Vision Graph Construction in Wireless Multimedia Sensor Networks

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1 University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln CSE Conference and Worksho Paers Comuter Science and Engineering, Deartment of 21 Vision Grah Construction in Wireless Multimedia Sensor Networks Xin Dong University of Nebraska-Lincoln, xdong@cse.unl.edu Mehmet C. Vuran University of Nebraska-Lincoln, mcvuran@cse.unl.edu Follow this and additional works at: htt://digitalcommons.unl.edu/cseconfwork Dong, Xin and Vuran, Mehmet C., "Vision Grah Construction in Wireless Multimedia Sensor Networks" (21). CSE Conference and Worksho Paers htt://digitalcommons.unl.edu/cseconfwork/285 This Article is brought to you for free and oen access by the Comuter Science and Engineering, Deartment of at DigitalCommons@University of Nebraska - Lincoln. It has been acceted for inclusion in CSE Conference and Worksho Paers by an authorized administrator of DigitalCommons@University of Nebraska - Lincoln.

2 Vision Grah Construction in Wireless Multimedia Sensor Networks Xin Dong and Mehmet C. Vuran Cyber-Physical Networking Laboratory Deartment of Comuter Science & Engineering University of Nebraska-Lincoln, Lincoln, NE {xdong, Abstract In Wireless multimedia sensor networks (WMSNs), the camera nodes connected in the vision grah share overlaed field of views (FOVs) and they deend on the densely deloyed relay nodes in the communication network grah to communicate with each other. Given a uniformly deloyed camera sensor network with relay nodes, the roblem is to find the number of hos for the vision-grah-neighbor-searching messages to construct the vision grah in an energy efficient way. In this aer, mathematical models are develoed to analyze the FOV overla of the camera nodes and the multi-ho communications in two dimensional toologies, which are utilized to analyze the relation between vision grah construction and maximum ho count. In addition, simulations are conducted to verify the models. I. INTRODUCTION Recently, the advances in low cost CMOS imaging sensors have made wireless multimedia sensor networks (WMSNs) ossible [1][5]. In WMSNs, multile camera sensors are deloyed to monitor an area. Potential alications of WMSNs include surveillance, traffic tracking, wildlife monitoring, and battlefield monitoring. The challenges faced by scalar wireless sensor networks, such as energy constraints, limited rocessing caabilities, unreliability and low accuracy of obtained data, are only exacerbated in WMSNs. To imrove the sensing quality, a certain level of collaboration among sensor nodes are required. In [1], collaborative multimedia in-network rocessing is suggested, which can utilize the comutational caacity of sensors as well as reduce communication cost and energy consumtion. In [2], scalar sensors are exloited to hel camera nodes detect events in WMSNs. More directly, camera sensors can collaborate with each other to accomlish tasks. This is achieved by exloiting the overlaed field-of-views of the camera sensors. In a WMSN, each camera sensor has its own directional sensing range, known as the field-of-view (FOV), and cameras may have overlaed FOVs such that if an event occurs in this overlaed area, several cameras may cature this event in different ersectives. These camera nodes form a vision grah [4], in which an edge between two cameras indicates they share an overlaed FOV and the two cameras are called vision grah neighbors. Some research exloits the characteristics of the overlaed FOVs in collaboration of camera sensor nodes. In [6], routing aths are established based on the overlaed FOVs of camera nodes. In [3] and [8], overlaed FOVs are exloited to define correlation among camera nodes and this correlation is used for cooerative video rocessing. Meanwhile, in [4], the images of the overlaed FOVs have been exlored to calibrate the camera nodes. To construct vision grahs in WMSNs, two methods are widely used in literature. The cameras nodes may know their locations and directions ariori[3], or reference objects are used for camera nodes to calculate overlaed FOVs [7][8]. However, in these works, simle flooding is emloyed to exchange information among camera nodes. It is well known that for large scale WSNs, flooding is imractical in terms of communication cost and network congestion. In this aer, we roose a limited-ho-number multi-ho communication for constructing the vision grah in WMSNs. Given a uniformly deloyed camera sensor network with relay nodes, we are interested in finding the maximum allowed ho count for the vision-grah-neighbor-searching messages (hello message) in order to construct the vision grah in an energy efficient way. Mathematical models are develoed to analyze the robability of constructing the vision grah for different message lifetime (maximum ho count). This is achieved by develoing a robabilistic model of the overlaed FOV for different distance and the robabilistic model of the roagation distance for different message life time. In [9], the authors have roosed a method to analyze the robability distribution of multi-ho communications in WSNs. However, only one dimensional toology is considered and the channel is assumed to be erfect. In this aer, we roose a recursive method to analyze the multi-ho communications of WMSNs in two dimensional toologies. Moreover, a more ractical channel model is adoted to cature the feature of wireless communication. In addition, simulations are conducted to verify our models. To the best of our knowledge, this is the first aer to address the communication roblem of constructing the vision grah in WMSNs. Our main contributions are: The robabilistic model of two cameras having an overlaed FOV with resect to their distance; The 2-D multi-ho communication model that mas maximum ho number to connectivity; The mathematical model to calculate the needed maximum ho number to construct the vision grah for a given WMSN. The remainder of this aer is organized as follows: The robabilistic models for the overlaed FOV, the multi-ho communication and the vision grah construction are develoed in Section II. Simulations and Numerical analysis of those models are rovided in Section III. Furthermore, the conclusions are

3 r v 1 2 c d c 1 2 Camera Node drawn in Section IV. Fig. 1. Overlaed FOV The system overview. II. SYSTEM MODEL Relay Node We consider alications in which the camera sensors are randomly deloyed. To connect these camera sensors, other relay nodes are also randomly deloyed among them by Poisson random rocess. After deloyment, the camera sensors send hello messages that have a maximum allowed ho count to find their vision grah neighbors. In each transmission, the sender broadcast a hello message unless the message achieves its maximum allowed ho count. When a camera sensor receives a hello message from its eers, it uses the location and direction information to calculate if the source of the message is its vision grah neighbor. Hence the vision grah is constructed in a distributed manner. Denote the robability of constructing the vision grah v, our goal is to relate this robability to the maximum allowed ho count, n, of the hello message. v is given as v (n) = vc (d, n)dd, (1) v (d)dd where vc (d, n) is the robability of successfully connected vision grah neighbors given the distance d and the maximum ho number n whereas v (d) is the robability of having vision grah neighbors given distance d. v (d) is related to the FOV of the camera and it is develoed in Section II-A, while vc (d, n) is related to the multi-ho communication of the sensors, and the model is rovided in Section II-B. In Section II-C, those two models are utilized to develo the model for vision grah construction. A. Overlaed Field of View The FOV of a camera is modeled as a fan sector in a 2D lane, as shown in Fig. 1. It is defined by a tule (r v,α), where r v is the FOV radius, which determines the maximum distance the camera can observe, and α is the visual angle, which deicts the width of the FOV. The overla model is shown in Fig. 1. It is observed that given the distance d of two cameras, when these two cameras are at some secific directions, they will have overlaed FOV and become vision grah neighbors. Given the assumtion that the direction of the camera is uniformly distributed, the robability that two cameras are vision grah neighbors is equal to the ortion of directions at which they have an overlaed FOV. When given the direction of the first camera at angle θ 1, there exists a range [θ2 min,θ2 max ], such that when the direction of the second camera, θ 2, is in this range, these two cameras have an overlaed FOV. As θ 1 changes, the range of θ 2 changes too. With the ranges of θ 1 and θ 2 in which the two camera nodes can have an overlaed FOV at distance d, the robability of having an overlaed FOV at distance d, which is denoted as o (d), is the integral of the ranges divided by the maximum range. Thus, o (d) = 1 2π 2 i θ max,i 1 θ min,i 1 (θ max,i 2 θ min,i 2 )dθ 1. (2) In Table I, the ranges of θ 1 and θ 2, in which two camera nodes have an overlaed FOV for different distance, d, are listed. For a given d, the range of θ 1 is divided into categories, and in each category, the range of θ 2 can be exressed by the value of θ 1. Note in the tables, the range of θ 1 is only considered as in range [,π]. For the range [π, 2π], it is a mirror of [,π]. Also note that the camera visual angle α imacts the boundary conditions in (2), as shown in Table I and in three different cases ([, π 4 ], [ π 4, π 3 ], [ π 3, π 2 ]), the exressions are different. Here, we assume the visual angle of the camera α is in the range of [ π 4, π 3 ]. The variables a 1 a 6 in Table I are given as follows: a 1 =cos 1 d, (3) 2r v a 2 = tan 1 r v sin (θ ) d r v cos (θ ), (4) a 3 =sin 1 r v d, (5) a 4 =cos 1 d tan2 (θ )+ rv 2 + rv 2 tan 2 (θ ) d 2 tan 2 (θ ) r v (1 + tan 2, (θ )) (6) a 5 =cos 1 d tan2 (θ ) rv 2 + rv 2 tan 2 (θ ) d 2 tan 2 (θ ) r v (1 + tan 2, (θ )) (7) a 6 =cos 1 d tan2 (θ + )+ rv 2 + rv 2 tan 2 (θ + ) d 2 tan 2 (θ + ) r v (1 + tan 2, (θ + )) (8) where θ = θ 1 α and θ + = θ 1 + α. As exected, it is noticed from Table I that when the two cameras are close to each other, the ranges in which they can be vision grah neighbors are larger, which means the robability that they are vision grah neighbors is greater. B. Multi-ho Communication In this section, we develo a model to analyze multiho communication of two camera nodes in wireless sensor networks. In the analysis, the distance of camera node A and B is denoted as l and the density of the relay nodes is λ. In addition, log-normal shadowing model is emloyed to reresent the channel. In our model, Cd n reresents the event that two nodes at distance d can communicate through exactly n hos, while C d n reresents the oosite. The robability of event Cn d is

4 TABLE I THE POSSIBLE RANGES OF θ 1 AND θ 2 TO HAVE AN OVERLAPPED FOV FOR DIFFERENT DISTANCE d. 2rv <d 2r v 1 [,α cos 1 d ] [π a 2r 1 α, π + a 1 + α] v 2 [α cos 1 d,α] 2r v [π a 1 α, π a 2 + α] 3 [α, cos 1 d + α] [π a 2r 1 α, π a 4 + α] v r v <d 2r v 1 [,α cos 1 rv d ] [ a 3 + π α, a 3 + π + α] 2 [α cos 1 r v d,α] [ a 3 + π α, π a 2 + α] 3 [α, cos 1 rv d + α] [ a 3 + π α, π a 4 + α] 4 [cos 1 rv d + α, cos 1 + α] [π a d 2r 2 α, π a 4 + α] v 5 [cos 1 d + α, sin 1 rv 2r v d + α] [π a 5 α, π a 4 + α] 2r v cos(2α) <d r 1 [,α] [, 2π] 2 [α, cos 1 d + α] 2r v [π + a 2 α, π + α] 3 [cos 1 d + α, π α] 2r v [π a 5 α, π + α] 4 [π α, α + π [π a 5 α, a 6 + π + α] 5 [α + π 2,π] [π a 4 α, a 6 + π + α] <d 2r v cos(2α) 1 [,α] [, 2π] 2 [α, π α] [π a 2 α, π + α] 3 [π α, cos 1 d + α] 2r v [π a 2 α, a 6 + π + α] 4 [cos 1 d 2r v + α, α + π [π a 5 α, a 6 + π + α] 5 [α + π 2,π] [π a 4 α, a 6 + π + α] denoted as c (d, n) and the robability of event C n d is q c(d, n). In addition, P c (d, n) denotes the robability that two nodes can communicate at a distance d through u to n hos. Adoting the shadowing channel model [11], the signal noise ratio (SNR), φ, in db is exressed as φ(x σ,l)=p t PL(d ) 1η log 1 ( d d ) X σ P n, (9) where P t is the transmission ower, PL(d ) is the attenuation at the reference distance d, X σ is the shadowing effect random variable and P n is the noise floor. The symbol error rate, s (X σ,d) is calculated by s (X σ,d)=q (β 2 (φ(x σ,d) β 1 )), (1) where β 1 and β 2 are two arameters obtained by exeriments [12]. Note that other error rate models can be used in our scheme. For examle, a means to calculate the error rate for MicaZ mote is develoed in [1]. The robability that two nodes can communicate in one ho is: c (d, 1) = { Cd 1 } = (1 s (N,d)) L f Xσ (X σ )dx σ, (11) where L is the acket length in symbols, and f Xσ (X σ ) is the df of the shadowing effect random variable, X σ, which is Gaussian. For the one ho situation, the robability that two nodes can communicate within u to 1 ho is given simly by P c (d, 1) = c (d, 1). (12) Fig. 2. The multi-ho model. When the number of hos is greater than 2, we develo our model as shown in Fig. 2. The event that node A has a n- ho communication ath to node B equals to the event that there is node x at osition (ρ x,θ x ), which has a 1-ho ath to A a (n 1)-ho communication ath to node B. Assume the location of the intermediate node, x, is(ρ x,θ x ), where ρ x is the distance between x and B, and θ x is the angle of x with resect to vector BA. Thus, the distance between x and A can be exressed as ρ xa = (l ρ x cos θ x ) 2 +(ρ x sin θ x ) 2. (13) Given Poisson rocess density λ, the robability that at osition (ρ x,θ x ) there is a node is e (ρ x,θ x )=1 e λρxδρxδθx λρ x Δρ x Δθ x. (14) The aroximation holds when the area ρ x Δρ x Δθ x. The ranges of ρ x and θ x are <ρ x and θ x 2π. The robability of 1-ho communication between x and A is c (ρ xa, 1), where ρ xa is the distance from A to x. Recursively, the robability that node x has a (n 1)-ho communication ath to node B is c (ρ x,n 1). Therefore, c (d, n) =1 ρ x θ x (1 (λρ x Δρ x Δθ x ) c (ρ xa, 1) c (ρ x,n 1)). (15) In (15),1 (λρ x Δρ x Δθ x ) c (ρ xa, 1) c (ρ x,n 1) defines the robability that there is no intermediate node at (ρ x,θ x ) which satisfies the requirements. Since the relay nodes are deloyed indeendently, the roduct over ρ x and θ x is the robability that there is no intermediate node at the whole lanar which has 1-ho communication to A and n 1 communication to B. This is equal to the robability that A and B cannot communicate in n hos. Finally, subtracting that robability from 1 is the robability that the two camera nodes, A and B, can have a n-ho communication. Also, the robability that two nodes at distance l can communicate within u to n hos is P c (d, n) = { Cd} 1 { + C1 d,cd} 2 + { + C1 d, C } d,..., 2 (n 1) C d,cd n. (16)

5 The first term in (16) is the robability of communication in 1 ho, the second term is the robability that the two camera nodes cannot communicate in 1 ho but can communicate in 2 hos. Generally, the nth term is the robability that the two camera nodes cannot communicate within u to (n 1) hos but can communicate in n hos. The sum is the robability that the two nodes can communicate within u to n hos. Assume that given distance, d, C1 l,..., C d n and C1 d,...,cn d are indeendent1, thus, we have P c (d, n) = { Cd} 1 { } { } + C1 d C 2 d + + { } { } C1 d C(n 1) d {Cd n } = c (d, 1) + q c (d, 1) c (d, 2) + (17) ( n 1 ) + q c (d, i) c (d, n). i=1 C. Vision Grah Construction The communication range of nodes in WSNs is short, hence a camera node s vision grah neighbors may be several hos away. On the other hand, two closely located camera nodes may not be vision grah neighbors. Given a uniformly deloyed camera sensor network with relay sensors, we show the robability of vision grah construction as a function of the maximum allowed ho count of the hello messages. Assume the camera node deloyment is a Poisson oint rocess and denote the camera node density as κ. Giventhe distance d, the robability that a camera node has vision grah neighbors at distance d is v (d) = ( 1 e κaμ) o (d) κa μ o (l), (18) where o (d) is the robability that two cameras have an overlaed FOV when the distance is d, which is rovided in Section II-A, and A μ is the size of an infinitely small circle area, which is exressed as A(μ) =2πd dd. The aths to some far away vision grah neighbors may not be established because of the limitation of the maximum message ho number. Thus, we consider the robability of constructing the vision grah as the ratio of the connected vision grah neighbors against all vision grah neighbors. Given a camera node A, the robability that there are camera nodes at distance d which are vision grah neighbors of A and they can communicate within n-hos is vc (l, n) = v (d)p c (d, n), (19) where v (d) is given in (18) and P c (d, n) is given in (17). The robability of constructing the vision grah using n-ho communication is v (n) = = = vc (d, n)dd v (d)dd 2πκd o (d)p c (d, n)dd 2πκd o (d)dd o (d)p c (d, n)d dd, o (d)d dd (2) 1 In [9], it is ointed out that in reality it is not the case, however, the simulation shows it is a reasonable simlification. TABLE II PARAMETER LIST. Parameter r v P t d PL d η Value 1 m dbm 1 m 55.4 dbm 4.7 Parameter σ P n λ β 1 β 2 Value dbm Probability of vision grah conscruction (%) Theoretical analysis Simulation Maximum ho number Fig. 3. The comarison of the theoretical analysis and the simulation results for constructing the vision grah. III. NUMERICAL ANALYSIS In this section, numerical analysis of the system model is erformed using Matlab. We first use TOSSIM simulation to verify our model in Section III-A, after which the camera FOV overla model, the multi-ho communication model as well as the model for constructing vision grah in WMSNs are analyzed in Section III-B. The arameters used in the analysis are listed in Table II. A. Model Verification To verify the models, we have simulated the WMSNs using TOSSIM. In the simulations, 1 network toologies are generated by a Poisson rocess, and the size of the field is 5 m 5 m. In each toology, two cameras nodes are set with random distance and random direction. Unless otherwise noted, he vision angle of each camera is 5π 18. Note all the camera airs in the 1 toologies are vision grah neighbors. Since we consider the ratio of the successful connected vision grah neighbors over all vision grah neighbors, if the two cameras are not vision grah neighbors, they do not have imact on the result. The other arameters are set the same as in Table II. In Fig. 3, the theoretical and the simulation results of the robability of constructing the vision grah are shown. It is observed from Fig. 3 that the mathematical model catures the characteristics of the FOV overla and the multi-ho communication. For our settings, instead of unlimited flooding, 5-ho broadcast is sufficient to construct the vision grah with a high confidence (91%). In other words, when deloying the WMSN, the camera nodes need to broadcast a hello message with maximum ho count of 5 to find the vision grah neighbors. B. Model Analysis In this section, the mathematical models are analyzed. In Fig. 4(a), the robability of camera FOV overlaing over

6 Probability of overla (%) α=π/4 α=5π/18 α=11π/36 α=π/ Distance (m) (a) Probability of multi ho connectivity (%) ho 2 hos 3 hos 4 hos 5 hos 6 hos 7 hos 8 hos Distance (m) (b) Probability of vision grah conscruction (%) α=π/4 2 α=5π/18 α=11π/36 α=π/ Maximum ho count (c) Fig. 4. (a) The robability of FOV overla, (b) the robability of multi-ho connectivity and (c) the robability vision grah construction. distance is shown for different camera vision angles. It is observed that when the camera vision angle is larger, the robability that two cameras have an overlaed FOV is greater. At the distance of 5 m, if the camera vision angle is π 3,itis 12% more likely to have a vision grah neighbor than camera vision angle of π 4. Also, the decrease of the robability over distance is not constant. Around distance of 1 m, which is the vision range, there is a shar dro. Thus, most vision grah neighbors will be in a close distance. The robability of connectivity for the multi-ho communication is deicted in Fig. 4(b), where the ho counts are the maximum allowed ho counts. It is shown that if the 1- ho coverage is r, the coverage for n-ho is slightly more than nr. For examle, at 9% connectivity, the coverage of 1-ho is 4.57 m, however, the coverage of 3-ho is 14.73, m and the overage of 5-ho is m. The reason behind this is that the log-normal channel model does not have a cut-off value as the maximum transmission range. Thus, beyond the 9% connectivity range, there are still some nodes that receive the message. Accordingly, their transmission can increase the coverage in the next ho. In addition, because the maximum distance of two vision grah neighbors in our setting is 2 m, we would assume the needed ho count is 4. The robability of constructing the vision grah as a function of maximum ho counts is shown in Fig. 4(c) for different camera vision angles. It is exected that because when the camera vision angle is greater, the two cameras are more likely to be vision grah neighbors, thus given a maximum ho count, the robability of constructing the vision grah is lower. However, the analysis shows the decrease of the robability is not significant. In fact, when the maximum ho count is 2, where the difference is most notable, the robability of constructing the vision grah for camera vision angle of π 4 is 52.8%, and for camera vision angle of π 3, the robability is 48.28%. IV. CONCLUSIONS In this aer, we address the issue of constructing vision grahs in WMSNs. A mathematical model for the camera field of view overlaing is develoed to analyze the robability of having vision grah neighbor over distance. Meanwhile, a multi-ho communication model with a realistic channel model is develoed to analyze the robability of multi-ho connectivity. Simulations are established to verify these models, which show that the mathematical models cature the characteristics of the FOV overlaing and the multi-ho communication. For our settings, instead of unlimited flooding, 5-ho broadcast is sufficient to construct the vision grah with high robability. REFERENCES [1] I. F. Akyildiz, T. Melodia, and K. R. Chowdhury, A survey on wireless multimedia sensor networks, Comuter Networks, vol. 51, no. 4, , 27. [2] A. Czarlinska and D. Kundur, Reliable Event-Detection in Wireless Visual Sensor Networks Through Scalar Collaboration and Game-Theoretic Consideration, IEEE Transactions on Multimedia, vol. 1, no. 5, , 28. [3] R. Dai and I. F. Akyildiz, A satial correlation model for visual information in wireless multimedia sensor networks, IEEE Transactions on Multimedia, vol. 11, no. 6, , 29. [4] D. Devarajan, Z. Cheng, and R. Radke, Calibrating distributed camera networks, Proceedings of the IEEE (Secial Issue on Distributed Smart Cameras), vol. 96, no. 1, 29. [5] S. Stanislava and H. Wendi, A Survey of Visual Sensor Networks, Advances in Multimedia, vol. 29, 29. [6] T. Ko and N. Berry, On scaling distributed low-ower wireless image sensors, in Proc. System Sciences, 26. HICSS 6. Proceedings of the 39th Annual Hawaii International Conference on, vol. 9, 26. [7] P. Kulkarni, P. Shenoy, and D. Ganesan, Aroximate initialization of camera sensor networks, Lecture Notes in Comuter Science, vol. 4373,. 67, 27. [8] H. Ma and Y. Liu, Correlation based video rocessing in video sensor networks, in Proc. IEEE Intl. Conf on Wireless Networks, Communications and Mobile Comuting, vol. 2, 25. [9] S. Vural and E. Ekici, Probability distribution of multiho distance in one-dimensional sensor networks, Comuter Networks Journal (Elsevier), vol. 51, no. 13, , 27. [1] M. C. Vuran and I. F. Akyildiz, Error control in wireless sensor networks: a cross layer analysis, IEEE/ACM Transactions on Networking (TON), vol. 17, no. 4, , 29. [11] M. Zuniga and B. Krishnamachari, Analyzing the transitional region in low ower wireless links in Proc. IEEE SECON 4, , Oct. 24. [12] htt://