Spatio-Temporal Monitoring using Contours in Large-scale Wireless Sensor Networks

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1 Spatio-Temporal Monitoring uing Contour in Large-cale Wirele Senor Network Hadi Alati Electrical and Computer Engineering Univerit of North Carolina at Charlotte 9 Univerit Cit Boulevard, Charlotte, NC 8 halati@uncc.edu Ai Naipuri Electrical and Computer Engineering Univerit of North Carolina at Charlotte 9 Univerit Cit Boulevard, Charlotte, NC 8 anaipur@uncc.edu ABSTRACT Thi paper preent algorithm for efficientl detecting the variation of a ditributed ignal over pace and time uing large cale wirele enor network. The propoed algorithm ue contour for etimating the patial ditribution of a ignal. A contour tracking algorithm i propoed to efficientl monitor the variation of the contour with time. Ue of contour reduce the communication cot b reducing the participation of enor node for the monitoring tak. The propoed cheme ue multi-enor collaboration technique and non-uniform contour level to reduce the error in recontructing the ignal ditribution. Reult from computer imulation are preented to demontrate the performance of the propoed cheme. Categorie and Subject Decriptor C. [Special-purpoe and Application-baed Stem]: Realtime and embedded tem, ignal proceing tem. eneral Term: Algorithm, deign, performance, theor. Keword Wirele enor network, image proceing, contour detection and tracking, collaborative proceing.. INTRODUCTION Batter conervation i a ke iue for deigning mot practical wirele enor network that are intended to operate for etended period of time. The problem i eacerbated in large-cale wirele enor network coniting of hundred or even thouand of enor in the ame network. We conider application requiring monitoring of the patial and temporal variation of a ditributed ignal uing a large-cale wirele enor network. Tpical eample include the monitoring of urface temperature, oil humidit, or preure over large and remote region (e.g. polar region or deert. In uch application, the patial ditribution of the ignal need to be Permiion to make digital or hard copie of all or part of thi work for peronal or claroom ue i granted without fee provided that copie are not made or ditributed for profit or commercial advantage and that copie bear thi notice and the full citation on the firt page. To cop otherwie, or republih, to pot on erver or to reditribute to lit, require prior pecific permiion and/or a fee. FOWANC 9, Ma 8, 9, New Orlean, Louiiana, USA. Copright 9 ACM /9/5...$5.. etimated over large area. Moreover, the tem mut etimate the variation of the ignal over time, which ma be changing lowl. Deigning uch network require additional conideration to meet the heav demand on it batter life. In thi paper we etend the idea preented in [] to realize efficient algorithm for patial and temporal monitoring of a ignal ditributed over a large area b detecting and tracking a et of contour line. The ke contribution of thi paper are: (a definition of an energ-efficient mechanim for etimating the patial ditribution of a ignal from a et of contour node (or edge node uing collaborative ignal proceing in the WSN; (b election of non-uniform contour level to reduce the error in recontructing the ignal from it contour; and (d introduction of a practical cheme for tracking the temporal variation of contour line uing collaborative proceing. The formal decription of the problem i preented in ection. The related work i reviewed in ection. The contour detection method uing collaborative proceing that wa introduced in [] i reviewed in ection, where we alo decribe the pecific deign conideration for patio-temporal monitoring of a ditributed ignal uing contour detection. The iue of contour level election i eplored in ection 5. In ection 6, we propoe a ditributed algorithm for tracking contour line. Performance evaluation of the propoed patial and temporal monitoring algorithm are preented in ection 7.. PROBLEM STATEMENT We aume a cenario where a large number of wirele enor node are randoml ditributed over a given area of interet. Each enor can obtain periodic obervation of the ignal in the enor field, uch a the temperature, humidit, barometric preure, etc. It i aumed that uch phical quantitie are patiall correlated o that it patial ditribution i band-limited and can be effectivel decribed with it contour at pecific level a illutrated in Figure. Ue of contour for depicting a ignal ditribution over a two-dimenional pace (i.e. D ignal i commonl ued in field uch a geological urveing, medical imaging, pattern recognition, and other. Our objective i to appl thi principle in large cale wirele enor network (WSN to conerve computation, communication cot, and torage requirement for etimating the ditribution of ignal over a large area. Note that thi proce i not epected to provide an accurate recontruction of the D ignal. However, uch a technique would be worthwhile if it provide ignificant aving in cot with reaonable accurac. We propoed a ditributed collaborative proceing algorithm b which wirele enor can 77

2 Figure : Modeling a ignal ditribution with it contour. Figure : Illutration of a ingle contour in a enor field and edge enor near it. detect if the are located near a pecific contour in the preence of noie []. Here, we propoe algorithm b which the contour detection principle i effectivel etended to etimating the patial a well a temporal variation of a ignal ditributed over a large region b involving onl a mall ubet of enor in the WSN. A contour in the enor field i defined a the line of demarcation between region that are above and below a threhold S. For decribing a contour uing wirele enor node, a tolerance ditance r i ued [], which define the region near a contour uch that a enor node located in the region i termed a a contour or edge node. Thi i illutrated in Figure. An algorithm for detecting edge node can have two tpe of deciion error. When a node decide that it i an edge node when it i not within a ditance r from the true contour, we have a fale detection. On the other hand, when a node that i actuall an edge node (i.e. located within a ditance r from the true contour fail to be detected, we have a mied detection. We ue thee two deciion error a performance meaure for edge detection a well a tracking of the contour. Error in detecting edge node can occur due to two reaon. Firt, although the actual edge or boundar demarcate two region having different ignal propertie, the true ditribution of the ignal acro the edge uuall ha a gradual change and not harp edge-like variation. In thi ene, a contour detection problem i different from edge or boundar detection a conidered in []. Secondl, quantization noie and other environmental noie ource introduce additional cope of detection error. In addition, we aim to keep the communication cot for collaboration to a minimum. With thee objective, a contour detection algorithm wa propoed in [] that ue a twotage proce for the detection of edge enor near a contour in the enor field. In the firt tage, all node periodicall ue their local obervation to decide if the are probable edge node (which can be obtained b checking if it local obervation lie between two given threhold. In the econd tage, onl thoe node that tet poitive in the firt tage tranmit quer meage to their neighbor and proce the returned information uing a patial filtering approach to confirm their deciion (ee Figure. Recontructing a D ignal from it contour require an appropriate number of contour a well a the level at which the contour are obtained to conve the ignal variation adequatel. Mot ignal recontruction problem aume uniforml ditributed contour. Since cot i a eriou contraint in large cale WSN, we eplore the ue of non-uniform contour level that reduce the recontruction error from contour at uniform level. The propoed olution i baed on ome general aumption about the ignal ditribution. We conider an elementar pline baed recontruction algorithm for obtaining the D ignal from a et of contour, and firt determine the optimum contour level that minimize the recontruction error under the aumption that the pdf of the ignal ditribution i known. For etimating error of the ignal ditribution, we ue the root mean quare of error (RMSE of the recontructed ignal. Finall, we conider the problem of monitoring the temporal variation of a contour b uing an algorithm that track edge node efficientl. Thi involve performing periodic tet at eiting edge node to determine if the edge node tatu hould be handed over to it neighbor. We ue etimate of ignal gradient at edge node to perform thi tak, and call thi the gradient compa technique.. RELATED WORK The ue of contour for ignal ditribution repreentation wa eplored in [6], however, without conidering noie. Moreover, there temporal monitoring wa performed b repeating the contour detection algorithm periodicall. A data-driven ditributed algorithm for earching a collection of enor repreenting the io-contour of a patial ignal ditribution within a pecified ignal range wa propoed and dicued in [7]. The developed a gradient-baed routing algorithm from quer meage of an quer node that wa alo ued for dicover of the contour-tree. Similar to [], the quering wa localized in the immediate neighborhood of each node for finding the io-contour. The alo conidered the preence of noi data reading, but the effect of noie intenit on qualit of the propoed algorithm wa not dicued. 78

3 A light-weight ditributed algorithm for repairing the broken line of a contour in order to track it variation uing binar enor wa propoed and dicued in [8]. The focued on information proceing and topolog maintenance apect of the contour tracking problem. Although the generall conidered the preence of noie, but it effect wa not eplored. The problem of approimating a famil of io-contour with topologicall equivalent polgon in wirele enor field uing a imple and efficient algorithm wa dicued in [9]. The evaluated their algorithm for real and nthetic data uing imulation. The effect of uncertaint in enor reading and tracking the variation of the contour were not taken into account.. EFFICIENT SPATIAL FILTERIN FOR CONTOUR DETECTION. Spatial Filtering uing Prewitt Filter Spatial filtering ha been widel ued in image proceing for edge detection application. Thi i commonl accomplihed b performing a patial differentiation of the image field followed b a threholding operation to determine point of teep amplitude change. Horizontal and vertical patial derivative are defined a []: F(, F(, (, =, (, = ( where F(, i the value of the ignal at the point (,. With thi, the gradient at the point (, can be written a: F (, = (, + (, ( There are two major limitation for appling thi edge detection method in enor network. Firtl, the enor are not uuall ditributed uniforml over the enor field uch a piel location. Secondl, the correlated ignal ditribution are uuall mooth and the pecific defined contour level ma have no harp edge, to be detected. To adapt to thee condition, we propoe a Prewitt difference filtering approach that i eplained in detail in [,]. In thi approach, the ignal from the neighboring node i quantized to dicrete tep in order to artificiall introduce an edge at the quering enor (ee Figure. For intance, a -level quantizer would perform an ideal edge (in the abence of noie imilar to a Signum function. In [] it wa hown that multi-level quantization (i.e. > level actuall improve the performance of detection of contour of two dimenional auian ignal ditribution uing a localized wirele enor network. The iue of non-uniform ample point a well a that of unequal (and random number of node that are epected to lie on either ide (above and below, right and left of the quering node were olved b adding a weighting function for calculation of the gradient. Accordingl, the gradient vector component of Prewitt difference filter at node S are defined a follow: ( = W (, [ N ( ( = W (, [ N ( where W (. and (. QV MAX H (, QV ] ( QV H (, QV ] MAX W are the weighting function a introduced in [] and are calculated a follow: > nright W (, = (- < nleft > nup W (, = (- < ndown Here n left, n right, n up, and ndown are the number of node in the neighborhood of the quering node to the left (i.e. <, right (i.e. >, above (i.e. >, and below (i.e. < the node, repectivel. H (. and H (. are alo the continuou Prewitt filter a defined and ued in [,]: (, = if <, if (, = if <, if H < H < and QV i the quantized value of the neighboring node. A caling factor QV MAX i required with H (. and H (. in equation ( to take into account the multi-level quantization of (5 Figure : Illutration of the collaborative proceing cheme. Figure : Illutration of multi-level quantization of the enor ignal. In thi figure, MAX=QV Ma number of quantization level. 79

4 the enor value received from the neighboring node. The propoed two-tage contour detection algorithm for detecting edge node at S i decribed a follow: l M S(t In tage-, all enor node determine if the are probable edge enor b comparing it obervation ample F( to two threhold a follow: if F( S < R' probable edge enor If an node tet poitive in the tet in tage-, it proceed to tage- where it tranmit a quer packet. When an node receive a quer packet, it replie b ending it own value (ee Figure. Upon receiving the quer replie, the quering node map the oberved ample of the neighboring node to a quantized value QV (ee Figure. With thee, the deciion variable for the tet for detecting edge enor i decribed a: DV( = ( + ( The quering node procee all replie to obtain a deciion variable DV (. It then decide if it i an edge enor or not b performing a threhold tet a follow: if DV( < γ edge enor ele not edge enor. Conideration for Reducing Communication Cot Two cheme for conerving the communication cot of the collaborative edge detection algorithm were propoed in []: Scheme-: Decreaing the number the poible edge node: Thi i implemented b introducing a threhold parameter R ', R MAX, uch that onl thoe node for which F ( S < R are conidered to be probable edge node, although quantization i till performed according to the multilevel cheme decribed in Figure. Scheme-: Opportunitic neighbor litening (ONLi: According to thi cheme, each node repond to a quer packet onl once, auming that neighboring node that alread received it QV (ent in repone to an earlier quer packet have aved it for future ue for Prewitt difference filtering. Conequentl, for each quer packet, onl thoe node repond that have not alread ent their QV. Thi eliminate multiple tranmiion of the ame information from node in repone to multiple quer packet. The contour baed patial etimation of a ditributed ignal require that contour detection i performed on a number of predefined contour level. All detected edge enor report their location (aumed to be known to a centralized bae tation that ue a ignal recontruction tool to recontruct the D ignal from the et of edge node. 5. ESTIMATIN THE SPATIAL DISTRIBUTION USIN CONTOURS Modeling a ignal ditribution with it contour level i ver common in viualization, medical imaging, etc. The error between the ignal recontructed from a et of contour and the original ignal will depend on the accurac of the contour detection cheme, the number of contour, the elected et of contour level, and the recontruction cheme. It mut be noted that although we evaluate the performance of the contour detection cheme decribed in the previou ection uing fale detection and mied detection of edge node, thee meaure do not directl determine the recontruction error of the D recontruction method. It i clear that a larger number of fale detection increae the contour thickne and higher mied detection might lead to lo of information about part of the contour. However, it i hard to quantitativel relate fale and mied detection to the error in ignal recontruction, which i our main objective. Hence, we appl a firt order linear pline method for recontructing the D ignal from it contour, and ue the RMSE to evaluate the performance of the propoed contour baed patial etimation method. Although other recontruction tool can provide maller error, a hown in Figure 5 for a one-dimenional ignal, the propoed imple recontruction tool capture the effect of both fale and mied detection. Net, we eplore election of the non-uniforml ditributed contour level for reducing the error in ignal recontruction from it contour. 5. Optimization of Contour Level under when the Signal pdf i Known Llod and Ma eparatel howed that auming M level, there i an optimal et of level which minimize the flat-top recontruction error of the ignal ditribution (quantization ditortion [5]. Thee optimal level for a ignal ditribution with probabilit denit function (pdf f X ( in the known internal L, can be obtained b olving the et of equation: ( L M + l l i+ f X ( d i Li = i+, i =,,..., M f ( d i X p p Figure 5: Illutration of the flat-top linear recontruction cheme. It i oberved that fale detection (etra croe and mied detection (level both increae the recontruction error when uing thi cheme. p M t (6-8

5 Pat Contour Li + Li i =, i =,,..., M + (6- We ue thee optimum level a a benchmark for evaluating the performance of our propoed ub-optimal olution for level election that doe not require knowledge of the pdf of the ignal. 5. A Practical Solution for Selecting Nonuniform Contour Level A a-priori knowledge of ignal pdf ma not be available, we propoe a practical cheme that i baed on the following baic principle:. In general, the level at which the ignal reide and croe mot frequentl are the mot uitable level for definition of ampling level. Thi implie that ample of the ignal obtained at thee level provide the mot information about the ignal. In other word, the tatitical mode of the pdf are the bet candidate of the ampling level.. The frequenc of occurrence of a correlated ignal i epected to be maimum near it mean. Baed on thee idea, we conider non-uniform contour level where the level are choen uing a cheme imilar to a logarithmic (μ-law compander for peech coding. Equation (7 define the logarithmic level for the cae where the tatiticalmode i in the middle of the range. In (7, { LU } M i i = are the uniforml paced level and { Lμ } M are the μ-law baed level in i i= the known interval L,. ( L M + New Contour Figure 6: Prompting the neighboring node with noi gradient in an angle interval LM + L LM + + L ( i + L LU M i = LM + L gn( LU i μ LM + L Lμi = [( + LU i ] + μ LM + + L i =,,..., M If the tatitical mode of the ignal i not in the middle of the ignal range, caling hould be applied before appling μ-law. (7 6. TEMPORAL MONITORIN OF SINAL DISTRIBUTION USIN CONTOURS In thi ection an efficient contour tracking algorithm i propoed to reduce the energ conumption for temporal monitoring of a ditributed ignal uing contour. The baic idea i to ue periodic ample of the eiting edge node to determine a direction of it gradient vector (termed a the gradient innovation, which point in the direction of the diplacement of the contour at that point. When the change in the magnitude of the gradient vector eceed a threhold, the current edge node broadcat an alerting packet that wake up neighboring node. Thee alerted node perform a collaborative edge detection tet imilar to that decribed in the patial monitoring algorithm to determine if the are to be elected a the new edge enor. With thi approach, jut a limited number of neighboring node are needed to be prompted to appl the collaboration proce for contour detection, which mean the communication cot of the contour tracking will be much lower than that requiring for repeating the patial monitoring algorithm at periodic interval. For thi reaon, conider a temporal variation of part of the contour during time update interval Δ t, a hown in Figure Direction of Diplacement The and component of gradient equation ( can be rewritten a the ummation of the two lateral deciion variable in Prewitt difference gradient a follow: ( ( = [ QV Ma QV ] N ( n : > right right + [ QV Ma QV ] N ( n : < left left = [ QV Ma QV ] N ( n : > up up + [ QV Ma QV ] N ( n : < down down Equation (8 can be rewritten in brief according to ( = DVright + DVleft (9 ( = DVup + DVdown Baed on the above re-definition of the gradient DVright and DVup are alwa non-negative and DV and left DV are alwa down non-poitive. After a change in ignal trength caued b temporal variation of the ignal, the pat edge node might no longer be edge node. In that cae ( and/or ( value of a previoul edge node increae. The ign of ( and ( alo ha the information of relative poition of the edge node veru the contour. Before (8 8

6 dicuion on the and component of gradient, let define gradient innovation operator between time t and t at the poition of enor node : Δ Δ ( Δt, = ( t, ( t, ( Δt, = ( t, ( t, ( If for a pat edge node Δ ( Δt, value i poitive and larger than detection threhold γ, then the poitive part of t, dominate it negative part, which mean: ( DV right > DV left In other word the contour ha moved to the left. Similar implication i valid for the vertical diplacement of the contour. Therefore, the gradient vector innovation act like a compa which how the direction of the contour diplacement and it i onl required that the enor which are along the direction of the diplacement are prompted to appl for edge detection algorithm. To take into account the noie in the ignal ample and the uneven ditribution of enor, we conider an acceptance angle α within which node appl edge the edge detection algorithm to determine if the are probable edge node. Figure 6 illutrate the gradient vector innovation and the acceptance angle. 7. PERFORMANCE EVALUATION In thi ection, we preent the performance of the propoed algorithm for patial and temporal monitoring of a ignal ditribution uing imulation. 7. Performance Evaluation of Spatial Monitoring Scheme: We evaluate the performance of the propoed collaborative patial monitoring cheme, under variou condition and compare with a non-collaborative cheme a decribed below. In addition, we compare the reult obtained uing the propoed non-uniform level with that uing uniform and optimum level. Non-collaborative cheme: In the non-collaborative cheme it i aumed that the enor whoe obervation are within a margin of δ nc from the cloet contour level end their enor obervation to the ink without conulting an of it neighbor. At the ink, the etracted noi contour are ued to recontruct the ignal ditribution. For all reult, we ue the piecewie linear recontruction cheme for recontructing the ignal ditribution from it contour. Aumed ignal ditribution: To evaluate the performance of the algorithm, we generated correlated random ignal ditribution with a mmetric auian pdf. To generate the random correlated ignal ditribution with auian pdf, 6 two-dimenional auian wave with tandard deviation and uniforml ditributed random height between - and were placed in random poition of the enor field within a quare area. Then 5 weak auian wave with uniforml ditributed random amplitude between - and with tandard deviation 5 were added. The amplitude of the reultant D ignal wa normalized to lie between and. 7.. Simulation Aumption: - We aumed 6 enor that were placed on grid point of the enor field of the urface area of. - In non-collaborative cheme the edge enor election wa done within the margin δ nc = of each contour level. - Additive noie wa aumed zero-mean auian. - The μ-law factor (μ wa aumed after inpection for optimalit for auian pdf Simulation Reult: Figure (7- to (7-6 compare the performance of collaborative and non-collaborative algorithm. - Effect of noie (σ: Figure (7- compare the performance of ignal ditribution etimation baed on etracted information uing collaborative and non-collaborative cheme under variou noie intenitie. Thi figure how that with the choen detection threhold (here γ =.5, the etimation baed on the collaborative cheme i le affected b noie than the noncollaborative cheme. The performance of the collaborative cheme with μ-law and optimal level are ver cloe and lightl better than collaborative cheme with uniform level. - Radio range (R: Figure (7- evaluate the effect of varing the radio range. Thi figure how that there i an optimal radio range that minimize the error in ignal recontruction. Thi figure alo how that the μ-law baed definition of level ha le RMSE than uniforml paced level and fairl cloe to RMSE of optimal level. - Detection threhold (γ: Figure (7- preent the effect of varing the detection threhold. In thi figure, the tandard deviation of noie i σ =5. It i oberved that the recontruction RMSE i minimized at γ =.5. When γ i choen properl the qualit of ignal recontruction uing μ-law baed level i cloe to optimal cae and better than ignal ditribution with uniforml paced contour level. - Collaboration margin (R' : Effect of varing collaboration margin on the ignal recontruction i hown in Figure (7-. It i oberved that the performance of the collaborative cheme i improved b increaing thi parameter. The effect of increaing (R' on the performance of contour detection wa hown in [] alo. In thi Figure the tandard deviation of noie σ = 5 and threhold γ =.5 were aumed. - Number of contour level (L: Figure (7-5 tudie the effect of increaing the number of contour level on recontruction RMSE. A epected, the performance improve with increaing the number of contour level. It again prove the ub-optimalit of μ-law baed election of contour level. For thi figure, the threhold γ wa.5 and σ = 5. - Effect of the number of quantization level (Q: Figure (7-6 tudie the performance of collaborative cheme on ignal ditribution etimation. A thi figure how, b increaing the number of quantization level from to 7, the recontruction RMSE increae. It alo how that the quantization with level i better than binar cae. For thi figure, the threhold γ wa.5, σ = 5, R = 5 and L = 8. 8

7 Recontruction RMSE Noncollaborative - Uniform level Noncollaborative - μ-law level Noncollaborative - Optimal level Collaborative - Uniform level Collaborative - μ-law level Collaborative - Optimal level Recontruction RMSE Noncollaborative - Uniform level Noncollaborative - μ-law level Noncollaborative - Optimal level Collaborative - Uniform level Collaborative - μ-law level Collaborative - Optimal level 6 8 Noie td (σ Figure (7-: Stud of the variation of the recontruction RMSE veru Noie Intenit (γ=.5, δ=.7, μ=, δ nc =., L = 8, R = 5,Q = Radiu (R Figure (7-: Stud of the variation of the recontruction RMSE veru Radio Range (γ=.5, σ = 5, δ=.7, μ=, δ nc =., L = 8, Q=.5 Recontruction RMSE.5.5 Noncollaborative - Uniform level Noncollaborative - μ-law level.5 Noncollaborative - Optimal level Collaborative - Uniform level Collaborative - μ-law level Collaborative - Optimal level Threhold (γ Figure (7-: Stud of the variation of the recontruction RMSE veru Threhold (σ = 5, δ=.7, μ=, R = 5, δ nc =., L = 8, Q= Recontruction RMSE Noncollaborative - Uniform level Noncollaborative - μ-law level Noncollaborative - Optimal level Collaborative - Uniform level Collaborative - μ-law level Collaborative - Optimal level Level (L Figure (7-5 Stud of the variation of the recontruction RMSE veru the number of Level (γ=.5, δ=.7,σ = 5, μ=, R = 5, δ nc =., Q= Recontruction RMSE.5.5 Noncollaborative - Uniform level Noncollaborative - μ-law level Noncollaborative - Optimal level Collaborative - Uniform level Collaborative - μ-law level Collaborative - Optimal level Margin (δ Figure (7- Stud of the variation of the recontruction RMSE veru Collaboration Margin (γ=.5, σ = 5, μ=, R = 5, δ nc =., L = 8, Q= Recontruction RMSE Noncollaborative - Uniform level Noncollaborative - μ-law level Noncollaborative - Optimal level Collaborative - Uniform level Collaborative - μ-law level Collaborative - Optimal level # of Quantization Level (Q Figure (7-6: Stud of the variation of the recontruction RMSE veru the number of Quantization Level (γ=.5, δ=.7,σ = 5, μ=, R = 5, δ nc =., L=8 8

8 Simulation were repeated for correlated ignal ditribution with a harper pdf (lower patial correlation. The reult were ver imilar to thoe obtained with the auian pdf and are omitted due to pace contraint. 7. Performance Evaluation of Contour Tracking Algorithm: For inpection of the performance of the contour tracking algorithm, we ued a two dimenional auian ignal ditribution a hown in Figure (8-. Mied detection rate and the number of fale detection are obtained to tud the qualit of contour detection. The radio range wa fied to 7 and all other aumption are the ame a before. The following reult were achieved in the preence of additive white auian noie with tandard deviation of. To tud the temporal effect, the auian ignal i moved diagonall with contant peed in each time update and the qualit of contour tracking under different parameter i inpected. Figure (8- how the average cot ratio of the tracking algorithm veru detection threhold, over the cot of tatic cae for the ame ignal (two-dimenional auian. It i oberved that increaing the acceptance angle, generall increae the cot but it i till lower than that periodicall performing the tatic procedure. Hence, the propoed tracking algorithm i more cot efficient than repeating the tatic contour detection algorithm a dicued in []. Figure (8- and (8- how the performance of the propoed contour tracking algorithm uing mied detection rate and the number of fale detection. Figure (8- how that b increaing the acceptance angle the mied-detection increae while the fale detection decreae. Unlike the acceptance angle, a higher peed of movement of the contour increae the mied detection rate while reducing the fale detection. Figure (8-5 and (8-6 how the reult of tud of the effect of mied detection and fale detection when jut the peed of move change and the detection threhold and other parameter are contant. Baed on thee two figure b increaing the peed of move, the fale detection decreae and mied detection increae which upport the reult of Figure ( CONCLUSION We addre the etimation of a random correlated ignal ditribution uing a large-cale wirele enor network b detecting and tracking it contour at different level. A collaborative ignal proceing cheme i propoed for etraction of the contour. It i aumed that enor obervation are heavil affected b noie. The propoed collaborative proceing algorithm avoid the communication cot that would be incurred b obtaining periodic ample from all enor in the network. Optimal definition of contour level that give minimal etimation error i eplored and a practical approach for election of contour level that need le information of the random ignal wa preented. Performance iue of the propoed algorithm for etimating ignal ditribution baed on the etracted contour under variou detection parameter were eplored. We alo preent an efficient contour tracking algorithm to reduce the energ conumption for etimating the temporal variation of the ignal, and evaluate it performance under variou tracking parameter. The imulation reult how that the contour tracking algorithm reduce the cot of communication in comparion to that uing periodic contour detection at a mall price of the recontruction error. 9. REFRENCES [] Digital Image Proceing, rd edition b William K. Pratt, John Wiel & Son, Inc.,. [] W. R. Armtrong, Localized contour detection in wirele enor network, MSEE Thei, Univerit of North Carolina at Charlotte, 5. [] H. Alati, W. Armtrong, A. Naipuri, Performance of a Robut Filter-baed Approach for Contour Detection in Wirele Senor Network, in Proceeding of ICCCN 7, 7. [] K. K. Chintalapudi and R. ovindan, Localized edge detection in enor field, in IEEE International Workhop on Senor Network Protocol and Application, pp. 59-7,. [5] Introduction to data compreion, b Khalid Saood, Publihed b Morgan Kaufmann,. [6] J. Lian, L. Chen, K. Naik, Y. Liu, and. B. Agnew, radient Boundar Detection for Time Serie Snaphot Contruction in Senor Network, IEEE TRANS. on Parallel and Ditributed Stem, VOL. 8, 7. [7] R. Sarkar, X. Zhu, J. ao, L.J. uiba, J.S.B. Mitchell, Io- Contour Querie and radient Decent with uaranteed Deliver in Senor Network, in Proceeding of INFOCOM 8, 8. [8] X. Zhu, R. Sarkar, J. ao, J.S.B. Mitchell, Light-Weight Contour Tracking in Wirele Senor Network, in Proceeding of INFOCOM 8, 8. [9] S. andhi, J. Herhberger, S. Suri, Approimate Iocontour and Spatial Summarie for Senor Network, in Proceeding of IPSN 7, 7. 8

9 8 6 Average cot ratio α = 5 o α = o α = 5 o α = 9 o Figure (8-: Two dimenional auian ignal in enor field and it contour which ha been ued in tracking algorithm Detection Threhold (γ Figure (8-: Average cot ratio of the tracking algorithm (The tandard deviation of noie wa. Mied Detection Acceptance Angle (α = 9 o Mied Detection Rate (P MD Figure (8-: Stud of the effect of acceptance angle in the performance of tracking algorithm. Mied detection rate Detection Threhod (γ γ =.5 γ =. γ =.6 γ =.9 Acceptance Angle α = 9 o Acceptance Angle α = o Acceptance Angle α = 5 o 5 6 V or V (Diplacement per update Figure (8-5: Variation of mied detection veru the peed of move for ome detection threhold. - Number of Fale Detection (N FD Mied Detection Rate (P MD Threhold (γ Figure (8-: Stud of the effect of the peed of move in the performance of tracking algorithm. Number of Fale detection (N FD Mied Detection 8 6 V = V = V = V = V = V = γ =.5 γ =. γ =.6 γ = V or V (Diplacement per update Figure (8-6: Variation of fale detection veru the peed of move for ome detection threhold. - Number of Fale Detection (N FD 85