A Distributed Approach to Contour Line Extraction Using Sensor Networks 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 — An algorithm to extract contour lines using wireless sensor networks is proposed in this work. In con- trast with previous work on edge detection that is primarily concerned with the region of a certain phenomenon, contour lines offer more detailed information about the underlying phenomenon such as signal’s amplitude, density and source location. A distributed algorithm to extract the contour lines information from local measurements is developed so that the phenomenon can be monitored in the basestation without demanding excessive raw data transmission. Sim- ulation results are provided to demonstrate the efficiency of the proposed algorithm. Furthermore, a thorough per- formance analysis is conducted to understand the effects of the sensor density and the background noise power on the performance of the system. Keywords: Contour line extraction, edge detection, gradi- ent estimation, distributed algorithm, wireless sensor net- works. I. Introduction Technology advance in wireless sensor networks prompts new applications such as environmental monitoring, indus- trial sensing and diagnostics, infrastructure protection, etc. to emerge quickly in recent years. However, due to the scarce bandwidth, the expensive communication cost, and the limited processing power in wireless sensor networks, data aggregation from sensors would be a huge burden if data processing and fusion are not done properly in a dis- tributed manner. Distributed data fusion is one of the most common ways to tackle this problem. For some practical applications, the underlying physical phenomena are described by a range of values (rather than a binary decision) such as the temperature, the density, the velocity, etc. Though several distributed approaches to edge detection were proposed in the context of sensor net- works, e.g., [1] and [2], they only offer a binary decision (in- side or outside the phenomenon) based on measured noisy data. Therefore, some details of the monitored phenom- enon are lost due to binary quantization. A contour line is defined as a two-dimensional curve on which the value of a function of interest is a constant. Thus, contour lines can provide more detailed information about the physical phe- nomenon in terms of the spatial distribution and a refined set of values of measured data. Contour line extraction finds useful applications in forest fire preventing, pollution monitoring, weather forecasting, etc. A distributed algorithm to determine contour lines is proposed to monitor a noisy field in this work. The ex- tracted contour lines can be used to describe the underly- ing phenomenon of interest concisely. The measured data contains noise as well as the spatially-varying signal and they have to be effectively separated using a distributed algorithm. The sensor density and the signal-to-noise ratio are key issues in system design, which are related to the cost of the monitoring system and the condition of the sur- rounding environment, respectively. It is of great interest to investigate the impact of these two on the performance of the proposed algorithm, which helps us understand the behavior of the underlying sensor system. The main contribution of this work is to develop an algo- rithm to overcome the aforementioned obstacle so that con- tour lines of a particular phenomenon can be detected with confidence. Furthermore, the performance analysis also fa- cilitates the design of a robust sensor network in meeting a certain performance requirement under a certain operating environment. II. Problem Formulation Consider a wireless sensor network that is deployed over a large geographical area to monitor a physical phenom- enon. In this work, a uni-modal scalar field is considered first since a multi-modal system can be viewed as multi- ple uni-modal systems. It is assumed that the underlying physical phenomenon may vary very fast and the memory of a local sensor is limited. This means that only the sen- sor measurements at the present time point are available for current contour lines extraction. Besides, the sensor measurements are corrupted by background noise. Thus, the measurement of a sensor located at position (x, y) and time t i can be written as m(x, y, t i )= s(x, y, t i )+ n(x, y, t i ), (1) where s(x, y, t i ) represents the signal value of a physical phenomenon and n(x, y, t i ) denotes the noise. The noise is assumed to be the white Gaussian noise over the sensor field. Under these assumptions, we will develop an efficient algorithm to extract contour lines without aggregating raw measured data from sensors. III. Proposed Contour Line Extraction Algorithm Given data samples observed by sensors, a distributed algorithm is developed to estimate the locations of a set of contour lines, each of which has the same signal value. An overview of the algorithm is given in Sec. III-A, which consists of 3 major steps. Then, each step is described in detail separately in the following subsections. A. Overview of the Algorithm The proposed algorithm consists of the following three main steps. 2716 0-7803-9152-7/05/$20.00 © 2005 IEEE