Image Processing Reference

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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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