Fig. 13. An example of a boundary approximated by a set of sensor nodes.
Let Si, Si+1 be neighbors on the boundary where they are within the
radio range D (i.e., d(Si, Si+1) < D). At any instant of time, Si and Si+1
observe the same phenomena given by the probability distribution of the local
measurements, m(Si) and m(Si+1) respectively, as shown in Figure 13. Let
Bn be a set of nodes that observe the same events,
Bn = {Si|1 ?· i ?· n, d(Si, Si+1) < R,m(Si) = m(Si + 1)}. (23)
S1 and Sn are defined to be in the same region if there exists a sequence
m(S1) = m(S2) = ?· ?· ?· = m(Sn). If these nodes happen to be on the boundary,
then a trace of the position of these nodes can be considered part of the
boundary. Note that neighboring nodes on the boundary may be outside the
transmission range of each other. In most cases, they are not. So now we
need a scheme to figure out the extent of the region where a set of spatially
distributed sensors are located.
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Chapter 6 Boundary Detection for Sensor Networks
4.2 Growing Algorithm
Here we will introduce a region growing algorithm which was originally presented
in [10]. Suppose the geographic location, (xS, yS), is available for node
S, which can be determined by distributed localization algorithm [7], and each
node has a unique identity IS (e.g., geographic location). Let us also assign
each node a region identifier RS, which indicates a region the sensor node
belongs to.
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