Image Processing Reference
In-Depth Information
Figure 8.8.
Four examples of mean operators. First line: harmonic and geometric means.
Second line: arithmetic and quadratic means
Within the class of mean operators, we also have weighted means, OWAs (Ordered
Weighted Average) [YAG 88] and the fuzzy integrals discussed above [GRA 95].
In OWAs, the weights are defined by the ranks of the values to combine. Let
a
1
,a
2
,...a
n
be these values. They are arranged in a sequence
a
j
1
,a
j
2
,...a
j
n
such
that:
a
j
1
≤
a
j
2
≤···≤
a
j
n
.
Then, for a set of weights
w
i
that verifies:
n
w
i
=1
,
∀
i,
1
≤
i
≤
n, w
i
∈
[0
,
1]
,
i
=1
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