Image Processing Reference
In-Depth Information
where μ
mn
is the membership function of the fuzzified image that is calcu-
lated as
mn
gg
g
−
−
min
μ
mn
=
g
max in
g
max
and
g
min
are the maximum and minimum grey values of the image,
respectively.
λ is calculated using the intuitionistic fuzzy entropy [6]:
N
M
1
∑
∑
1
−
π
(
x
)
IE A
()
=
π
xe
Amn
(
)
⋅
Amn
N
n
=
1
m
=
1
π
mn
,
π
1
, is the hesitation degree.
The optimum value of λ is
=−ʹ − ʹ
μ
ν
mn
mn
mn
λ
=
max( (,))
IE A
λ
opt
λ
The structuring element used is
08 02 08
02 08 02
08 02 08
.
.
.
⎡
⎤
⎢
⎢
⎢
⎥
⎥
⎥
.
.
.
.
.
.
⎣
⎦
Erosion and dilation are defined as
DAB
(,) up
=
i By xAy
(
−
),()
⎣
⎦
yS
∈
EAB
(,) inf
=
u cByxAy
yS
⋅
(
−
),()
⎣
⎦
∈
where
i
is any
t
-norm (fuzzy intersection)
u
is any
t
-conorm (fuzzy union)
c
is a complement
Using
t
-norm and
t
-conorm, erosion and dilation are defined as
⎡
⎤
1
−−+
By xAyAyByx Ay
(
) () () (
−
⋅ −−− ⋅ − −
)
(
1
γ
) ()(
1
By x
(
)
)
EAB
(,) inf
=
⎢
⎥
11
−−⋅
(
γ
Ay
) ()(
⋅ −−
1
By x
(
))
yS
∈
⎣
⎦
Search WWH ::
Custom Search