Several physical phenomena (for instance, contaminant flows [3] and seismic disturbances) can span large geographic extents. Fine-grain sensing of these time-varying phenomena can help scientists understand what factors (e.g., soil density variations) affect the spread of these phenomena. One way to architect an energy-efficient sensor network for studying these phenomena is to store the detections of the phenomena within the network and provide a query interface which enables scientists to understand the temporal and spatial properties of these phenomena.
We anticipate that one common query will ask for the spatial extent of the phenomenon at a given time: for example, “Which sensors saw the primary wave before time T?”. For energy-efficiency reasons, it makes more sense for to design the spatial query that returns a boundary that captures all or most nodes that satisfy the query predicate. A geometric representation of the boundary has the potential to be more concise (and therefore more energy-efficient) than an enumeration of all nodes. Examples of such representations include contours, hulls, or bounding boxes.
An energy-efficient boundary finding algorithm will need to carefully choose nodes in the sensor network and compute the boundary “in-network”. A key component of such an algorithm is a localized edge detection scheme: a technique by which each node locally determines (perhaps by gathering information from other nodes within its neighborhood) whether it lies on or near the boundary specified by the query. If a reliable technique existed for localized edge detection, then, conceptually at least, boundary finding is simply a matter of sequentially traversing all nodes that determine themselves to be on the edge. Localized edge detection will be an essential component of boundary tracking as well; as the phenomenon evolves with time, nodes at the edge may alert neighboring nodes (in a manner similar to target tracking [4]). We think of localized edge detection as a powerful primitive upon which a variety of applications might be built.
Edge detection has been widely studied in the context of digital image processing. Filtering [1] is one of the most common approaches to detecting edges in images. To determine whether an image pixel is at an edge or not, this approach applies a filter to values of a set of neighboring pixels. As such, these techniques can be directly applied to localized edge detection.
However, one fundamental difference between images and a sensor field is the spatial regularity of information. A digital image is a regular grid of pixels, and information is sampled at regular intervals. Almost all standard digital image processing techniques (Fourier transforms, high-pass filtering) rely on having information about the image at regular intervals. Deployment and maintenance of thousands of sensors in a grid like regular fashion over large geographical extents is clearly infeasible. It is expected that sensors will be arbitrarily placed in the sensor field and will be prone to failures or even node displacement. With this relaxation of regularity, it is less clear that digital image filtering can be applied to localized edge detection.
In fact irregular node placement makes it hard to even define precisely whether a node is at an edge or not. In Section 2, we show how to circumvent this difficulty and define some metrics for localized edge detection. Because the efficacy of edge detection based on digital image filtering is unclear, we consider two other classes of edge detection schemes in Section 3: a statistical scheme and a classifier based scheme (that is suggested by the pattern recognition literature [2]). We find that, over a fairly broad range of operating conditions, the classifier scheme out-performs the other schemes. We present our evaluation results in Section 4, and conclude in Section 5.
To our knowledge, no prior work has considered localized edge detection in sensor networks. Concurrently, Nowak and Mitra [5] describe a scheme for estimating the boundary of a large-scale phenomenon by aggregating readings along a pre-defined hierarchical structure within the network. Their approach is somewhat complementary to ours, in that our localized edge detection is a primitive that might be used in a variety of boundary estimation applications (not just in their algorithm, but also in applications that estimate more concise, but approximate, boundary descriptions such as ellipses and hulls).
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