Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l.
5, N
o
. 5
,
O
c
tob
e
r
201
5, p
p
. 1
035
~104
4
I
S
SN
: 208
8-8
7
0
8
1
035
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJECE
New Method to Optimize Initial
Point Values of Spatial Fuzzy c-
means Algorithm
Iman
Omid
var Tehrani*,
S
ubari
ah I
b
rah
i
m*,
Habib H
a
ron*
* Departement o
f
Computi
ng, Universiti Teknolo
g
i Ma
lay
s
ia, Joh
o
r, Malay
s
ia
Article Info
A
B
STRAC
T
Article histo
r
y:
Received
May 10, 2015
Rev
i
sed
Au
g 5, 201
5
Accepted Aug 23, 2015
Fuzzy
b
a
sed segmentation algo
rithms
are known to be performing well on
m
e
dical
im
ages
.
S
p
atial fu
zz
y C
-
m
eans
(S
F
C
M
)
is
broadl
y us
ed
for m
e
dical
im
age segm
enta
tion but
it suff
ers from
optimum selection
of
seed poin
t
initi
ali
z
a
tion wh
ich is don
e
eith
er m
a
nua
lly
or
randomly
. In
this paper, an
enhanced SFCM algorithm
is proposed b
y
optim
i
z
ing the SFCM initial poin
t
values. In th
is
method in ord
e
r
to in
creasing the algorithm sp
eed f
i
rst th
e
approxim
a
te in
it
ial va
lues are de
term
ined b
y
cal
c
u
lating th
e histo
g
ram
of the
original
im
age
.
Then b
y
uti
l
i
z
in
g the GW
O algorithm
the optim
um initia
l
values could b
e
achiev
e
d. Fin
a
lly
B
y
using th
e
achiev
e
d ini
tia
l
values, th
e
proposed method shows the significant
improvement in segmentation r
e
sults
.
Also the proposed method perfor
m
s faster
than previous algorithm i.e. SFCM
and has b
e
tt
er
converg
enc
e
.
Moreover, it
h
a
s noti
ceab
l
y
i
m
p
roved the
cluster
i
ng ef
fect.
Keyword:
Brain
GW
O
M
R
I Im
age
Seg
m
en
tatio
n
Spatia Fuzzy C
-
m
eans
Copyright ©
201
5 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
Habi
b Har
o
n,
Depa
rt
em
ent
of C
o
m
put
i
n
g,
Un
i
v
ersiti Tekn
o
l
o
g
i
Malaysia,
UTM Sku
d
a
i, Jo
hor, Malaysia.
Em
a
il:h
ab
ib
@u
tm
.
m
y
1.
INTRODUCTION
Th
e Th
e
p
r
o
c
ess of
d
i
v
i
d
i
n
g
th
e
o
r
ig
i
n
al im
a
g
e in
t
o
m
u
ltip
l
e
m
ean
in
g
f
u
l
reg
i
on
s in su
ch
a way th
at
th
ere is no
i
n
tersectio
n am
o
n
g
th
em
is called
im
ag
e se
gmen
tatio
n
.
Segmen
tatio
n
is
usu
a
lly d
i
fficu
lt to
be
d
o
n
e
b
ecau
s
e
o
f
r
e
g
i
on
inhom
o
g
e
n
e
ity, b
l
u
r
r
e
d r
e
g
i
on
bo
und
ar
ies and no
ise. Man
y
i
m
ag
e seg
m
en
tatio
n
algorithm
s
have bee
n
published
ove
r the
pa
st decade
[1-5
]
.
The
s
e algorit
h
m
s
have
been use
d
in applications
suc
h
as m
e
dical im
aging a
n
alysis, obj
ect cla
ssification a
n
d
im
age retrieval
[6
]. Gen
e
rally th
ese
algo
rithm
s
are
cat
ego
r
i
zed i
n
t
o
fo
ur
gr
ou
ps
i
n
cl
udi
ng
e
dge
det
ect
i
o
n, cl
u
s
t
e
ri
ng
,
regi
on
base
d a
n
d t
h
r
e
sh
ol
di
n
g
.
cl
us
t
e
ri
ng
base
d al
go
ri
t
h
m
s
pl
ay
an im
port
a
nt
rol
e
i
n
m
a
ny
appl
i
cat
i
ons [
7
]
su
ch as m
e
di
cal
-im
a
ge proc
ess
i
ng [
8
]
.
Th
ese algor
ithm
s
d
i
v
i
d
e
th
e o
b
j
ects
o
r
p
a
tter
n
s i
n
to
d
i
f
f
er
en
t gr
oup
s in
such
a w
a
y t
h
at th
e sam
p
les in
a g
r
oup
are m
o
re sim
ilar to each ot
he
r th
a
n
t
h
e sam
p
les of ot
her group.
K-m
eans
also known
as hard c-m
ean
s is on
e o
f
th
e
go
od
exa
m
p
l
es o
f
clu
s
t
e
r
i
ng
b
a
sed algo
r
ith
m
s
[
9
,
10]
.
T
h
e i
m
age pi
xel
s
are
gr
ou
pe
d i
n
t
o
seg
m
ent
s
base
d
o
n
t
h
ei
r i
n
t
e
nsi
t
y
l
e
vel
i
n
suc
h
a
way
t
h
at
eac
h
pi
xe
l
can be
onl
y
i
n
one se
gm
ent
.
Fuzzy
c-m
eans (FC
M
) w
h
i
c
h
was fi
rst
prese
n
t
e
d
by
Du
n
n
[1
1]
i
s
consi
d
e
r
ed as
anot
her
ap
pr
o
ach
fo
r i
m
age cl
ust
e
ri
n
g
.
It
was
use
d
by
Bezdak [12] a
s
the
universa
l classification base
d
al
go
ri
t
h
m
.
The
FC
M
al
g
o
ri
t
h
m
cl
assi
fi
es im
age
pi
xel
s
i
n
t
o
gr
o
u
p
s
ho
we
v
e
r eac
h
pi
xel
c
a
n
be ass
o
ci
at
e
d
i
n
t
o
m
u
l
tip
le g
r
oups b
a
sed
on
a d
e
gr
ee of
m
e
m
b
er
sh
ip
. FC
M h
a
s p
r
ov
en to
h
a
v
e
ou
tstan
d
i
n
g
p
e
rfo
rman
ce on
vari
ous
m
e
di
cal
appl
i
cat
i
o
ns
[
1
3
,
14]
.
In sp
ite
o
f
good
p
e
rform
a
n
ce of FCM, th
ere are s
till so
m
e
w
eakn
e
sses in
th
e algo
rith
m
su
ch as t
h
e
sensitivity to
noise a
n
d the la
ck
of a
good st
rategy for the
initial seed
poi
nt
placem
ent [15]. Chua
ng et a
l
. [14]
pr
o
pose
d
Spat
i
a
l
FC
M
(S
FC
M
)
al
g
o
ri
t
h
m
t
o
ove
rc
om
e t
h
e FC
M
noi
se
i
ssue
by
m
odi
fy
i
n
g
t
h
e
FC
M
ob
ject
i
v
e
fu
nct
i
o
n an
d t
a
ki
n
g
t
h
e a
d
va
nt
age
of
t
h
e
n
e
i
g
h
b
o
r
ho
o
d
p
i
xel
s
. R
e
ga
rdl
e
ss o
f
t
h
e
FC
M
noi
se i
s
s
u
e
w
h
i
c
h i
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE Vo
l. 5
,
N
o
. 5
,
O
c
tob
e
r
20
15
:
103
5
–
10
44
1
036
en
h
a
n
c
ed
b
y
SFCM techn
i
que, in
itializatio
n
step
of th
e al
go
rith
m
also
p
l
ays a prin
ci
p
a
l ro
le
o
n
th
e qu
al
ity of
segm
ent
e
d im
ages an
d st
a
nda
rd S
F
C
M
al
go
r
i
t
h
m
fai
l
s
t
o
have a p
r
o
p
e
r
st
r
a
t
e
gy
fo
r t
h
i
s
c
a
se [1
5]
. I
n
o
r
der t
o
ove
rc
om
e
the i
n
itialization is
sue of FCM, recently a hybr
idization algori
thm of pa
rticle swarm
opti
m
i
zation
(PS
O
)
whi
c
h i
s
a t
echni
q
u
e o
f
p
o
p
u
l
a
t
i
on
b
a
sed cl
ust
e
ri
ng
wi
t
h
FC
M
na
m
e
l
y
(PSO+
F
C
M
) was p
r
o
p
o
se
d by
research
ers [7
, 15
-1
9
]
.
Zh
ang et al. [1
6
]
u
s
ed
PSO as
an initializa
tio
n
step
in
po
ssib
ilistic c-m
ean
s clu
s
tering
(PCM)
[17
]
to
lo
cate th
e
b
e
st
in
itial p
o
s
itio
ns of cluster centers.
In
order t
o
enhance t
h
e spe
c
t
ral characteris
tics of f
eatures
for clusteri
ng, Liu
Ha
nl
i
et
al
[19]
used
the PSO-FCM
on the im
age data to enha
nce
the accuracy
of
wetland e
x
traction. Farha
d
et al [7] used PSO-
FCM with
four iteratio
n
s
t
o
t
h
e p
a
rticles in
th
e swarm
fo
r
ev
ery eigh
t gen
e
ration
s
su
ch
th
at th
e fitn
ess v
a
lu
e
of eac
h
pa
rticle was im
prove
d
. T
h
e
res
u
lt of using PS
O-FCM on
hype
rs
pectral
data, in two
spaces
da
ta and
featu
r
e sh
owed its h
i
gh
er ab
ili
ty in
se
gm
entation t
h
an fuzzy
clustering
[7].
A hy
bri
d
f
u
zz
y
cl
ust
e
ri
n
g
al
go
ri
t
h
m
t
h
at
inco
r
p
o
r
at
es F
C
M
i
n
t
o
Q
u
a
n
t
u
m
-
behave
d
PSO
nam
e
l
y
Q
P
SO
+FCM
alg
o
r
ith
m
w
a
s pr
opo
sed
b
y
W
a
ng
et.al
[1
8
]
. The
Q
P
SO
h
a
s less par
a
m
e
ter
s
an
d
h
i
gh
er
co
nv
erg
e
n
t
cap
a
b
ility o
f
th
e
g
l
ob
al op
timiz
in
g
th
an
PSO
alg
o
rith
m
.
So
th
e iteratio
n
al
g
o
rith
m
was rep
l
aced
b
y
th
e QPSO b
a
sed
on
th
e g
r
ad
ien
t
d
e
scen
t of
FCM,
w
h
ich
m
a
k
e
s th
e alg
o
r
ith
m
h
a
v
e
a
str
ong g
l
ob
al
searchi
ng ca
pa
ci
t
y
and av
oi
ds
t
h
e l
o
cal
m
i
nim
u
m
pro
b
l
e
m
s
of FC
M
a
nd i
n
a l
a
r
g
e de
gre
e
avoi
d de
pe
nd
i
n
g
o
n
th
e in
itializatio
n
v
a
lu
es.
Alth
oug
h
it is p
o
s
sib
l
e to
fi
n
d
t
h
e op
tim
u
m
in
itial
p
o
s
itio
n
v
a
lu
es
b
y
PSO and
QPSO
b
u
t
th
e
resulted
value
s
are not always optim
i
zed because both
of the
m
are trappe
d into local optimal solution a
nd
fail
t
o
fi
n
d
t
h
e gl
o
b
al
best
val
u
e
[2
0, 2
1
]
.
The
pr
obl
em
of t
r
appi
ng i
n
l
o
ca
l
sol
u
t
i
on
was
fi
xed
by
gray
wol
f
alg
o
rith
m
(GWO) [2
2
]
. The GWO alg
o
rith
m
is ab
le to
p
r
ov
id
e v
e
ry co
m
p
etitiv
e res
u
lts co
m
p
ared
to
PSO,
gra
v
i
t
a
t
i
onal
s
earch al
go
ri
t
h
m
(GS
A
),
di
f
f
ere
n
t
i
a
l
evol
u
t
i
on (
D
E
)
, e
v
ol
ut
i
o
nary
pr
o
g
ram
m
i
ng (EP
)
, a
n
d
ev
o
l
u
tio
n strat
e
g
y
(ES) m
e
ta-
h
euristics.
In
th
is research
, GWO is u
tilized
in
stead
of PSO to
find
th
e g
l
ob
al b
e
st
in
itial seed
p
o
s
itio
n
s
of
SFCM
algo
rithm
for M
R
I i
m
age segm
entation. M
o
re
o
v
e
r,
the
histogra
m
of im
age is use
d
to i
n
crease the
con
v
e
r
ge
nce s
p
eed
. The re
st
of t
h
e
pape
r i
s
org
a
ni
ze
d as f
o
l
l
o
w
s
. I
n
Sect
i
on 2
,
cl
ust
e
ri
n
g
base
d al
g
o
ri
t
h
m
s
includi
ng FC
M and SFCM
are introdu
ced. Th
e GWO as
an
o
p
tim
izat
io
n
algorith
m
is p
r
esen
ted in sectio
n
3
.
In
Sect
i
o
n 4
,
t
h
e
pr
op
ose
d
al
go
ri
t
h
m
whi
c
h
i
s
base
d
on
i
m
provi
n
g
t
h
e
SFC
M
usi
n
g
G
W
O i
s
pr
ese
n
t
e
d.
T
h
e
resul
t
s
of
t
h
e
p
r
o
p
o
sed
m
e
t
hod a
r
e
prese
n
t
e
d i
n
Sect
i
o
n
5.
Fi
nal
l
y
,
we
ha
ve
dra
w
n t
h
e
c
oncl
u
si
o
n
i
n
S
ect
i
o
n
6.
2.
CLUSTE
RI
N
G
BASE
D
AL
GOR
ITHM
S
FCM is known as the
m
o
st com
m
on par
titioning m
e
thod [23]
. Assum
i
ng
that
X=
{
i
1
,
…
,i
N
} be a set
of
i
m
age
pi
xel
s
, FC
M
di
vi
de
s
t
h
ese
pi
xel
s
base
d o
n
a
de
gree
of
m
e
m
b
ershi
p
b
y
calcu
latin
g th
e cluster
centers {
v
1
,…,
v
C
} and
m
i
nim
i
zi
ng t
h
e
f
o
l
l
o
wi
n
g
s
u
m
of s
q
uare
d
o
b
ject
i
v
e
f
unct
i
o
n:
|
|
|
|
(1
)
Whe
r
e
l
is a v
a
riab
le wh
i
c
h
is g
r
eater
th
an
1
and
it co
n
t
ro
ls th
e
lev
e
l o
f
fu
zzi
n
e
ss of th
e
seg
m
en
tatio
n
resu
lt;
C
and
N
are the total num
b
er of
regi
ons and im
age pixels re
specti
v
ely. The
following
co
nd
itio
ns m
u
st b
e
satisfied
in th
e FCM
ob
j
e
ctiv
e fu
n
c
tion
.
1
;
0
1
;
0
.
(2
)
Th
e m
e
m
b
ership
fu
n
c
tion
s
μ
mn
and t
h
e ce
ntroids
v
m
are
up
d
a
ted
iteratively b
y
th
e fo
llo
wi
n
g
two
equat
i
o
ns:
||
||
/
∑
||
||
/
(3
)
∑
∑
(4
)
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
ISS
N
:
2088-8708
New Meth
od
t
o
Op
timize In
itia
l Po
in
t Va
lu
es o
f
Sp
a
tia
l Fuzzy c-mea
n
s
Al
g
o
r
it
h
m
(Hab
ib
H
a
ron
)
1
037
Whe
n
the
pixe
ls that are close to their centroids
are
ha
vi
n
g
hi
g
h
m
e
m
b
ershi
p
val
u
e
s
an
d t
h
o
s
e t
h
at
are fa
r a
w
ay are ha
ving low
values, it ca
n
be
con
c
lud
e
d th
at
th
e FCM al
g
o
rith
m
is o
p
tim
iz
ed
.
Al
t
h
o
u
gh FC
M
al
gori
t
h
m
per
f
o
r
m
s
wel
l
ho
weve
r t
h
e
l
ack of s
p
at
i
a
l
i
n
fo
rm
at
i
on is one
of t
h
e
weak
nesse
s o
f
FC
M
[13
,
1
4
,
24]
. B
y
t
a
ki
n
g
i
n
t
o
acc
ou
n
t
sp
atial in
formatio
n
,
it is p
o
s
sib
l
e to
m
a
k
e
FCM
robust agai
nst i
m
age
artifacts and
noise.
Spatial FCM (SFCM) was
proposed
by Chua
ng
et al.
[
14]
. T
h
i
s
al
g
o
r
i
t
h
m
has
m
odi
fi
ed FC
M
o
b
j
ectiv
e fu
n
c
t
i
o
n
t
o
in
cl
ud
e sp
atial in
fo
rm
at
io
n
b
y
fo
llowi
n
g
equ
a
tion
s
:
∑
(5
)
Whe
r
e,
p
and
q
are con
t
ro
llin
g th
e lev
e
l o
f
fuzzin
e
ss and
th
e lev
e
l o
f
effect
o
f
th
e sp
atial in
fo
rm
atio
n
respectively. The
va
riable
h
mn
wh
ich
in
clu
d
e
s sp
atial in
fo
rm
atio
n
can
b
e
calcu
lated
b
y
th
e fo
ll
o
w
i
n
g
equat
i
o
n:
∈
(6
)
whe
r
e
N
n
indicates a local
window whic
h
is placed around the im
a
g
e pixel
n
. The t
w
o
ot
he
r
vari
a
b
l
e
s
μ
mn
an
d
v
m
ar
e upd
ated
iter
a
tiv
ely based
on
Eq
s. (3)
an
d (4
).
3.
GREY WOLF OPTIMIZ
A
TION
(GWO)
GWO is a m
e
t
a
-h
eu
ristic op
t
i
m
i
zat
io
n
algorith
m
in
sp
i
r
ed
by
grey
wol
v
e
s
(C
ani
s
l
u
p
u
s
)
[
22]
. T
h
e
GWO algorithm
mimics the lead
ers
h
ip hierarchy
a
nd hunti
n
g
m
ech
an
ism o
f
grey wo
lv
es in
n
a
ture.
In
t
h
is
al
go
ri
t
h
m
t
h
e po
p
u
l
a
t
i
on i
s
d
i
vi
ded i
n
t
o
f
o
u
r
gr
o
u
p
s
:
al
pha
(
α
),
b
e
ta (
β
), d
e
lta (
δ
), and om
ega (
ω
). T
h
e first
th
ree fittest wolv
es are co
nsidered
as
α
,
β
, a
nd
δ
wh
o g
u
i
d
e ot
her w
o
l
v
es
(
ω
) t
o
wa
r
d
pr
om
i
s
i
ng areas of t
h
e
search
space. During opti
m
i
z
a
tion,
t
h
e
wol
v
es update their
positions a
r
ound
α
,
β
, or
δ
as fo
llo
ws:
|
|
(7
)
1
(8
)
Whe
r
e
t
ind
i
cates th
e cu
rren
t iteratio
n
,
2
.
,
2
.
,
is
th
e po
sitio
n
vecto
r
o
f
th
e
prey,
indicates the
position vect
or of a
grey
wol
f
,
a
is lin
early d
e
creased
from
2
to
0
,
an
d
r
1
,
r
2
a
r
e
ra
n
dom
v
ector
s in [0
,1
]. Th
e co
n
c
ep
ts
o
f
po
sitio
n updatin
g
u
s
ing
Eqs. (7
) an
d (8
) ar
e illu
str
a
ted in Figu
r
e
1
.
Fig
u
re
1
.
Po
sitio
n upd
atin
g mech
an
ism
o
f
search ag
en
ts and
effects
o
f
A
on
it [25
]
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE Vo
l. 5
,
N
o
. 5
,
O
c
tob
e
r
20
15
:
103
5
–
10
44
1
038
It m
a
y b
e
seen in
th
is
figu
re
th
at a wo
lf in
p
o
s
ition
(
X
,
Y
) is able t
o
rel
o
cate itself around the
prey
wi
t
h
t
h
e
pr
op
o
s
ed eq
uat
i
o
ns.
Al
t
h
o
u
gh se
ve
n o
f
p
o
ssi
bl
e l
o
cat
i
o
n
s
ha
ve
been s
h
ow
n i
n
Fi
gu
re 1
,
t
h
e
r
a
nd
om
param
e
ters
A
an
d
C
allow the
wol
v
es t
o
rel
o
c
a
te to any
pos
ition i
n
the
c
onti
n
uous s
p
ace a
r
ound the
prey.
In
t
h
e
GWO al
g
o
rith
m
,
it is always assu
m
e
d
th
at
α
,
β
, a
n
d
δ
are lik
ely to
b
e
th
e po
sition o
f
th
e
prey
(o
pt
i
m
u
m
). Duri
ng
opt
i
m
i
z
at
i
on, t
h
e
fi
rst
t
h
ree
best
sol
u
t
i
ons
obt
ai
ne
d
so fa
r are ass
u
m
e
d as
α
,
β
,
and
δ
respectively. T
h
en, othe
r wol
v
es are c
onsi
d
ered as
ω
an
d
ab
le to
re-po
s
itio
n
with
resp
ect to
α
,
β
, and
δ
. The
m
a
t
h
em
at
i
c
al
m
odel
pr
op
ose
d
t
o
re
-ad
j
ust
t
h
e
po
si
t
i
on
of
ω
wo
lv
es
a
r
e as
fo
llo
w
s
:
|
|
(9
)
|
|
(1
0)
|
|
(1
1)
whe
r
e
X
α
sh
ows th
e
po
sitio
n
o
f
th
e
α
,
X
β
sho
w
s th
e po
sition
o
f
th
e
β
,
X
δ
is
th
e p
o
s
ition
o
f
δ
,
C
1
,
C
2
,
C
3
are ra
ndom
vectors a
n
d
X
i
ndi
cat
es t
h
e
po
si
t
i
on
of t
h
e c
u
rre
nt
s
o
l
u
t
i
o
n.
Eq
uat
i
ons
(9
-
1
1) cal
cul
a
t
e
ap
pr
o
x
im
a
t
e distance bet
w
een t
h
e curre
nt
sol
u
t
i
on an
d al
p
h
a,
bet
a
, an
d
d
e
lta resp
ectively. After
d
e
fi
n
i
ng
th
e
d
i
stan
ces, the fin
a
l
p
o
s
ition
of the cu
rren
t so
lu
t
i
o
n
is calcu
lat
e
d
as
Eq
uat
i
ons
(
1
2-
15
):
(1
2)
(1
3)
(1
4)
1
3
(1
5)
Whe
r
e X
α
shows th
e
po
sition
of th
e alph
a, X
β
sh
ows t
h
e
p
o
s
ition
o
f
t
h
e b
e
ta,
X
δ
is the p
o
sitio
n
o
f
del
t
a
, A
1
, A
2
,
A3 a
r
e ra
nd
o
m
vect
ors, a
n
d
t
i
ndi
cat
es t
h
e num
ber o
f
i
t
e
rat
i
ons
. As m
a
y
be seen i
n
t
h
ese
equat
i
o
ns
, t
h
e
equat
i
o
ns (
9
-
1
1
)
de
fi
ne t
h
e
st
ep si
ze of t
h
e
ω
wo
lf toward
α
,
β
, a
n
d
δ
res
p
ective
l
y. The
equat
i
o
ns
(
1
2-
15
)
t
h
en
defi
n
e
t
h
e fi
nal
p
o
si
t
i
on of
t
h
e
ω
wol
v
es. It m
a
y also be
ob
se
rved that t
h
ere
are two
vectors: A a
n
d C. T
h
ese t
w
o
vectors a
r
e random
a
nd adapt
i
v
e
vec
t
ors t
h
at
pr
o
v
i
de ex
pl
o
r
at
i
o
n an
d
ex
p
l
o
itatio
n
for th
e GWO algo
rith
m
.
As sh
o
w
n i
n
F
i
gu
re 1, t
h
e e
x
pl
o
r
at
i
on
occu
r
s
whe
n
A is greater than 1
or
le
ss than -1. T
h
e vector C
al
so p
r
om
ot
es expl
orat
i
o
n
wh
en i
t
i
s
greater than
1. In c
o
ntrary, the
e
x
pl
oi
t
a
t
i
on i
s
em
phasi
zed
w
h
en
|
A
|
<
1
and
C
<
1.
It
s
h
o
u
l
d
be
n
o
t
e
d
here t
h
at
A
i
s
decrease
d
l
i
nearl
y
d
u
r
i
n
g
opt
i
m
i
zati
on i
n
or
der t
o
em
pha
si
ze
ex
p
l
o
itatio
n
as th
e iter
a
tio
n
co
un
ter
incr
eases. Ho
w
e
v
e
r
,
C
is g
e
n
e
r
a
ted
r
a
n
d
o
m
ly
th
r
ough
ou
t op
timizati
o
n
t
o
em
phasi
ze ex
pl
o
r
at
i
on/
e
xpl
o
i
t
a
t
i
on at
any stage, a very
helpful m
ech
an
ism
fo
r reso
lv
ing
lo
cal op
ti
m
a
entra
p
m
e
nt.Aft
er all, the
ps
eudo code
of
th
e
GWO al
g
o
rithm
is p
r
esen
ted
in
Figure
2
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
New Meth
o
d
t
o
Op
timize In
itia
l Po
in
t Va
lu
es o
f
Sp
a
tia
l Fuzzy c-mea
n
s
Al
g
o
r
it
h
m
(Hab
ib
H
a
ron
)
1
039
In
itialize th
e grey wo
l
f
p
opu
latio
n
X
i
=
(
i=
1,
2,
…,
n
)
In
itialize
a
,
A
an
d
C
Calculate the fi
tness
of each s
earch age
n
t
X
α
= the
best se
arch age
n
t
X
β
= the
second
best sea
r
ch a
g
ent
X
δ
=
th
e th
ird
b
e
st search ag
en
t
While
(t
<M
ax num
ber of
i
t
e
r
a
t
i
ons)
For
eac
h se
arc
h
a
g
ent
U
p
d
a
te
th
e po
sitio
n
of
th
e
cu
rr
e
n
t s
e
ar
ch
ag
en
t b
y
equ
a
tion
(
1
5
)
End F
o
r
Up
date
a
,
A
and
C
Calculate the fi
tness
of all search age
n
ts
Up
date
X
α
, X
β
,
X
δ
t=t+1
End While
Retu
rn
X
α
Fi
gu
re 2.
Pse
u
do
co
de o
f
G
W
O
al
g
o
r
i
t
h
m
The e
x
pl
o
r
at
i
o
n
of
t
h
i
s
al
go
ri
t
h
m
i
s
very
hi
gh
an
d
re
qui
re
s i
t
t
o
a
v
oi
d l
o
cal
o
p
t
i
m
a
. M
o
re
o
v
er,
t
h
e
bal
a
nce
o
f
e
x
p
l
orat
i
o
n a
n
d
e
xpl
oi
t
a
t
i
on i
s
very
si
m
p
l
e
an
d e
ffect
i
v
e
i
n
sol
v
i
n
g
chal
l
e
ngi
ng
p
r
obl
em
s as
pe
r
th
e resu
lts
o
f
t
h
e
real prob
lem
s
in
[2
2
]
.
4.
Prop
osed
Al
g
o
ri
thm
Th
e go
al of the p
r
o
p
o
s
ed
algo
rith
m
is to
seg
m
ent the given MRI brain
im
age into three regions
i
n
cl
udi
ng
Whi
t
e M
a
t
t
e
r (W
M
)
, G
r
ay
M
a
t
t
e
r (GM
)
a
n
d C
e
r
e
br
os
pi
nal
Fl
ui
d (C
SF
). I
n
t
h
i
s
al
gori
t
hm
, fi
rst
t
h
e
ori
g
i
n
al
i
m
age as s
h
o
w
n i
n
F
i
gu
re
3 i
s
pr
o
v
i
ded t
o
t
h
e algorithm
then t
h
e num
b
er
of s
earch age
n
ts a
n
d the
max
i
m
u
m
n
u
m
b
e
r of iterations are i
n
itialized
.
Fi
gu
re
3.
The
ori
g
i
n
al
M
R
I i
m
age
The fl
o
w
c
h
art
of p
r
op
ose
d
al
go
ri
t
h
m
i
s
depi
ct
ed i
n
Fi
gu
re
5. I
n
t
h
i
s
m
e
t
hod
, i
n
o
r
de
r t
o
spee
d u
p
t
h
e
o
p
tim
izat
io
n
,
t
h
e search ag
en
ts are in
itialized
b
y
approx
im
a
tin
g
th
e
in
itial seed
po
in
ts
wh
ich
can
b
e
cal
cul
a
t
e
d by
ou
r p
r
o
p
o
sed
hi
st
o
g
ram
based m
e
t
hod
. T
h
e hi
st
o
g
ram
of t
h
e o
r
i
g
i
n
al
im
age i
s
shown i
n
Fi
gu
re 4.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE Vo
l. 5
,
N
o
. 5
,
O
c
tob
e
r
20
15
:
103
5
–
10
44
1
040
Fi
gu
re
4.
Hi
st
o
g
ram
of t
h
e
ori
g
inal im
age and its
peaks
The
horizontal axis shows the intensity of t
h
e im
ag
e and t
h
e ve
rtical axis
shows t
h
e tota
l num
ber of
pi
xel
s
h
a
vi
ng t
h
e i
n
t
e
n
s
i
t
y
pr
esent
e
d i
n
t
h
e
ho
ri
zo
nt
al
vect
or i
n
Fi
g
u
re
4.
Fi
nal
l
y
as sho
w
n
by
pi
nk a
r
r
o
ws i
n
Figure 4, the
peaks of the
his
t
ogram
are located and the intensity of the
p
eaks ca
n be c
o
nside
r
ed as
potential
seed point values and the com
b
ination
of these values is used as the in
itia
l value for each searc
h
age
n
t.Now,
th
e fitn
ess fu
nctio
n
th
at is g
o
i
ng
to
b
e
u
s
ed
b
y
GWO is ach
iev
e
d
b
y
calcu
latin
g
th
e Eu
clid
ean
d
i
stan
ce
betwee
n ce
ntroid
poi
nts and all pixels for
each re
gion.
T
h
e res
u
lt is a decim
a
l num
ber that is the les
s
er the
b
e
tter.
||
||
(1
6)
In E
quat
i
on
16
,
N
is th
e to
tal
n
u
m
b
e
r of p
i
x
e
ls,
C
i
s
t
h
e num
ber of regi
on
s i
n
t
h
e ori
g
i
n
a
l
im
age,
i
n
is
th
e in
tensity o
f
n
t
h p
i
x
e
l an
d
v
m
is th
e in
ten
s
ity o
f
in
itial poin
t
of th
e
m
th
re
g
i
o
n
.
After calcu
latin
g th
e fitn
ess
fu
n
c
tion
,
th
e positio
n
s
o
f
s
e
ar
ch
ag
en
ts
a
r
e
u
p
d
a
te
d b
y
GW
O a
l
go
r
ith
m.
The
pr
ocess
of
up
dat
i
n
g sear
ch age
n
t
p
o
si
t
i
ons a
n
d fi
t
n
e
s
s
fu
nct
i
o
n cal
cu
l
a
t
i
on are re
pe
at
ed i
t
e
rat
i
v
el
y
unt
i
l
t
h
e m
a
xim
u
m
num
ber
of
i
t
e
r
a
t
i
ons i
s
reac
h
e
d
or
t
h
ere
i
s
no
significant
im
provem
en
t that can be cal
culated
base
d on
t
h
e fo
l
l
o
wi
n
g
e
quat
i
on:
|
|
(1
7)
Whe
r
e,
is th
e fitn
ess
o
f
t
h
e
b
e
st ach
iev
e
d so
l
u
tio
n i
n
t
th
iteratio
n and
less th
an 0.01
.
Finally, th
e
o
p
tim
ized
in
it
ial p
o
i
n
t
s are ach
iev
e
d
and th
ey are
u
s
ed
d
i
rectly in
SFCM alg
o
rith
m
to
p
e
rfo
r
m th
e
segm
ent
a
t
i
on p
r
oce
d
ure.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
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New Meth
o
d
t
o
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timize In
itia
l Po
in
t Va
lu
es o
f
Sp
a
tia
l Fuzzy c-mea
n
s
Al
g
o
r
it
h
m
(Hab
ib
H
a
ron
)
1
041
Fig
u
r
e
5
.
Th
e flo
w
ch
ar
t
o
f
th
e pr
opo
sed algor
ith
m
5.
R
E
SU
LTS AN
D ANA
LY
SIS
In
In
o
r
de
r to
verify
t
h
e p
r
o
pos
ed al
go
rith
m
,
thir
ty searc
h
age
n
ts a
r
e ut
ili
zed to find t
h
e optim
u
m
resu
lt with
m
a
x
i
m
u
m
o
f
fifteen
iteratio
n
s
.
Th
e inp
u
t
to
t
h
e algorithm
is a brain MRI im
age as shown i
n
Figure
2 a
n
d the
out
put is t
h
ree i
n
tensity
values
wher
e
each
of t
h
em
represe
n
ts one
regi
on of t
h
e
brai
n.
Fin
a
lly in
o
r
d
e
r to ev
al
u
a
te the propo
sed m
e
t
h
od
, three
d
a
t
a
set
s
fr
om
ISB
R
[2
6]
have
be
en use
d
. T1
we
i
ght
ed
im
ages are selected for t
h
e evaluation
purpose beca
us
e th
ey h
a
v
e
b
e
tter
wh
ite m
a
tter /
g
r
ay m
a
tter (WM/GM
)
in
ten
s
ities [2
7
]
.
Aft
e
r
pe
rf
orm
i
ng t
h
e p
r
op
ose
d
m
e
t
hod o
n
t
h
e o
r
i
g
i
n
al
im
age i
n
Fi
gu
re
2, t
h
e
f
o
l
l
o
wi
n
g
o
p
t
i
m
u
m
in
itial p
o
i
n
t
s
(V
1
, V
2
an
d V
3
)
we
re obtaine
d whe
r
e
eac
h represents
one region of
the
brain:
v
1
=0
.4
922
7,
v
2
=0
.2
470
8,
v
3
=0
.6
635
Tho
s
e
o
p
tim
u
m
in
itial v
a
lu
es are t
h
en u
s
ed
in th
e stan
dard
SFCM algorith
m
an
d
th
e
seg
m
en
tatio
n
r
e
su
lts ar
e show
n in
Figu
r
e
6. Th
e seg
m
en
ted
r
e
g
i
o
n
is sh
own as
wh
ite colo
r i
n
th
e seg
m
en
tatio
n
resu
lts.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
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08
I
J
ECE Vo
l. 5
,
N
o
. 5
,
O
c
tob
e
r
20
15
:
103
5
–
10
44
1
042
Fi
gu
re 6.
Se
gm
ent
a
t
i
on res
u
l
t
of
t
h
e pr
o
p
o
s
e
d
S
F
C
M
-G
WO
al
go
ri
t
h
m
The c
o
n
v
e
r
ge
n
ce cur
v
e
of
t
h
e
pr
o
pos
ed m
e
tho
d
i
s
s
h
ow
n i
n
Fi
gu
re
7.
Ac
cor
d
i
n
g t
o
t
h
e
di
ag
ram
,
i
t
can
be ob
serv
ed
th
at th
e error rate wh
ich
is
calcu
late
d by
t
h
e fi
t
n
e
ss f
u
nc
t
i
on h
a
s reac
he
d i
t
s
m
i
nim
u
m
val
u
e
after fifteen
iterations
.
Fi
gu
re
7.
The
c
o
n
v
e
r
ge
nce c
u
r
v
e
of
t
h
e
pr
o
p
o
s
ed m
e
t
hod
In order t
o
achiev
e th
e qu
an
titativ
e an
alysis
o
f
th
e propo
sed
m
e
th
o
d
, th
e
ex
p
e
rim
e
n
t
was p
e
rfo
r
m
e
d
on
t
h
ree M
R
I
brai
n
dat
a
set
s
and
m
a
nual
se
gm
ent
a
t
i
on f
o
r
al
l
of
t
h
e
dat
a
set
s
are
p
r
o
v
i
d
ed
by
m
e
di
cal
expe
rt
s.
The res
u
l
t
s
t
h
at
are obt
ai
ne
d fr
om
t
h
e pr
op
ose
d
m
e
t
hod i
s
com
p
ared wi
t
h
m
a
nual
one
s based
on si
m
i
l
a
ri
ty
in
d
e
x
(SI), true p
o
s
itiv
e (TP), false po
sitive (FP) and
false n
e
g
a
tiv
e
(FN). Th
e resu
lt
s th
at are ach
iev
e
d
i
n
Tabl
e
1 i
n
di
cat
e t
h
at
t
h
e si
m
i
lari
t
y
bet
w
ee
n t
h
e
pr
op
os
e
d
m
e
thod a
n
d m
a
nual segm
entation are
ve
ry close and
al
so i
t
ca
n
be
obs
er
ved
t
h
at
SI a
n
d T
P
a
r
e
abo
v
e
0
.
7
an
d
0.
8
res
p
ect
i
v
el
y
whi
c
h s
h
ow
hi
g
h
si
m
i
l
a
ri
ty o
n
t
h
e
ot
he
r
han
d
FP
an
d
FN
are
b
e
l
o
w
0
.
1
9
w
h
i
c
h m
eans a
fe
w
num
ber
o
f
pi
xel
s
a
r
e
n
o
t
m
a
t
c
h wi
t
h
m
a
nua
l
segm
ent
a
t
i
on.
14
16
18
20
22
24
26
28
30
123456789
1
0
1
1
1
2
1
3
1
4
1
5
E
r
ro
r R
a
t
e
Number
of Iteration
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
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:
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0
8
New Meth
o
d
t
o
Op
timize In
itia
l Po
in
t Va
lu
es o
f
Sp
a
tia
l Fuzzy c-mea
n
s
Al
g
o
r
it
h
m
(Hab
ib
H
a
ron
)
1
043
Table 1. Num
e
rical
analysis
of the
propose
d
m
e
thod
with
a
u
tom
a
tic point
initialization
Brain
Tissue
SI
TP
FP
FN
Dataset 1
W
M
0.
8571
0.
9492
0.
1074
0.
0505
GM 0.
7611
0.
8202
0.
0776
0.
1794
Dataset 2
W
M
0.
8431
0.
9079
0.
0769
0.
0917
GM 0.
7394
0.
8327
0.
1262
0.
1670
Dataset 3
W
M
0.
8578
0.
8928
0.
0408
0.
1068
GM 0.
7002
0.
8006
0.
1434
0.
1990
Th
e orig
i
n
al SFCM alg
o
r
ithm with
rand
om in
itia
liza
tio
n
is p
e
rform
e
d
o
n
t
h
e sam
e
d
a
tasets an
d
the
resu
lts are com
p
ared
with
man
u
a
l seg
m
en
tatio
n
(Tab
le 2
)
. I
t
can
b
e
ob
serv
ed
th
at
go
od
r
e
su
lts ar
e ach
iev
e
d
in
d
a
taset
1
howev
er t
h
e algorith
m
fails to
ob
tain
g
ood
SI on
o
t
h
e
r d
a
tasets.
Tab
l
e
2
.
Ori
g
inal SFCM algo
rith
m
with
rando
m
p
o
i
n
t
in
itializatio
n
Brain
Tissue
SI
TP
FP
FN
Dataset 1
W
M
0.
8508
0.
9363
0.
1005
0.
0633
GM 0.
7721
0.
9341
0.
2098
0.
0656
Dataset 2
W
M
0.
5793
0.
9841
0.
6986
0.
0156
GM 0.
4935
0.
6068
0.
2294
0.
3929
Dataset 3
W
M
0.
5718
0.
9942
0.
7387
0.
0055
GM 0.
7538
0.
9785
0.
2981
0.
0212
B
y
com
p
ari
n
g
t
h
e p
r
o
p
o
sed
m
e
t
hod a
n
d
S
F
C
M
, i
t
i
s
concl
u
ded t
h
at
t
h
e achi
e
ve
d re
sul
t
s
by
t
h
e
pr
o
pose
d
m
e
t
hod
ha
ve
hi
g
h
er
sim
i
l
a
ri
ty
i
ndex v
a
l
u
es
wi
t
h
l
e
ss err
o
r
s
.
In
t
a
bl
e 3, a
co
m
p
ari
s
on
bet
w
een t
h
e
pr
o
pose
d
m
e
t
hod
an
d
SFC
M
i
s
per
f
o
rm
ed b
a
sed
o
n
t
h
e
av
erage
n
u
m
b
er
of i
t
e
rat
i
o
ns
an
d a
v
era
g
e
n
u
m
b
er
o
f
runn
ing
th
e algo
rith
m
.
Tabl
e
3.
A c
o
m
p
ari
s
on
bet
w
een S
F
C
M
an
d
G
W
O
-
SFC
M
Average Algorith
m
Execution Nu
mber
Average nu
m
b
er o
f
iterations
SFCM 5
27
GW
O-
SFC
M 1
4
Acco
r
d
i
n
g t
o
Tabl
e 4
.
3
,
t
h
e
pr
o
pose
d
m
e
t
hods
can ac
hi
ev
e t
h
e res
u
l
t
i
n
t
h
e fi
r
s
t
at
t
e
m
p
t
s
an
d wi
t
h
4
iteratio
n
s
ho
wev
e
r SFCM al
g
o
rith
m
n
eed
s to
b
e
ex
ecu
t
ed
fiv
e
tim
es i
n
av
erag
e
and it will p
e
rfo
r
m
th
e
seg
m
en
tatio
n
after twen
ty seven
iteration
s
.
Also
t
h
e
p
r
op
osed
m
e
th
o
d
does no
t r
e
qu
ir
e
an
y adju
stm
e
n
t
s pr
ior
th
e seg
m
en
tati
o
n
pro
cess.
6.
CO
NCL
USI
O
N
In
t
h
is
p
a
p
e
r,
an
en
h
a
n
c
ed
SFCM alg
o
rithm
was p
r
esen
t
e
d
.
In
o
r
d
e
r to i
m
p
r
ov
e t
h
e i
n
itializatio
n
st
ep of SFC
M
,
we have use
d
G
W
O al
g
o
r
i
t
h
m
t
o
fi
nd t
h
e
opt
i
m
u
m
i
n
i
t
i
al
poi
nt
val
u
es
. Three dat
a
set
s
from
ISBR were used
to
ev
alu
a
te th
e p
r
op
osed
al
g
o
rith
m
an
d
it
was ob
serv
ed
th
at g
ood
resu
lts were ach
iev
e
d
as
com
p
ared wit
h
standard SFCM algor
ith
m. Mo
reo
v
er we h
a
v
e
seen
th
at th
e seg
m
en
tatio
n
resu
lts were
obt
ai
ne
d i
n
sm
al
l
e
r n
u
m
b
er o
f
i
t
e
rat
i
o
ns
wh
en
usi
n
g t
h
e
pr
op
ose
d
al
go
ri
t
h
m
.
REFERE
NC
ES
[1]
Tran,
T
.
T
., V
.
T
.
P
h
am
, and
K
.
K
.
S
h
yu,
Imag
e s
e
gmentation using fuzzy en
ergy
-
based active co
ntour with shap
e
prior.
Journal of
Visual Communication
and Im
age Repr
esentatio
n, 2014
. 25(7): 1
732-1745.
[2]
Zhang, X
., e
t
a
l
.
,
Hybrid region
merging method
for segmentatio
n
of high-resolution remote sensin
g images.
ISPRS
Journal of Photo
g
rammetr
y
and
Remo
te Sensing, 2014. 98(0): 19
-
28.
[3]
Pa
t
i
no-Correa
,
L
.
J.,
et
al
.,
Whi
t
e
matt
er hyper-i
n
tensiti
es autom
atic
iden
tifi
cat
i
o
n
and segmenta
tion in
magneti
c
resonance images.
Exper
t
S
y
stem
s with Appl
ications, 2014. 41(16
): 7114-7123.
[4]
Aja-F
e
rnánde
z,
S
., A.H.
Curia
l
e,
and G. Vegas-Sánchez-Ferr
ero,
A loca
l fuzz
y thresholding
methodology for
multiregion
ima
g
e segmenta
tion
.
Knowledge-Bas
ed
S
y
ste
m
s,
(0).
[5]
L
i
, B.
N.,
et
a
l
.,
Integrating s
patial
fuzzy clu
s
tering with
le
vel set methods for automated
medica
l ima
g
e
segmentation
.
C
o
mputers in Bio
l
og
y
and Medicin
e
, 2011
. 41(
1): 1
-
10.
[6]
U
g
arriza
, L
.
G
.,
et al
.,
Automati
c Image Segment
a
tion by Dynam
ic
Reg
i
on Growth and Multires
olution Merging
.
Ieee Tr
ansaction
s
on Image Pr
ocessing, 2009
. 18
(10): 2275-2288
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE Vo
l. 5
,
N
o
. 5
,
O
c
tob
e
r
20
15
:
103
5
–
10
44
1
044
[7]
S
a
m
a
dzadegan
,
F
.
and A.A
.
Nae
i
ni.
Fuzzy clustering of hyp
e
rspectral data
based
on partic
le swa
r
m optimization
.
in
Hyperspec
tral Image and Sign
al Processing:
E
v
olutio
n
in
Rem
o
te Sensing
(
W
HISPERS)
,
2011 3
r
d Workshop on
.
2011. IEEE.
[8]
Maxwell, J.C. an
d J.J.
Thompson,
A
treatise on
electricity and mag
n
etism
. Vol. 1
.
1
892: Clarendon
.
[9]
Hartigan
, J.A
.
,
C
l
ustering a
l
gorithms.
1975.
[10]
M
acQueen
, J
.
So
me methods for classifica
tion an
d
analysis of mu
ltivaria
te observations
. in
Proceedings of th
e fifth
Berkeley symposium on mathema
tical
stat
istics an
d probabilit
y
. 19
67. Oakland, CA
, USA.
[11]
Dunn, J.C.,
A fuzzy relative of
the ISODATA p
r
ocess and its us
e in detecting
compact
well-separated clusters.
1973.
[12]
Bezdek
, J
.
,
Pattern recognition w
ith fuzzy
objective fun
c
tion
algorithm.
New York:
Plenum Press, 1981.
[13]
Cai, W.L., S.C.
Chen, and
D.Q.
Zhang,
Fast and
robust fuzzy c-
means cluste
rin
g
algorithms incorporating local
information for
image segmentation.
Pattern
Reco
gnition, 2007
. 4
0
(3): 825-838
.
[14]
Chuang, K.S.,
et al.,
Fuzzy c-m
e
ans clustering
with spatia
l
inf
o
rmation for image segmenta
tio
n.
Computerized
Medical Imagin
g and Gr
aphics,
2006. 30(1): 9-1
5
.
[15]
Benaichouche,
A., H. Oulh
adj,
and P. Siar
r
y
,
I
m
proved spatial fuzzy c-means
cl
ustering
for image segmentation
using PSO initia
lization, Mahala
nobis di
stance a
nd post-segment
a
tion correction.
Digital Signal P
r
ocessing, 2013
.
23(5): 1390-140
0.
[16]
Zhang,
Y
., et al
.,
Image segm
entation using
PSO and PCM with Mahalanob
is distance.
Expe
rt S
y
ste
m
s with
Applications, 20
11. 38(7): 9036-
9040.
[17]
Krishnapuram, R. and J.M. Keller,
A possibilist
i
c approach to clustering.
F
u
zz
y S
y
st
em
s, IEEE Transac
tions on
,
1993. 1(2): 98-1
10.
[18]
Wa
ng,
H.
,
e
t
al
.
Scalability of h
y
brid fuzzy c-means
algorithm based on quantu
m
-behaved PSO
. i
n
Fuzzy
sy
ste
m
s
and knowledge d
i
scovery, 2007
.
fskd 2007.
fourth internationa
l co
nference
on
. 200
7. IEEE.
[19]
L
i
u, H.
, et
al
.
Multi-t
e
mporal
MODIS-data-based PSO-FCM
clustering
appli
e
d to
wet
l
and
extraction
in th
e
Sanjiang Pla
i
n
. i
n
Internation
a
l Conference
on Earth Ob
servation Data Processing and Analysis
. 2008
.
Interna
tiona
l So
cie
t
y fo
r
Optics
and Photonics.
[20]
Liu, B., et al.,
Improved particle swarm optimi
z
ation combined
with chaos.
Chaos, Solitons & Fractals, 2005
.
25(5): 1261-127
1.
[21]
Noe
l
,
M.
M. a
nd
T.
C. Ja
nne
tt.
S
i
mulation of a
new hybrid parti
cle swarm optimization algorithm
. in
Sys
t
em T
h
eor
y
,
2004. Proceed
in
gs of th
e Thirty-
S
ixth
Southeastern Symposium on
. 2004
. IEEE.
[22]
Mirja
l
ili,
S.
,
S
.
M.
Mi
rjal
ili
, and
A. Lewis
,
Grey
wolf opt
imizer.
Advances in
En
gineer
ing Software, 2014. 69
: 4
6
-
61.
[23]
Coleman, G.B
.
and H.C. Andrews,
Image segmentation by
cluster
i
ng.
Proceedings
of the IEEE, 19
79. 67(5): 773-
785.
[24]
Li,
B
.
N
., et al
.,
Integrating
FC
M and Level S
e
t
s
for Liver Tumor Segmentation
.
13th Internatio
nal Confer
ence
on
Biomedical Eng
i
neering
,
Vols 1-
3, 2009
. 23(1-3)
: 202-205.
[25]
Mi
rj
a
l
il
i,
S.
,
How eff
e
c
tiv
e is
th
e Grey Wo
lf op
t
i
mize
r in train
i
n
g
multi-la
yer p
e
rceptrons.
Applied Intelligence,
2015: 1-12.
[26]
The datsets are
provided
from IS
BR w
e
bsite
.
Available from: http://www.
cm
a.
mgh.
harvard.
edu/ibsr/.
[27]
Schultz, R
.
T. an
d A. Ch
akraborty
,
Magnetic reso
nance
image an
alysis
, in
N
e
uroimaging I
. 1996,
Springer. 9-
51.
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