Image Processing Reference

In-Depth Information

These operators are generally not associative; the medians are the only ones that

are, where
m
(
x, y
) is the median value of
x
,
y
and a parameter
α
in [0
,
1]:

⎧

⎨

≤

≤

≤

≤

x

if
y

x

α
or
α

x

y

m
(
x, y
)=
med
(
x, y, α
)=

y

if
x

≤

y

≤

α
or
α

≤

y

≤

x

[8.69]

⎩

α

if
y

≤

α

≤

x
or
x

≤

α

≤

y

Figure 8.7 illustrates a few median operators.

α

Figure 8.7.
Three examples of medians, for

equal to 0.1, 0.5 and 0.8, respectively

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