Performance of a Robut Filter-baed Approach for Contour Detection in Wirele Senor Network Hadi Alati, William A. Armtrong, Jr., and Ai Naipuri Department of Electrical and Computer Engineering The Univerity of North Carolina at Charlotte, Charlotte NC halat@uncc.edu, wartr2@bellouth.net, anaipur@uncc.edu Abtract A robut filter-baed approach i propoed for wirele enor network for detecting contour of a ignal ditribution over a 2-dimenional region. The motivation for contour detection i derived from application where the patial ditribution of a ignal (uch a temperature, oil moiture level, etc.) i to be determined over a large region with minimum communication cot. The propoed cheme applie multi-level quantization to the enor ignal value to artificially create an edge and then applie patial filtering for edge detection. The patial filter i localized and i baed on an adaptation of the Prewitt filter ued in image proceing. Appropriate mechanim are introduced that minimize the cot for communication required for collaboration. Simulation reult are preented to how the error performance of the propoed contour detection cheme and the aociated communication cot (ingle-hop communication with immediate neighborhood in average) in the network. Keyword- wirele enor network; collaborative proceing; contour detection; Prewitt filter. I. INTRODUCTION A key deign objective in wirele enor network i to derive benefit from the collective proceing power of a large number of energy and hardware contrained wirele enor node that are ditributed over a region of interet. The type of information required depend on the application, which include obtaining periodic ignal level uch a in environmental monitoring, generating alarm baed on pecific ignal condition, tracking a mobile target within an area of interet, and more. However, in almot all cae, the combination of information from a group of enor can make the ytem more robut and accurate. The main challenge i to deign ditributed collaborative information proceing cheme under the limited proceing, energy and communication capabilitie of the mall enor node. Thi paper addree the deign of collaborative proceing algorithm for detecting contour of a ignal ditribution in a enor field. Contour detection i ueful in a large number of environmental monitoring application. A typical application cenario i where patial variation of a ignal ditribution need to be detected over a large region uing an array of enor. To minimize the communication cot for obtaining periodic ignal ample from all enor in the region, the patial ditribution can be etimated from a et of contour correponding to pecific ignal level [3]. Our approach for contour detection i to ue the contour level a a threhold to introduce an artificial edge that demarcate two different region within the enor field (on either ide of the contour) and then apply a filter-baed edge detection algorithm. The algorithm ue collaborative proceing among a group of randomly ditributed enor node in the region of interet. Appropriate meaure are incorporated to acertain that the abence of a true edge, i.e. a region characterized by a harp variation of the ignal level, doe not introduce much error in etimating the contour. Primary deign conideration are minimization of error of etimated contour and the communication cot incurred for collaborative proceing. Thi paper i organized a follow. In ection II, we review exiting work on edge detection in enor network that are related to thi work. In ection III, we decribe the ditributed contour detection problem targeted in thi paper. In ection IV, the filter-baed approach for edge detection and iue on robutne and communication cot are decribed. Performance reult of the propoed cheme obtained from computer imulation are preented in ection V. In ection VI, we preent our concluion and decribe ome future work on edge tracking. II. RELATED WORK Edge detection ha been widely reearched for image proceing, where ignal level are available at regularly located ample point, i.e. pixel, and the algorithm aume the availability of information from all data point for proceing [8]. Conequently, adaptation of efficient edge detection algorithm from image proceing for application in enor network have been explored in literature. The primary goal of thee algorithm i to detect edge node, i.e. node that are located within a certain tolerance ditance from the ideal edge of the ignal that i to be determined. Chintalapudi, et al. [1] propoed three general approache for localized edge detection: a) a tatitical approach, b) a filter-baed approach and c) a claifier-baed approach. While the tatitical approach doe not require location information at the enor node, the other two can only function when all node are aware of their geographic location. The author 1-4244-1251-X/7/$25. 27 IEEE. 159
howed that although the tatitical approach i more robut in the preence of noie, it ha higher error and i more difficult to apply in practice due to difficultie in electing a proper threhold. Liao, et al. [2] propoed an approach that i baed on one and two level deciion baed on the local and global maximum likelihood ratio to enhance the tatitical approach propoed by [1] for edge detection. Their work preented in [4] enhanced the detection of the edge region in tatitical approach uing Neyman-Pearon (NP) criteria. Baed on NP criteria they propoed an idea that addree to olve the threhold election problem. They alo compared the performance of their approach with claifier-baed approach under the aumption of location error and how that their tatitical approach perform better than claifier approach. The work in [5-7] propoe the uage of contour line detection intead of edge detection to not only recognize the region of a certain phenomena, but alo extract other information uch a ignal amplitude and ource location. The propoed method in [5-7] i baed on regional clutering and having communication between cluter-head. It can track change, but i not a localized approach and ome enor node require additional capabilitie to be a cluter-head. In thi work, we generalize the notion of the binary edge decribed in [1] to a contour line that i decribed with multiple level and how that by thi aumption the probabilitie of mied and fale detection of edge node are reduced. We evaluate the error in etimating a contour by meauring the ditance of the detected edge node from the true contour. In addition, we determine the expected aving in communication cot of the propoed ytem. Although our approach ha been evaluated uing both the tatitical and filter-baed algorithm, in thi paper we preent reult that are obtained primarily uing the filter-baed approach due to it uperior performance. A comparion of the performance of the two approache i alo hown. III. PROBLEM STATEMENT AND APPROACH USED FOR CONTOUR DETECTION IN SENSOR NETWORKS We aume a cenario where a large number of wirele enor node are randomly ditributed in a given area of interet. Each enor can obtain periodic obervation of the ignal in the enor field, uch a the temperature ditribution over a given area. A contour in the enor field i defined a the line of demarcation between region that are above and below a S. For the ake of etimating error in etimation, threhold we ue a tolerance ditance r to determine the contour thickne, which i the region near a contour uch that a enor node located in the region i termed a an edge node. Thi i illutrated in Figure 1. There can be two type 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 actually an edge node (i.e. located within a ditance r from the true contour) fail to be detected, we have a mied detection. The enor node perform local and collaborative proceing of their oberved ignal ample to determine if they are edge node. Error in detecting edge node can occur due to Figure 1: Illutration of a contour in a enor field and edge enor near it. two reaon. Firt, although the actual edge or boundary demarcate two region having different ignal propertie, the true ditribution of the ignal acro the edge may not have a harp change. In thi ene, a contour detection problem i different from edge detection. Secondly, quantization noie and other environmental noie ource introduce additional cope of detection error. The primary goal of collaborative proceing i to reduce the effect of thee error. In addition, we aim to keep the communication cot for collaboration to a minimum. With thee objective, we propoe a two-tage proce for the detection of edge enor near a contour in the enor field. In the firt tage, all node periodically ue their local obervation to decide if they are probable edge node (which can be obtained by checking if it local obervation lie between two given threhold). In the econd tage, node that tet poitive in the firt tage tranmit query meage to their neighbor and proce the returned information uing a filterbaed algorithm to confirm their deciion (ee Figure 2). IV. Figure 2: Illutration of the collaborative proceing cheme. PROPOSED CONTOUR DETECTION METHOD USING SPATIAL FILTERING The propoed contour detection algorithm i decribed a follow: Initially all node map their oberved ample to a quantized value (QV) uing a multi-level quantizer a depicted in Figure 3. The quantizer produce output value that are integer in the range ( MAX, MAX ) centered around 1-4244-1251-X/7/$25. 27 IEEE. 16
the contour threhold S. The quantization tep ize i τ = 2.MAX / L, where L i the number of quantization level. A node determine if it i a probable edge enor or not by comparing it obervation ample F() to two threhold a follow: if F( ) S < MAX probable edge enor A probable edge enor broadcat a query packet to obtain quantized value of obervation from it neighbor. When any node receive a query packet, it replie by ending it own quantized obervation value. The querying node procee all replie to obtain a deciion variable DV (). It then decide if it i an edge enor or not by performing a threhold tet a follow: if DV ( ) < γ ele edge enor not edge enor We note that the multi-level quantization of obervation ample a decribed in Figure 3 introduce an artificial edge having value MAX and MAX at either ide of the contour threhold S. Although the edge i expected to be granular, depending on the number of quantization level L, we can apply an edge detection algorithm to the quantized ample at the enor node for detecting edge enor. We how later that uing a value of L > 2 a oppoed to binary quantization actually reduce the error in contour detection. The edge detection problem in enor network i imilar to that in image proceing except for the following factor [1]. One factor i that a oppoed to pixel that are located on a uniform grid, wirele enor node are uually located in a random fahion. Hence, appropriate meaure mut be taken to account for the non-uniform location of the ampled data while applying filtering in enor network. A econd factor i that enor node are typically required to perform on-ite and collaborative proceing of data. Hence, there i ome cot for communication that i aociated with obtaining data from different node in the network, which i not an iue in image proceing. Figure 3: Illutration of multi-level quantization of the enor ignal. In thi figure, MAX=QV Max x number of quantization level. A number of technique may be applied to obtain the deciion variable for performing the threhold tet at the probable edge enor. In the tatitical approach, DV () i obtained a the abolute value of the average of all quantized obervation value received from the neighbor of the querying node [1,3]. Here we decribe an edge detection cheme that i baed on an adaptation of the Prewitt filter for edge detection in image proceing. A. Spatial Filtering uing Prewitt Filter Edge detection in image proceing i commonly accomplihed by performing a patial differentiation of the image field followed by a threhold operation to determine point of teep amplitude change. Horizontal and vertical patial derivative are defined a: F( x, y) dx =, F( x, y) d y = (1) x y where F(x,y) i the value of the ignal at the point (x,y). The gradient magnitude of F(x,y) i then 2 2 F( x, y) = dx + dy (2) An edge i then judged to be preent if the gradient exceed a given threhold. To reduce computational load, the gradient at point (x,y) can be implified to: F ( x, y) = d x + d y (3) In digital image proceing pixel replace coordinate, and an edge detection algorithm perform patial proceing on an image to create a new image with pronounced change in patial amplitude of the original image. The proceed image G( j, k) i uually decribed a the combination of two gradient component: the row gradient G R (j, k), and the column gradient G C (j, k) a follow G( j, k) = GR( j, k) + GC( j, k) (4) where j and k are horizontal and vertical indice of a pixel. The implet method of dicrete gradient generation i to form the running difference of pixel along row and column of the image. In that cae, the row gradient i defined a: G R (j,k) =F(j, k) -- F(j, k-1) (5) and the column gradient i: G C (j,k) =F(j, k) -- F(j+1, k) (6) where F( j, k) repreent the original image. Alternatively, a differential filter may be applied to generate the gradient vector from the original image. For example, in Prewitt filtering, the row and column gradient vector are obtained a: G R (j,k) = F(j,k) H R (j,k) (7) G C (j,k) = F(j,k) H C (j,k) where H R (j,k), H C (j,k) for a filter of ize 3 (i.e. operate on three adjacent pixel to produce one value) are: 1 1 1 1 1 1 H R (j,k) = 1 1 1 3 H C (j,k) = (8) 3 1 1 1 1 1 We introduced everal modification to the baic Prewitt filter decribed above, to uit the requirement for detecting edge enor from their quantized value according to the propoed cheme. One iue i the poibility of detecting multiple 1-4244-1251-X/7/$25. 27 IEEE. 161
edge caued by multi-level quantization. We olve thi problem by introducing the notion of Prewitt difference filtering where difference intead of multiplication are ued in the filtering operation. Eentially, thi caue the quantized ignal obtained from different node to be ubtracted from an (patially) odd function at the probing node. In thi way while the pat gradient remain the ame for the real edge node, the gradient of the non-edge node increae. A candidate odd function i the Signum function decribed a ig ( x) = 1 if x, and ig ( x) = 1 otherwie. Accordingly, we adopt H x (.) and H y (.) to be caled Signum function, with their maximum value being the maximum value of QV or QV Max, received from the neighboring node. The problem of random node location can be reolved by utilizing the concept of a continuou Prewitt filter [3]: ( x, y) = 1 H x if x < x, 1 if x > x ( x, y) = 1 H y if y < y, 1 if y > y. Here, we ue a weighted continuou Prewitt filter, to account for the random number of node on different ide (above and below, right and left) of any node where the proceing i to be performed. Thi i implemented uing weighting function W x (.) and W y (.) that are calculated a follow: 1 x > x nright W x( x, y) = 1 x < x nleft (1) 1 y > y nup W y ( x, y ) = 1 y < y ndown where n left, n right, n up, and ndown are the number of node in the neighborhood of the querying node to the left (i.e. x < x ), right (i.e. x > x ), above (i.e. y > y (9) ), and below (i.e. y < y ) the node, repectively. With thee, the deciion variable for the tet for detecting edge enor i decribed a DV( ) = G x_diff () + G y_diff () where G x _ diff () = W x ( x, y )[ H x ( x, y ) QV ] N ( ) (11) G = W x, y [ H ( x, y ) QV ] y _ diff () y ( ) N ( ) B. Conideration for Reducing Communication Cot We now preent two cheme that are propoed to decreae the communication cot for the propoed collaborative edge detection algorithm: y Scheme-1:Decreaing the number the poible edge node: Thi i implemented by introducing a threhold parameter R, R MAX, uch that only thoe node for which F ( ) S < R are conidered to be probable edge node, although quantization i till performed according to the multi-level cheme decribed in Figure 3. Thi reduce the number of query packet and replie generated in the network without affecting the tep-ize (accuracy) of quantization. However, thi reduction in communication cot will be achieved at the poible cot of higher probability of mied detection. Scheme-2: Opportunitic neighbor litening (ONLi): According to thi cheme, each node repond to a query packet only once, auming that neighboring node that already received it QV (ent in repone to an earlier query packet) have aved it for future ue for Prewitt difference filtering. Conequently, for each query packet, only thoe node repond that have not already ent their QV. Thi eliminate multiple tranmiion of the ame information from node in repone to multiple query packet. V. PERFORMANCE EVALUATION In thi ection, we preent reult obtained from computer imulation to illutrate the performance of the propoed contour detection cheme. We aume a network of 261 enor node that are uniformly ditributed on a 1x1 m2 area. Each enor node i equipped with an omni-directional antenna having a tranmiion range of 7 m. The tolerance radiu that i ued to define true edge enor i aumed to be 1 m. It i aumed that the data i gathered in a ingle hop neighborhood of each node. We alo aume that each node know it coordinate and broadcat it poition to it neighbor. For our imulation, we aume that the ignal ditribution ha a Gauian ditribution in the enor field, centered at (5,5) with a peak value of 1. Although a contour at a pecified ignal level with thi ignal ditribution i a cloed circle, it i worth mentioning that the propoed algorithm work equally well for non-cloed contour a well. The noie in the enor obervation i aumed to have a Gauian ditribution. Figure 4 depict the ignal ditribution along with a naphot of detected edge enor from one of our imulation run that were performed to detect a contour at ignal level 5. The true edge enor are marked by blue quare and the enor that are detected by the propoed algorithm are marked in red. The ret of the node are marked by green dot. In Figure 5, we compare the performance of the tatitical and Prewitt filter baed approache for localized edge detection. Here, the variation of the fale detection and mied detection rate are plotted uing 8 quantization level and two different noie level. The reult how that the Prewitt filter baed approach generate lower detection error in comparion to the tatitical approach. Henceforth, we preent all reult obtained from the Prewitt filter baed approach only. 1-4244-1251-X/7/$25. 27 IEEE. 162
1 8 6 4 2 1 8 6 4 2 Figure 4: A naphot of the outcome of edge detection uing the propoed cheme depicting true edge enor in blue and detected edge enor in red. 2 4 6 8 1 We next evaluate the effect of L (the number of quantization level) and the value of MAX on the error performance of the propoed contour detection cheme by plotting the probability of mied detection againt the deciion threhold γ for different L and MAX value. The reult, hown in Figure 6, indicate that multi-level quantization reult in ignificant improvement in performance. The probability of mied detection drop noticably when the number of quantization level i increaed from 2 to 8, however the relative improvement i le pronounced when it i increaed to 16. The performance alo improve with a higher value of MAX. Hence, we ue L=8 and MAX=1 for mot of our other imulation. Note that our propoed cheme with binary quantization become imilar to that preented in [1] when applied to contour detection. Hence, the reult uing multi-level quantization in Figure 6 alo indicate the comparative performance improvement obtained uing the propoed cheme and that preented in [1], which i mot related to thi work. Fale-Detection Rate We evaluate the effect of noie on the propoed contour.3.25.2.15.1.5 Filter-Baed Approach Statitical Approach Filter-baed, Noie Std: Statitical, Noie Std: Filter-baed, Noie Std: 4 Statitical, Noie Std: 4.1.2.3.4.5.6.7.8.9 Mied-Detection Rate Figure 5: Comparion of detection performance uing the tatitical and Prewitt filter baed approache.. detection cheme by determining the variation of the probability of mied detection and the number of falely detected node at a contour level of 5 under different noie level (Figure 7). Thee reult how that a higher amount of noie increae the probability of mied detection but ha negligible effect on the number of fale detection. Note that there are detection error even when there i no noie. Thi i explained from the fact that depending on the lope of the ignal ditribution at the contour threhold S, the et of node within the artificial edge created by our quantization proce may not be exactly the ame a thoe conidered to be true edge enor. The reaon i that while the firt et include only thoe node whoe ignal value are within a certain range of the contour threhold S, true edge enor are defined by the tolerance ditance r. Depite thee apparent inconitencie of detection error with repect to noie, we till conider probability of mied detection and the number of fale alarm to be indicative of the error performance of the propoed contour detection cheme. For intance, if the location of the detected edge enor are ued to predict the location of the contour, higher mied Mied-Detection Rate 1 1-1 1-2 1-3 1-4 Q-Level=16 Q-Level=8 Q-Level=4 Q-Level=2 MAX = 4 MAX = 1 Noie Std = 2 (Fale Detection Rate < 1 %).1.2.3.4.5.6.7.8.9 1 Threhold Figure 6: Probability of mied detection for different number of quantization level and MAX value. 1-4244-1251-X/7/$25. 27 IEEE. 163
Mied-Detection Rate 1 1-1 1-2 1-3 1-4 Mied Rate: Noie Std: 4 3 2 # of Fale Detection MAX = 1 # of Quantization = 8 Noie Std: 3 4.1.2.3.4.5.6.7.8.9 1 Threhold Figure 7: Probabilitie of mied detection and the number of falely detected edge node at a contour level of 5 with varying threhold γ. detection and fale detection both would contribute to a higher amount of error in the prediction. In that repect, our experiment indicate that fale detection affect the prediction of a contour location more than mied detection. Thi i oberved from the fact that average ditance from detected edge enor for MAX=1 and L=8 i found to be.63 when the threhold γ =. 25, where the probability of mied detection =.367 and the number of fale detection = 18.44. However, the average ditance increae to 1.44 at γ =.85, where the probability of mied detection=.1 and number of fale detection=185.4. The above finding provide the main motivation for reducing the number of probable edge enor uing the propoed Scheme-1 decribed in ection 4.2. We note that while a maller value of R will reduce the communication cot, it can alo increae the probability of mied detection. To evaluate thi effect, we obtain the average ditance of the detected edge node from the true contour a well a the communication cot (determined by the number of packet tranmiion) a obtained for pecific et of parameter, a hown in Table 1. The reult how that although a mall value of R generate a high level of mied detection, the mean ditance error i till low for R =.2 MAX. On the other hand, thi value of R reduce the communication cot by a factor of 5. Finally, we evaluate the aving in communication cot obtained by uing the propoed ONLi cheme. Table-II how the average number of tranmiion in the network, normalized to the total number of node in the network that were required for contour detection with and without uing the ONLi cheme. The reult indicate that avoiding TABLE I: Error ditance and communication cot v. R MAX = 1, Number of Quantization level = 8, Threhold =.55, Noie Std = 2 Ditance Error R' MAX Prob. of mi # of Fale 25 2 15 1 5 # of Fale Detection Comm. Cot Mean Standard Deviation.2.413 25.15.745.528 1.13.4.117 56.86.86.565 2.28.6.45 79.26.969.613 3.39.8.367 85.74.95.572 4.54 1..357 88.5 1.1.71 5.66 multiple tranmiion in repone to query packet can reduce the communication cot to about 12% of that without uing ONLi. TABLE II: Average Communication Cot (Noie Std:2, Threhold:.55, R = MAX) MAX With ONLi Without ONLi 1.73 5.68 7.56 3.9 VI. CONCLUSION AND FUTURE WORK A collaborative proceing cheme for enor network i preented for detecting contour of the ignal ditribution of the enor field. The propoed cheme ue a multi-level quantizer for emulating an edge in the ignal ditribution in the enor field and then applie patial filtering. Appropriate deign conideration are preented to apply a patial Prewitt filter to ditributed data proceing in enor network. The propoed cheme ha ufficient robutne to noie in ignal obervation and incur a low cot of communication. Overall, thi cheme can vatly reduce the number of tranmiion that would be required to etimate the patial ditribution of the ignal over a large area uing a wirele enor network by uing contour detection. The filter-baed approach preented in thi paper can alo be ued for tracking the temporal variation of ignal ditribution with low communication cot. A a continuation of contour detection in tatic cae, the author are working on an algorithm for tracking the peed, direction and deformation of contour uing localized computation and collaborative proceing in wirele enor network. REFERENCES [1] K. K. Chintalapudi and R. Govindan, Localized edge detection in enor field, in IEEE International Workhop on Senor Network Protocol and Application, pp. 59-7, 23. [2] Pie-Kai Liao, Min-Kuan Chang and C.-C. Jay Kuo, Ditributed Edge Senor Detection With One-And Two-Level Detection, Proceeding IEEE ICASSP, pp. 297-33, 24. [3] W. R. Armtrong, Localized contour detection in wirele enor network, MSEE Thei, Univerity of North Carolina at Charlotte, 25. [4] Pie-Kai Liao, Min-Kuan Chang and C.-C. Jay Kuo, Statitical Edge Detection with Ditributed Senor under the Neyman-Pearon (NP) Optimality, in Proceeding IEEE VTC, 26. [5] Pie-Kai Liao, Min-Kuan Chang and C.-C. Jay Kuo, Contour line extraction in a multi-modal field with enor network," Proceeding IEEE Global Telecommunication Conference (Globecom), 25. [6] Pei-Kai Liao, Min-Kuan Chang and C.-C. Jay Kuo, "A ditributed approach to contour line extraction uing enor network," in Proc. IEEE VTC, 25. [7] Pei-Kai Liao, Min-Kuan Chang and C.-C. Jay Kuo, "Contour line extraction with wirele enor network," in Proc. IEEE International Conference on Communication (ICC), 25. [8] Digital Image Proceing, 3rd edition by William K. Pratt, John Wiely & Son, Inc., 21. 1-4244-1251-X/7/$25. 27 IEEE. 164