Image Processing Reference
In-Depth Information
If α is very large, the membership
μ
A
()
≈
0
, which does not have any sense.
Couto et al. [10] suggested a thresholding method on general images.
Consider an image
A
of size
M
×
M
with maximum grey level
L
and
a
ij
is
the (
i
,
j
)th pixel of the image with
i
,
j
= 1, 2, 3, …,
M
. Suppose
h
(
g
) denotes
the number of occurrences of the grey level
g
in the image. Given a cer-
tain threshold '
t
' that separates the objects and the background regions, the
average grey levels of the object/background regions are computed using
Equation 6.6.
The membership function is defined using a dissimilarity function that is
expressed as
⎛
⎜
g
mt
L
()
⎞
⎟
⎛
⎜
⎞
⎟
B
μ
()
t Fd
=
,
B
L
−−
1
1
(6.10)
⎛
⎜
g
mt
L
()
⎞
⎟
⎛
⎜
⎞
O
μ
()
t Fd
=
,
1
⎟
O
L
−
1
−
where from Equation 6.7,
F
= 1 − 0.5
x
, with
e
= 0.5, and from Equation
6.4, the restricted dissimilarity function is written as
d
(
x
,
y
) = |
x
−
y
|.
Intuitionistic fuzzy set, π, is the ignorance of the expert in assigning the
membership function, that is, the hesitation degree. The choice of the
membership function depends on the expert's knowledge. If the expert is
very certain about the pixels' belongingness to the object or background,
then the hesitation degree, π, is zero and it decreases with the expert's cer-
tainty to the belongingness of the pixel. Also, the hesitation degree has the
least possible influence on the choice of the membership degree. Under
this condition, π(
g
), the quantification of the ignorance of the expert in
the selection of the membership function of the object and background is
computed as
π
() (
g
=− ⋅ −
1
μ
( )) (
g
1
μ
( ))
g
B
O
An intuitionistic fuzzy entropy by Burillo and Bustince [1] is used as a mea-
sure to find the optimal threshold, which is defined as
1
−
∑
L
1
IFEt
MM
hg g
()
=
()()
π
B
×
g
=
0
The grey level that corresponds to the lowest entropy is chosen as the opti-
mal threshold. This can be expended to multilevel image segmentation.
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