(13)
Based on (8), (9), (10), (11), (12), and (13), ??x and ??y are given by:
??x =
n1+ + n4+ ??’ n1??’ ??’ n4??’
n1+ + n1+ + n4??’ + n4??’ ??’
n2+ + n3+ ??’ n2??’ ??’ n3??’
n2+ + n2+ + n3??’ + n3??’
, (14)
??y =
n1+ + n2+ ??’ n1??’ ??’ n2??’
n1+ + n1+ + n2??’ + n2??’ ??’
n3+ + n4+ ??’ n3??’ ??’ n4??’
n3+ + n3+ + n4??’ + n4??’
. (15)
Based on (14) and (15), the final ?? = q??2x
+ ??2
y can be computed. This
?? value represents the gradient of values of event predicates collected from
neighborhoods of S0. If ?? is larger than a pre-selected threshold ??0, then the
image processing approach regards S0 as an edge sensor.
2.3 Classifier-based approach
As the image processing approach comes from the image process literature,
the classifier-based approach is based on the pattern recognition literature.
Generally, a sensor adopting the classifier-based approach attempts to partition
the set of data gathered from its neighborhood into two di?®erent classes.
If the partition to be assessed by a partition validity measure is a successful
one, it implies the existence of an edge. Here, a successful partition is defined
as a bi-partite data set, such that data with similar attributes lie in the same
subset and data with dissimilar attributes lie in di?®erent subsets.
The simplest classifier is a linear classifier. If the classifier finds a line
L(a, b, c) ?? ax + by + c = 0, such that all sensors with equivalent values of
event predicates are on the same side and the distance of that line is within
the range of a predefined tolerance radius, the partition is said to be valid and
the sensor is regarded as an edge sensor.
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