Statistical Edge Detection with Distributed Sensors under the Neyman-Pearson (NP) Optimality Pei-Kai Liao † , Min-Kuan Chang ‡ and C.-C. Jay Kuo † Department of Electrical Engineering, University of Southern California, Los Angeles, CA 90089, USA † Department of Electrical Engineering, National Chung-Hsing University, Tai-Chung, Taiwan ‡ E-mails: pliao@usc.edu, minkuanc@dragon.nchu.edu.tw, cckuo@sipi.usc.edu Abstract —A statistical approach to distributed edge region detection in wireless sensor networks, which is optimized under the Neyman-Pearson (NP) criterion, is proposed in this work. The concept of edge nodes is adopted to label the defined edge region. Even though statistical methods have been proposed to detect edge nodes, a rigorous way to select the threshold value is lacking. Based on the NP criterion, a decision-fusion approach is developed to address the problem of threshold selection. Performance comparison of the proposed approach and the classifier-based approach is conducted. Simulation results show that the proposed approach is more stable and outperforms the classifier-based approach when there is a location error. Keywords: Decision fusion, edge detection, boundary esti- mation, distributed algorithm, wireless sensor networks. I. Introduction Wireless sensor networks can be potentially used in the monitoring of certain environmental phenomena, such as spreading of poisonous gas, fire outbreak and containment spreading. While being harmful, these phenomena often span over a large geographical area. Due to the large size and time-varying shape, they cannot be adequately moni- tored or tracked using traditional localization techniques with few isolated sensors. It is often that the edge or boundary region provides the most important information of our concern, which can be utilized to localize a phenom- enon so that proper action can be taken accordingly. There have been a few methods proposed for edge de- tection in the wireless sensor network literatures. Nowak and Mitra [1] presented an edge estimation scheme under the assumption that there exists a predefined hierarchical structure in the sensor network. This hierarchy could be difficult to build in a highly distributed sensor network en- vironment. Chintalapudi and Govindan [2] proposed three approaches to distributed edge sensor detection; namely, statistical- , the filter-, and the classifier-based approaches. Although the statistical approach is more robust with re- spect to noise, its performance cannot compete with the classifier-based approach and the threshold selection prob- lem makes it difficult to apply in practical applications. Since statistical methods behave well in a noisy environ- ment, another statistical solution to edge detection was proposed in [3] that has improved the edge detection per- formance and reduced the computational complexity. How- ever, the threshold selection problem remains unsolved. To determine the optimal threshold, we propose a new statistical approach under the Neyman-Pearson (NP) crite- rion for decision fusion in local sensors. Under the current framework, an edge region that encompasses true edge line is defined and detected edge nodes are used as markers to indicate such a region. Based on the NP criterion, a threshold selection rule can be rigorously derived. With this criterion, the behavior of the proposed statisitcal ap- proach can be quantified more conveniently. As a result, both the performance and the complexity of the statistical approach are significantly improved. Due to the use of geographical information of local sen- sors, the performance of the classifier-based approach may be affected by the accuracy of the geographical informa- tion as well as measurement noise. The location of every sensor is often assumed to be known perfectly for simplic- ity. However, there could be errors in sensor locations in practice. The effect of sensor’s location error is conducted for both approaches. Simulation results show that the pro- posed statisitcal approach outperforms the classifier-based approach by providing a lower false alarm rate when the location error becomes important. II. Sensor Measurement Model and Edge Region Definition A. Sensor Measurement Model Consider a wireless sensor network deployed in a large geographical area to monitor the edge (or boundary) of an event of interest. There may be thousands of senor nodes deployed in the field. The event of interest is assumed to be quasi-static, whose statistical properties remains un- changed during K time points. To detect the edge line, each sensor node measures local data and exchanges data with its neighboring sensor nodes for further data process- ing. Due to sensing noise and thermal noise, measured data may be affected. Suppose that the noise level is inde- pendent of the true signal value. Then, the received data from the sensor node at position (x, y) and time t can be modelled as m(x, y, t)= s(x, y, t)+ n(x, y, t), (1) where s(x, y, t) is the signal and n(x, y, t) is the noise. Fur- thermore, it is assumed that the signal takes a binary level, i.e., A and 0, with the following probability P (s(x, y, t)= A)= P A , P (s(x, y, t) = 0) = 1 - P A , and n(x, y, t) in (1) is white Gaussian noise in both the spatial and the temporal domains. B. Edge Region Definition In the system of our concern, sensor nodes do not have to be distributed uniformly over the sensor field although the uniform distribution is adopted in simulations. Instead of estimating the true location of an edge line, the tech- nique of edge node detection in [2] is adopted here to de- termine the edge region which encompasses the true edge