Image Processing Reference
In-Depth Information
If 0 ≤ λ
≤ 1, then
− +
+− −+
(
1
1
λ
)
by
y
yby
λ
)
,
for 0
b
>
λ
(
λ
)(
1
cby
(, )
=
0
,
for
b
=
0
(9.11)
x
)
,
for 0
b
>
λ
+
(
1
−+−
λ
)(
bxbx
ibx
(, )
=
1
,
for
b
0
=
Reichenbach
0
,
,
t
≤−
>−
1
1
b
Cby
(, )
=
t
t
b
(9.12)
Ibs
(,)
=−+
1
b
bx
An adjoint pair of fuzzy erosion and dilation is given as follows [15]:
DAx
( () sup((
=
c Bx yAy
−
),())
B
y
(9.13)
EAx
( () inf( (
=
i By xAy
−
),())
B
y
Several definitions for fuzzy erosion and dilation are proposed by many
authors.
9.3.1 Different Definitions of Fuzzy Morphology
All the definitions are given for any fuzzy set
A
and structuring element
B
,
which are defined over a space
S
at any point '
x
'.
1. Definition by De Baets and Kerre [1] and Bloch and Maitre [3]
DAx
1
() supmin (),( )
=
A yByx
−
⎣
⎦
yS
∈
(9.14)
EAx
1
() infmax (),
=
⎣
A y By
1
−
(
−
x
)
⎦
yS
∈
2. Definition by Bloch and Maitre [3]
DAx
2
() sup(),
=
A yByx
(
−
)
⎣
⎦
yS
∈
(9.15)
EAx
2
() inf
=
⎣
A y Byx
( ),
1
−
(
−
)
⎦
yS
∈
Search WWH ::
Custom Search