Let sensor S0 be the sensor performing classifier-based edge detection and
PAs be the set of sensors in its probing area. A line with the above characteristic
must have the highest classifier score Js0 :
155
Ren-Shiou Liu, Lifeng Sang, and Prasun Sinha
Fig. 4. A simple linear classifier cuts the probing area S0 into two regions such that
sensors with di?®erent values of event predicates are at di?®erent sides.
Js0 (a, b, c) = ????????????
X 8s2PAs0
VsSN(axs + bys + c)????????????
(16)
where
SN(x) = ??±??????
??’1 if x < 0,
0 if x = 0,
1 if x > 0.
(17)
The proof is straightforward. Based on (16) and (17), for all s above
the line, VsSN(axs + bys + c) > 0. If most of the sensors with 1 values of
event predicates lie on the same side, say above the line, then Js will reach a
maximum value. However, a partition is regarded as valid if and only if the
optimal line Lopt(a, b, c) satisfies axs0+bys0+c p(a2+b2) ?· r, which means that the line
lies within a predefined tolerance radius.
Generally speaking, as the radius of probing area or sensor density increases,
the more accurately the event boundary can be detected. This applies
to the statistical approach, image processing approach and the classifier-based
approach. However, the classifier-based approach has a far more qualitative
characteristic than the others. When the probing area or sensor density increases,
the unwanted detection rates for the statistical and image processing
approaches also increase, while it??™s a decrease for the classifier-based approach,
which means a thinner edge can be obtained.
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