Image Processing Reference
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
a j 1 ≤
a j 2 ≤···≤
a j n .
Then, for a set of weights w i that verifies:
w i =1 ,
n, w i ∈
[0 , 1] ,