Gx = ??®??°
??’1 0 1
??’1 0 1
??’1 0 1
?????»
, (3)
Gy = ??®??°
1 1 1
0 0 0
??’1 ??’1 ??’1
?????»
. (4)
Consider the following 3x3 image window:
Filter window = ??®??°
v1 v2 v3
v4 v5 v6
v7 v8 v9
?????»
(5)
where v1...v9 are grey levels of each pixel in the filter window. By applying
the masks to the filter window, we obtain the gradient magnitude along the
x and y directions respectively:
??x = ??’1 ?¤ v1 + 1 ?¤ v3 ??’ 1 ?¤ v4 + 1 ?¤ v6 ??’ 1 ?¤ v7 + 1 ?¤ v9, (6)
??y = 1 ?¤ v1 + 1 ?¤ v2 + 1 ?¤ v3 ??’ 1 ?¤ v7 ??’ 1 ?¤ v8 ??’ 1 ?¤ v9. (7)
A high value of Prewitt Gradient, ?? = q??2x
+ ??2
y, would indicate the existence
of an edge. Similarly, to apply this technique within the context of
sensor networks, we treat each node as a pixel, and the values (either 0 or 1)
of event predicates as the ???grey level??? for each node. However, sensor nodes
are arbitrarily deployed in a sensor field, thus, there is no spatially defined
3x3 filter window and the computed ?? value could be biased due to the uneven
deployment as well. To overcome these two problems, a new pair of
???convolution masks??? (Gx,Gy) and a weighting function W(x, y) which takes
sensors??™ location as argument for each of the perpendicular orientation must
be introduced.
153
Ren-Shiou Liu, Lifeng Sang, and Prasun Sinha
Let PAs0 be the set of sensors in the probing area of a sensor S0 at position
(xs, ys). Denote the binary value of event predicate for any sensor s 2 PAs0
as Vs.
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