detection probability becomes

ð1  pijk oijk r ijk Þ;

k¼1

ð6Þ

This model is equivalent to KIS with K = 1. A stricter ap¼ 0 if the detection proach would be to assume that pMDIS ij probability of the closest sensor is less than some threshold. Clearly, KIS and RIS definitions necessitate redundant deployment and they function in a similar way in terms of detection performance. More sensors must be put in the field to decrease target-to-sensor distances and increase the coverage degree. Consequently, while designing a network according to KIS, KRIS or RIS provides greater reliability compared to one designed following the MDIS formulation, it is also more costly because of the denser deployment requirement. When the SWSN designs based on these models are sorted in terms of decreasing reliability level, it follows the KRIS, RIS, KIS and MDIS order. Calculating the detection probabilities for each grid point produces the iso-sensing map (see Fig. 2). After

433

E. Onur et al. / Computer Networks 54 (2010) 428–441

generating the 2-D image (Fig. 3), the watershed algorithm can be applied to determine the breach paths. In image processing, the watershed algorithm is applied to a gradient image to find edges in the original image, or the highest peaks in the gradient image [15]. Therefore, our iso-sensing map may be interpreted as an inverted gradient image. In the following section, we point to an analogy between an iso-sensing map and a topographical relief and present how the breach paths can be revealed through the watershed algorithm.

4. Watershed segmentation In image processing, the gradient images which correspond to the topographic reliefs are often denoted with gray-scale pictures. The gray tones in the image depict the elevations in the region. Image segmentation is a process to discriminate the objects in an image from the background. A common approach is to find disjoint regions that are homogeneous with respect to some property. Watershed segmentation is a region-based approach and the idea behind this algorithm comes from nature. The watershed transform is a region-based segmentation approach. Watershed segmentation can be described analogously to water swamping from the minimal plateaus of a 3-D topographic surface, where the third dimension is the altitude. Minimal plateau is a set of points with an altitude from which it is impossible to reach a lower altitude without having to climb. As the water rises in the catchment basins, the floods will merge. Dams are built to separate the floods. The catchment basin associated with a minimal plateau is the set of points such that a water drop that falls on one of these points flows until it reaches the minimal

40

boundary

plateau. After the immersion, only the dams that separate the floods are visible. That is, the topographic surface is divided into regions separated by the dams referred as watersheds or the dividing lines that separate the catchment basins. The labelling process of the revealed regions is referred to as the watershed transform [39]. This approach is generally referred to as immersion analogy. The watershed segmentation algorithm by simulated immersion is presented by Vincent and Soille in [15]. When the miss probabilities are quantized to gray-scale color intensities, the iso-sensing map can be considered as a 2-D image on which the watershed segmentation can be easily applied. After deployment, the iso-sensing map of the SWSN can be computed. The iso-sensing map depicts hills and valleys where the altitude is mapped to the miss probability. The lowest points of the surface are the sensor positions. Therefore, analogously, water starts flooding from the sensor positions. The contours (dams) produced by the watershed segmentation correspond to possible breach paths. The watershed segmentation of the sample iso-sensing map is depicted in Fig. 4. The right and left sides are marked as boundary regions. These regions are not included in the analysis since they are not completely covered. When simulating the immersion process, there are two approaches: (1) the basins are found, then watersheds are formed by taking a set complement; (2) the image is completely partitioned into basins, and then, by boundary detection, the watersheds are discovered. There are several sequential and parallel algorithms for watershed transformation [39]. They can be divided into two classes: those based on the recursive algorithm by Vincent and Soille [15], and others based on distance functions by Meyer [40]. In this paper, we use the Vincent–Soille algorithm, which has two main steps: sorting and flooding. After

obstacle obstacle

20 10

boundary

30

obstacle

20

sensor

40

60

field

80

100

obstacle 120

140

Fig. 3. 2-D visualization of the sample iso-sensing surface in Fig. 2.

Fig. 4. The watershed contours of the sample iso-sensing surface in Fig. 3.

160

434

E. Onur et al. / Computer Networks 54 (2010) 428–441

sorting the gradient values of each pixel, the algorithm starts working with the pixels with the lowest gradient values and assigns a unique label to each minimum and its corresponding basin using a breach-first technique. If a pixel is adjacent to more than one basin it is marked as a watershed edge. The time complexity of the algorithm is linearly proportional to the number of pixels. For a grid, the intensity of grid point p is denoted by I(p) that takes discrete values in [0, N]. The path P between grid point p and q is described with an l-tuple, (p, x1, x2, . . . ,xl2, q) where p 2 G8(x1), xi 2 G8(xi+1), xl2 2 G8(q), i = 1, 2, . . ., l  2, and l is the length of the path P. A minimal plateau of I around point p denoted with M(I) is a connected plateau of grids from which it is not possible to reach a point with lower altitude (intensity) without having to climb. Then, the minimal plateau is defined with a set of points "q R M(I) such that I(q) P I(p) and "P = (p,x1, . . . ,xl2, q) such that I(xi) P I(p) where i = 1, 2, . . . , l  2. Then, the catchment basin C(M) associated with the minimal plateau M is the set of points around p with higher intensities that corresponds to the altitude to where a falling water drop flows until it reaches M. The dividing lines that separate the catchment basins are the watershed contours [15]. In watershed segmentation, oversegmentation occurs when tiny and insignificant regional minima form their own catchment basins. One solution is to modify the image to remove the minima that are too shallow. This is a common problem in image processing when the gradient field is not smooth. In our problem, the iso-sensing surface is quite smooth. Because the sensors are identical and their positions are random, tiny and insignificant regional minima cannot occur and oversegmentation is not probable. However, for other iso-sensing definitions, oversegmentation may increase the algorithmic time complexity. Undersegmentation occurs when a segment contains grid points from two regions that belong to two or more different sensors. Undersegmentation of the iso-sensing map implicitly suggests that there are other contours with smaller detection probabilities than the undersegmented. Therefore, some of the contours are not produced and those are not the ones we are after in this work. Therefore, undersegmentation, by its nature, does not impact the result and the performance of the model.

side. Among the alternative paths, the one with the least maximum detection probability measures the quality of secure side

degree = 2

degree > 2 contour

contour

any point on the contour

connection point

obstacle contour contour insecure side

contour

secure side 4

2

10

7

5 3

obstacle 1

6

9 8

insecure side

d

4

2

10 7

5 3

9 6

1

8

5. Deployment quality measure s

The most secure path for a target follows the grid points that are the most distant from the sensors in the field. From the WSN’s point of view, this path is the weakest breach path. Thus, the maximum detection probability on the weakest breach path provides a measure to analyze the quality of deployment [1]. Watershed segmentation produces several contours in which the weakest breach path resides. The watershed contours are the points in the iso-sensing map with the lowest detection probabilities, which is in favor of the target. Many combinations of watershed contours exist that connect the insecure side to the secure

Fig. 5. Demonstration of Algorithm 1 to produce the auxiliary graph based on the example shown in Fig. 1a.

E. Onur et al. / Computer Networks 54 (2010) 428–441

deployment. To determine the DQM, an auxiliary graph is constructed using the labelled watershed edges (as can be seen in Fig. 5). The objective of the labelling process is to assign a weight which shows the level of breach security. The watershed contours are denoted with nodes in the auxiliary graph and the nodes are assigned weights as the maximum detection probability of any grid point on the same watershed contour as shown in Fig. 5b. Watershed segmentation algorithm produces a labelled image where all the watershed contours have the same label. To discriminate between the individual watershed contours and to label them, we propose Algorithms 1 and 2. Suppose that each grid point (i, j) is marked with n(i,j) = 1 if (i, j) belongs to a watershed edge, and n(i,j) = 0, otherwise. The degree of the grid point (i, j) can be defined as d(i,j) = n(i+1,j) + n(i1,j) + n(i,j+1) + n(i,j1). The grid points which connect two or more watershed edges are referred to as the connection points and for a connection point (i, j), n(i,j) = 1 and d(i,j) > 2 as shown in Fig. 5a. With a minor modification of the watershed algorithm, the connection points can be obtained easily. Denoting the state of all of the grid points s(i,j) = unknown, for each connection point (i, j), if the state of an adjacent node s(‘,m) = unknown and n(‘,m) = 1, mark the adjacent node (‘, m) with a unique label and set s(‘,m) = known and record the maximum detection probability for this labelled edge and continue to apply the same algorithm to adjacent grid points of (‘, m) until it is another connection point or field borders are crossed. Each labelled edge (watershed contour) is represented as a node; e.g., as in Fig. 5a. The nodes are connected in the auxiliary graph if the respective edges originate from the same connection point. A sample auxiliary graph for the iso-sensing surface in Fig. 2 is shown in Fig. 6a. The connection matrix of the auxiliary graph is represented with C, and the vector W denotes the weights of the nodes that is the maximum detection probability of the respective edge in the iso-sensing map. The labels of each grid point are denoted with the vector L. The start node s and the destination node d denote the insecure and secure sides, respectively. If any edge crosses the boundary regions on either side of the field, remove the nodes from the auxiliary graph. If any edge touches the secure side, connect the representing node to the destination node, and if the edge touches the insecure side, connect the representing node to the start node. This algorithm constructs the auxiliary graph. Algorithms 1 and 2 have linear time complexities proportional to the number of points on the watershed contours. In Fig. 6a, nodes 2 and 11 are disconnected from the graph since their corresponding edges cross the boundary regions. Nodes 1, 5, 8 and 10 are connected to the start node s since they cross through the border of the insecure side and nodes 12, 13 and 14 are connected to the destination node since they cross the border of the secure side. The auxiliary graph shows the possible breach paths which a target may prefer. For example, in Fig. 6a among others, (s, 1, 3, 14, d), (s, 1, 3, 4, 14, d) or (s, 8, 7, 6, 13, d) are some breach paths. The path with a set of nodes which has the minimum weights is the best from the view point of the target.

435

Algorithm 1. ConstructAuxiliaryGraph 1: 2: 3: 4: 5: 6: 7: 8: 9: 10: 11: 12: 13: 14: 15: 16: 17: 18: 19: 20: 21: 22: 23: 24: 25:

if "(i,j)(i,j) is in boundary region then state(i,j) = boundary else state(i,j) = unknown end if c = 0/*labels and the nodes of the auxiliary graph*/ for all (i,j) where n(i,j) = 1 and d(i,j) > 2 and state(i,j) – boundary do Disconnect (i,j) from adjacent nodes A = ;/*Create an empty label set*/ for all (‘,m) 2 G4(i,j) do if n(‘,m) = 1 then if state(‘,m) = unknown then c = c + 1/*generate new edge label*/ ReturnValue=LabelGridPoint(c,(‘,m)) if ReturnValue=true then A = A + {c}/*Add the new label to label set*/ else c = c  1/*to reuse the edge label*/ end if else A = A + {L(‘,m)}/*Add the existing label to label set*/ end if end if end for end for

Algorithm 2. ReturnValue = LabelGridPoint(c,(i,j)) 1: 2: 3: 4: 5: 6: 7: 8: 9: 10: 11: 12: 13: 14: 15:

16: 17: 18: 19:

ReturnValue = true if state(i,j) – boundary then state(i,j) = known L(i,j) = c /*store the label of the grid point*/ if Wc > pij then Wc = pij /*store the weight of the node*/ end if if i = 0 then Ccs = Csc = connected; /*This contour touches to insecure side, connect to s*/ end if if j = N  1 then Ccd = Cdc = connected; /*This contour touches to secure side, connect to d*/ end if if $(‘,m) 2 G4(i,j) such that n(‘,m) = 1 and state(‘,m) = unknown and d(‘,m) = 2 then ReturnValue=LabelGridPoint(c,(‘,m)) /*For (‘,m) adjacent to (i,j) and not in the boundary regions, there is only one such grid point.*/ end if else ReturnValue =false end if Return ReturnValue

436

E. Onur et al. / Computer Networks 54 (2010) 428–441

d wd=0

d wd=0

w13=0.8

w14=0.78

w3=0.86

w4=0.97

6

7

w13=0.8

w14=0.78

12

11

w3=0.86

3

9

6

w10=0.93

8

5

w8=0.7

w5=0.73

w1=0.71

s

w6=0.94 w =0.85 9

7

w10=0.93

10

1

8

5

ws=0

d wd=0

w12=0.6

7

w13=0.8

w14=0.78

12

w9=0.85

3

11

w3=0.86

7

8

5 w5=0.73

w8=0.7

2

10

1

8

5 w5=0.73

w1=0.71

ws=0

s

d wd=0

w13=0.8

w14=0.78

w9=0.85

7

w8=0.7

ws=0

d wd=0

w12=0.6

13

14

11

9

w7=0.84 w10=0.93

s

12

w9=0.85

3

w7=0.84

1

w12=0.6

13

14

9

2 w1=0.71

10

s ws=0

13

w3=0.86

w8=0.7

w5=0.73

w1=0.71

w13=0.8

14

11

9

2

d wd=0

w14=0.78

12

w7=0.84

w7=0.84

2 1

w12=0.6

13

14

w6=0.94 w9=0.85

4

3

w12=0.6

13

14

w14=0.78

12

w13=0.8

w12=0.6

13

14

11

12

11 7

9

w7=0.84

w7=0.84

2

2 1 w1=0.71

8

5 w5=0.73

s

w8=0.7

ws=0

1 w1=0.71

8

5 w5=0.73

w8=0.7

s ws=0

Fig. 6. Trace of Algorithm 3. This is the auxiliary graph of the watershed contours in Fig. 4 for the iso-sensing surface in Fig. 3 produced using Algorithm 1.

On the auxiliary graph, instead of determining the weakest breach path, a simpler approach, described in Algorithm 3, can be employed to determine the bottleneck

edge through which the weakest breach path may pass. In this algorithm, the weights of the nodes are sorted, and the node with the largest weight is removed from the graph. If

437

E. Onur et al. / Computer Networks 54 (2010) 428–441

the start and destination nodes are disconnected, the weakest breach path must pass through this edge if there are no other edges with the same weight. If the graph is not disconnected, the same algorithm is applied on the residual graph until a disconnected residual graph is obtained. The weight of the final node that is removed produces the DQM. The weakest breach path cannot be determined with this approach because it may follow another edge with the same weight, whose removal does not disconnect the start and destination nodes. In Fig. 6, the trace of Algorithm 3 is depicted for the sample auxiliary graph in Fig. 6a. The DQM algorithm removes the nodes with the largest weight from the auxiliary graph to obtain a residual graph where the start and destination nodes are disconnected. Hence, the algorithm builds a heap using the weights of the nodes, extracts the index of the node with the largest weight and removes the node, as well as the incoming and outgoing edges and runs the depth first search algorithm to determine if the residual graph is disconnected. In the first step (Fig. 6a), the node with the largest weight is node 4 and it is removed and the disconnected residual graph shown in Fig. 6b is obtained. In the second step, node 6 is removed because it is the node with the largest weight in the residual graph and the connected residual graph in Fig. 6c is obtained. Continuing like this, in the sixth step, node 7 is with the largest weight in the residual graph so that it is removed, and the residual graph becomes disconnected now. Consequently, the algorithm stops and declares that the DQM is 0.84 because it is the weight of the last removed node. Algorithm 3. DeploymentQualityMeasure 1: 2: 3: 4: 5: 6: 7: 8:

buildHeap H using Wc while not H.empty() do h = H.extractMax() Remove node h.c from auxiliary graph if s and d are disconnected then Return h.Wc /*Depth first search can be used*/ end if end while

5.1. Complexity of the algorithm Denoting the number of nodes in auxiliary graph with V and the number of connections with E, Algorithm 3 has complexity O(VElogV). If R sensors are deployed, then the watershed segmentation produces a planar graph if we assume that all of the unbounded contours are connected to a common vertex at infinity. Then, there will be R regions (faces) bounded by the watershed contours. Euler’s formula states that the condition nv  ne + nf P 2 holds true where nv, ne and nf = R are the number of vertices, edges and the faces of any planar graph, respectively [41]. Every face touches at least three watershed contours so that 3nf 6 2ne. Hence, there will be at most 3nv  6 watershed contours which are represented as nodes in the auxiliary graph, and V 6 3R  6.

6. Simulation results and discussion To analyze the watershed segmentation, we developed a simulator coded in C++ integrated with Matlab. In the simulations, a 300  60 m2 surveillance field is made up of 1 m  1 m grids, and the boundary regions are 10 m wide. Sensors are deployed randomly with uniform distribution over the field. Thirteen obstacles are modeled as discs where the centers are also uniformly distributed and the radii are uniform random variables between 10 m and 20 m. The obstacles are assumed to disable sensing, as well as the traversal of the target. Sensors are modeled as Neyman–Pearson detectors, where the signalto-noise ratio is c = 20 dB and the signal attenuates with path-loss exponent g = 2. The sensor decisions are based on L = 100 samples where the reliability threshold probability is chosen as 0.9. For KIS and KRIS, the required degrees of coverage, K, is 3. The effect of the false alarm rate on DQM for MDIS is shown in Table 1 for 90 sensors. As the tolerance to false alarms increases, the deployment quality is enhanced. The results are the averages of 100 runs and the variance in the results is acceptably low as can be seen in Table 1 that indicates the 95% confidence intervals. The effect of the sensor count for the most-dominating sensor iso-sensing (MDIS), K-degrees of iso-sensing (KIS), reliable iso-sensing (RIS) and reliable K-degrees iso-sensing (KRIS) definitions are depicted in Figs. 7–10, respectively. The figures indicate that as the false alarm rate and the sensor count increase, so does the DQM. The chosen a values of 0.01, 0.05 and 0.1 can be considered as low, moderate and high false alarm rate scenarios, respectively. The sensor count parameter is arranged accordingly to depict sparse, moderate and dense deployment. For high false alarm rates, it is clear that sparse deployment satisfies the required DQM. When the false alarm rate is lowered, the number of deployed sensors is to be increased. The sensor count is more influential when a is allowed to be low. For sparse deployments, KIS produces a larger DQM value compared to MDIS (KIS where K = 1) because the detection probabilities of K sensors are combined to obtain a better decision. However, for dense deployments, increasing the value of K does not make a significant difference in the results. When KIS is bounded with a reliability threshold probability pt, sparse deployment produces apparent breach paths. That is, for some paths in the surveillance field, no sensors detect the phenomenon with a probability larger than pt. For example, when KIS with K = 3 is used, 40 sensors are sufficient to produce a DQM of 0.9 for a = 0.05. However, for the same false

Table 1 Effect of the false alarm rate on the DQM when 90 sensors are deployed for MDIS. False alarm rate

DQM

Variance

95% Confidence interval

0.050 0.075 0.100 0.125

0.93 0.96 0.97 0.98

0.020 0.015 0.012 0.010

(0.90–0.96) (0.94–0.98) (0.96–0.99) (0.97–0.99)

E. Onur et al. / Computer Networks 54 (2010) 428–441

1

1

0.9

0.9

0.8

0.8

0.7

0.7

0.6

0.6 DQM

DQM

438

0.5 0.4

0.4

0.3

0.3

0.2

0 20

0.2

α=0.01 α=0.05 α=0.1

0.1 30

40

50 60 70 Sensor count

80

90

100

1 0.9 0.8 0.7

DQM

0.6 0.5 0.4 0.3 0.2

α=0.01 α=0.05 α=0.1

0.1 0 20

30

40

50 60 70 Sensor count

80

90

100

Fig. 8. Effect of sensor count and false alarm rate on the DQM for KIS.

1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2

α=0.01 α=0.05 α=0.1

0.1 0 20

30

40

50 60 70 Sensor count

80

90

α=0.01 α=0.05 α=0.1

0.1

Fig. 7. Effect of sensor count and false alarm rate on the DQM for MDIS.

DQM

0.5

100

Fig. 9. Effect of sensor count and false alarm rate on the DQM for RIS.

alarm rate scenario, more than 70 sensors are required for RIS when pt = 0.9.

0 20

30

40

50 60 70 Sensor count

80

90

100

Fig. 10. Effect of sensor count and false alarm rate on the DQM for KRIS.

The effect of the reliability threshold is seen in Fig. 9. When fewer than 80 sensors are deployed, a growing area is not monitored reliably as a is lowered. Similarly, with fewer than 20 sensors, some parts of the field can be assumed to be monitored with zero probability since the associated detection probabilities are lower than the reliability threshold. Indeed, the DQM is zero for a = 0.05 for 20 sensors. When RIS is bounded with the coverage degree parameter K, the results do not change significantly as can be seen in Fig. 10. Because, to increase the detection probability at each grid point, dense deployment is required. Considering the spatial distribution of the sensors, to attain at least the threshold probability level, the required number of sensors provide a coverage degree greater than three. In other words, deploying more sensors to increase the detection probability at each grid point automatically increases the coverage degree and vice versa. For RIS and KRIS, when the required DQM value is achieved, it means that the deployment is saturated, and additional sensors will not improve performance. Thus, for RIS and KRIS, it is more appropriate to consider saturated and unsaturated deployment scenarios instead of sparse, moderate and dense deployments. For some applications such as battlefield surveillance, higher accuracy may be required. For those applications KIS with K > 1 can be employed. The effect of coverage degree on the deployment quality measure is analyzed in Fig. 11 where Elfes’s detectors (see Eq. (2)) are utilized. The sensing range and the decay of the detectors are ar1 2 ranged according to parameters dt ¼ 10 m, dt ¼ 30 m, k = 0.1 and b = 0.9. The same DQM level can be provided with fewer sensors for larger coverage degree requirement. For example, to attain a DQM of 0.9 for KIS with K = 1, K = 2 and K = 3, the required number of sensors are 100, 80 and 60, respectively. From the target’s standpoint, following the watershed contours is beneficial. However, the period of time the target spends in the field influences its detectability, as well. A discrete event simulation (DES) is coded in C++ using Matlab to verify this argument next. After applying the

E. Onur et al. / Computer Networks 54 (2010) 428–441

sensor counts is depicted in Fig. 12. If the target remains in the field for a longer time period, then its detection probability will be larger. For example, when nine sensors are deployed, for a target with a velocity of 5 g/s, the detection ratio is around 0.68, whereas for a velocity of 1 g/s, the same ratio rises to approximately 0.95. Consequently, the target should pass far from the sensors rapidly.

1 0.9 0.8 0.7 0.6 DQM

439

0.5

7. Conclusion

0.4 0.3 0.2

K=1 K=2 K=3

0.1 0 20

30

40

50

60

70

80

90

100

Sensor count Fig. 11. Effect of coverage on the DQM for KIS where Elfes’detectors are 1 2 utilized (dt ¼ 10 m, dt ¼ 30 m, k = 0.1 and b = 0.9).

1 0.95 0.9

Detection ratio

0.85 0.8 0.75

In this paper, we propose the utilization of the watershed segmentation algorithm to find the possible breach paths in a surveillance field with obstacles. In order to apply the watershed segmentation, the iso-sensing map is defined and a recursive algorithm is designed to find the deployment quality measure defined as the maximum detection probability on the weakest breach path. The simulations indicate the impact of the false alarm rate and the sensor count on the deployment quality measure. The wireless sensor network application designer may merely use MDIS (KIS with K = 1) if the required security level is not extremely high. KIS and KRIS are beneficial when large number of sensors are to be deployed and a sleep scheduling algorithm is to be implemented to prolong the lifetime of the network. As a future work, we plan to generalize the obstacle models by utilizing a 3-D topography and to analyze the effect of grid size on the sensitivity of the deployment quality.

0.7

Acknowledgement 0.65

1 g/s 2 g/s 3 g/s 4 g/s 5 g/s

0.6 0.55 0.5

5

6

7

8

9 10 Sensor count

11

12

13

Fig. 12. Effect of the sensor count on the detection ratio of a target following the watershed contours for several target speeds (g/s denotes the velocity of the target in terms of grids per second).

watershed segmentation algorithm, the potential breach paths are revealed. A target with a constant velocity traverses the region through the watershed contours starting at a random grid point on the contour where it touches the bottom line along the x-axis. The aim is to pass the field to reach the insecure side (see Fig. 1a). The 600  100 m2 field is comprised of 1 m  1 m grids. The iso-sensing map is determined according to MDIS after randomly deploying varying number of Neyman–Pearson detectors with uniform distribution on the field. The signal-to-noise ratio is c = 30 dB, the signal attenuates with path-loss exponent g = 2.5, the false alarm rate a = 0.01 and the sensor decisions are based on L = 100 samples. The simulation is repeated 2000 times per deployment and the results are the averages of 100 distinct deployments. Three circular obstacles are placed where the radii are uniformly randomly chosen between 8 m and 15 m. The detection ratio of targets with several constant velocities (denoted in grids per second, g/s) for varying

This work is supported by the State Planning Organization of Turkey under the Grant Number 03K120250, and by TUBITAK under the Grant Number 106E082. Parts of this work are presented in preliminary form in the IEEE Inter_ national Conference on Communications, Istanbul, Turkey, June 2006. References [1] E. Onur, C. Ersoy, H. Deliç, How many sensors for an acceptable breach probability level?, Computer Communications 29 (2) (2006) 172–182 [2] X.-Y. Li, P.-J. Wan, O. Frieder, Coverage in wireless ad hoc sensor networks, IEEE Transactions on Computers 52 (6) (2003) 753–763. [3] S. Megerian, F. Koushanfar, M. Potkonjak, M.B. Srivastava, Worst and best-case coverage in sensor networks, IEEE Transactions on Mobile Computing 4 (1) (2004) 84–92. [4] D.P. Mehta, M.A. Lopez, L. Lin, Optimal coverage paths in ad hoc sensor networks, Proceedings of the IEEE International Conference on Communications, vol. 26, Anchorage, USA, 2003, pp. 507–511. [5] T. Clouqueur, V. Phipatanasuphorn, P. Ramanathan, K.K. Saluja, Sensor deployment strategy for detection of targets traversing a region, Mobile Networks and Applications 8 (4) (2003) 453–461. [6] F.Y.S. Lin, P.L. Chiu, A near-optimal sensor placement algorithm to achieve complete coverage/discrimination in sensor networks, IEEE Communications Letters 9 (1) (2005) 43–45. [7] M. Younis, K. Akkaya, Strategies and techniques for node placement in wireless sensor networks: a survey, Ad Hoc Networks 6 (4) (2008) 621–655. [8] S. Megerian, F. Koushanfar, G. Qu, G. Veltri, M. Potkonjak, Exposure in wireless sensor networks: theory and practical solutions, Wireless Networks 8 (5) (2002) 443–454. [9] B. Cärbunar, A. Grama, J. Vitek, O. Cärbunar, Redundancy and coverage detection in sensor networks, ACM Transactions on Sensor Networks 2 (1) (2006) 94–128.

440

E. Onur et al. / Computer Networks 54 (2010) 428–441

[10] X. Wang, G. Xing, Y. Zhang, C. Lu, R. Pless, C. Gill, Integrated coverage and connectivity configuration in wireless sensor networks, in: Proceedings of the First International Conference on Embedded Networked Sensor Systems, 2003, pp. 28–39. [11] F. Aurenhammer, Voronoi diagrams – a survey of a fundamental geometric data structure, ACM Computing Surveys 23 (3) (1991) 345–405. [12] C. Wang, L. Schubert, An optimal algorithm for constructing the delaunay triangulation of a set of line segments, in: SCG ’87: Proceedings of the Third Annual Symposium on Computational Geometry, ACM, New York, NY, USA, 1987, pp. 223–232. [13] C.-H. Wu, K.-C. Lee, Y.-C. Chung, A delaunay triangulation based method for wireless sensor network deployment, Computer Communications 30 (14-15) (2007) 2744–2752. [14] M. Ma, Y. Yang, Adaptive triangular deployment algorithm for unattended mobile sensor networks, IEEE Transactions on Computers 56 (7) (2007) 847–946. [15] L. Vincent, P. Soille, Watersheds in digital spaces: an efficient algorithm based on immersion simulations, IEEE Transactions on Pattern Analysis and Machine Intelligence 13 (6) (1991) 583–598. [16] F. Meyer, Morphological segmentation produces a voronoi tessellation of the markers, in: International Conference on Image Processing, vol. 5, October 24–27, 2004, pp. 3077–3080. [17] S. Meguerdichian, F. Koushanfar, M. Potkonjak, M. Srivastava, Coverage problems in wireless ad hoc sensor network, in: Proceedings of the IEEE INFOCOM, Anchorage, USA, 2001, pp. 1380–1387. [18] I. Chatzigiannakis, G. Mylonas, S. Nikoletseas, A model for obstacles to be used in simulations of wireless sensor networks and its application in studying routing protocol performance, Simulation 83 (8) (2007) 587–603. [19] A. Kansal, E. Yuen, W.J. Kaiser, G.J. Pottie, M.B. Srivastava, Sensing uncertainty reduction using low complexity actuation, in: Proceedings of the Third International Symposium on Information Processing in Sensor Networks, Berkeley CA, USA, 2004, pp. 388–395. [20] S. Ganeriwal, A. Kansal, M.B. Srivastava, Self aware actuation for fault repair in sensor networks, in: Proceedings of the IEEE International Conference on Robotics and Automation, vol. 5, New Orleans, USA, 2004, pp. 5244–5249. [21] E. Onur, C. Ersoy, H. Delic, L. Akarun, Surveillance wireless sensor networks: deployment quality analysis, IEEE Network 21 (6) (2007) 48–53. [22] W. Wang, V. Srinivasan, B. Wang, K.-C. Chua, Coverage for target localization in wireless sensor networks, IEEE Transactions on Wireless Communications 7 (2) (2008) 667–676. [23] Q. Cao, T. Yan, J. Stankovic, T. Abdelzaher, Analysis of target detection performance for wireless sensor networks, Lecture Notes in Computer Science: Distributed Computing in Sensor Systems, vol. 3560, Springer-Verlag, 2005, pp. 276–292. [24] T.E. McEwan, Differential Pulse Radar Motion Sensor, United States Patent (5,966,090). [25] P.K. Dutta, A.K. Arora, S.B. Bibyk, Towards radar-enabled sensor networks, in: Proceedings of the Fifth International Conference on Information Processing in Sensor Networks, Nashville, TN, USA, 2006, pp. 467–474. [26] T.S. Rappaport, Wireless Communications: Principles and Practice, Prentice-Hall, Upper Saddle River, USA, 1996. [27] D. Kazakos, P. Papantoni-Kazakos, Detection and Estimation, Computer Science Press, New York, USA, 1990. [28] A. Elfes, Occupancy grids: a stochastic spatial representation for active robot perception, in: S.S. Iyengar, A. Elfes (Eds.), Autonomous Mobile Robots: Perception, Mapping, and Navigation, vol. 1, IEEE Computer Society Press, Los Alamitos, CA, 1991, pp. 60–70. [29] K. Mechitov, S. Sundresh, Y. Kwon, G. Agha, Cooperative tracking with binary-detection sensor networks, in: Proceedings of the First International Conference on Embedded Networked Sensor Systems, New York, NY, USA, 2003, pp. 332–333. [30] Y. Zou, K. Chakrabarty, Uncertainty-aware and coverage-oriented deployment for sensor networks, Journal of Parallel and Distributed Computing 64 (7) (2004) 788–798. [31] K. Chakrabarty, S.S. Iyengar, H. Qi, E. Cho, Grid coverage for surveillance and target location in distributed sensor networks, IEEE Transactions on Computers 51 (12) (2002) 1448–1453. [32] M. Cardei, J. Wu, Energy-efficient coverage problems in wireless ad hoc sensor networks, Computer Communications 29 (4) (2006) 413– 420. [33] J. Wu, S. Yang, Energy-efficient node scheduling models in sensor networks with adjustable ranges, International Journal of Foundations of Computer Science 16 (1) (2005) 3–17.

[34] S. Kumar, T.H. Lai, A. Arora, Barrier coverage with wireless sensors, Wireless Networks 13 (6) (2007) 817–834. [35] C. Liu, K. Wu, Y. Xiao, B. Sun, Random coverage with guaranteed connectivity: joint scheduling for wireless sensor networks, IEEE Transactions on Parallel and Distributed Systems 17 (6) (2006) 562– 575. [36] S. Ren, Q. Li, H. Wang, X. Chen, X. Zhang, Design and analysis of sensing scheduling algorithms under partial coverage for object detection in sensor networks, IEEE Transactions on Parallel and Distributed Systems 18 (3) (2007) 334–350. [37] S. Funke, A. Kesselman, F. Kuhn, Z. Lotker, M. Segal, Improved approximation algorithms for connected sensor cover, Wireless Networks 13 (2) (2007) 153–164. [38] A. Ghosh, S.K. Das, Coverage and connectivity issues in wireless sensor networks: a survey, Pervasive and Mobile Computing 4 (3) (2008) 303–334. [39] J.B.T.M. Roerdink, A. Meijster, The watershed transform: definitions algorithms and parallelization strategies, Fundamenta Informaticae 41 (1–2) (2000) 187–228. [40] F. Meyer, Topographic distance and watershed lines, Signal Processing 38 (1) (1994) 113–125. [41] M. de Berg, M. van Kreveld, M. Overmars, O. Schwarzkopf, Computational Geometry: Algorithms and Applications, second ed., Springer, 2000.

Ertan Onur received the B.S. degree in Com_ puter Engineering from Ege University, Izmir, Turkey in 1997, and the M.S. and Ph.D. degrees in Computer Engineering from Bog_ aziçi University, Istanbul, Turkey in 2001 and 2007, respectively. He is a BAL’93 graduate. After the B.S. degree, he worked for LMS Durability Technologies GmbH, Kaiserslau_ tern, Germany and Global Bilgi, Istanbul, Turkey. During the Ph.D degree, he worked as a R&D project manager at Argela Technolo_ gies, Istanbul. Presently, he is an assistant professor at Technical University of Delft, Netherlands. His research interests are in the area of telecommunications, personal networks, wireless and sensor networks. He is a member of IEEE.

Cem Ersoy received his B.S. and M.S. degrees in Electrical Engineering from Bogaziçi Uni_ versity, Istanbul, in 1984 and 1986, respectively. He worked as an R&D engineer in NETAS A.S. between 1984 and 1986. He received his Ph.D. in Electrical Engineering from Polytechnic University, Brooklyn, New York in 1992. Currently, he is a professor in the Computer Engineering Department of Bogaziçi University. His research interests include performance evaluation and topological design of communication networks, wireless networks and mobile applications. He is a senior member of IEEE.

Hakan Deliç received the B.S. degree (with honors) in Electrical and Electronics Engi_ neering from Bogaziçi University, Istanbul, Turkey, in 1988, and the M.S. and the Ph.D. degrees in Electrical Engineering from the University of Virginia, Charlottesville, in 1990 and 1992, respectively. He was a Research Associate with the University of Virginia Health Sciences Center from 1992 to 1994. In September 1994, he joined the University of Louisiana at Lafayette, where he was on the Faculty of the Department of Electrical and Computer Engineering until February 1996. He was a Visiting Associate Professor in the Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, during the 2001–2002 academic year. He is currently a professor of Electrical and Electronics Engineering

E. Onur et al. / Computer Networks 54 (2010) 428–441 at Bogaziçi University. His research interests lie in the areas of communications and signal processing, with current focus on ultra-wideband communications, iterative decoding, robust systems, and sensor networks. He frequently serves as a consultant to the telecommunications industry. He is a senior member of IEEE.

Lale Akarun received the B.S. and M.S. degrees in Electrical Engineering from _ Bogaziçi University, Istanbul, in 1984 and 1986, respectively. She obtained her Ph.D. from Polytechnic University, New York in 1992. Since 1993, she has been working as a faculty member at Bogaziçi University. She became a professor of Computer Engineering in 2001. Her research areas are face recognition, modeling and animation and human activity and gesture analysis. She has worked on the organization committees of IEEE NSIP99, EUSIPCO 2005, and eNTER-FACE2007. She is a senior member of the IEEE.

441