TELKOM
NIKA
, Vol.13, No
.1, March 2
0
1
5
, pp. 128~1
3
6
ISSN: 1693-6
930,
accredited
A
by DIKTI, De
cree No: 58/DIK
T
I/Kep/2013
DOI
:
10.12928/TELKOMNIKA.v13i1.1269
128
Re
cei
v
ed O
c
t
ober 7, 20
14;
Revi
se
d De
cem
ber 24, 20
14; Accepted
Jan
uary 10, 2
015
Fuzzy Clustering Image Segmentation Based on
Particle Swarm Optimization
Zhansh
e
n F
e
ng*, Bopin
g
Zhang
Dep
a
rtment of Information En
gin
eeri
ng,
Xu
Cha
ng Un
ivers
i
t
y
, Xu C
h
a
ng
461
00
0, Hena
n, Chin
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: fzs7879@
16
3.com
A
b
st
r
a
ct
Imag
e se
g
m
en
tation refers to
the techn
o
l
o
g
y
to
seg
m
e
n
t the i
m
age
into
different re
gio
n
s w
i
t
h
different c
har
a
c
teristics a
nd t
o
extract
usef
ul
obj
ecti
ves,
and
it is
a
key
step fro
m
i
m
age
proc
essi
n
g
to
imag
e an
alysi
s. Based o
n
the co
mpr
ehe
nsive stu
d
y of
imag
e seg
m
entatio
n tech
n
o
lo
gy, this pa
pe
r
ana
ly
z
e
s the
adva
n
tag
e
s an
d disa
dva
n
tag
e
s of the exis
t
i
ng fu
zz
y
cl
usterin
g
al
gorith
m
s; integrates t
h
e
particl
e sw
arm opti
m
i
z
at
io
n (
PSO) w
i
th the character
i
stics
of gl
oba
l o
p
ti
mi
z
a
t
i
o
n
a
nd r
api
d co
nverg
e
n
ce
and fu
zz
y
c
l
us
tering (F
C)
alg
o
rith
m w
i
th fu
zz
y
cl
usteri
ng e
ffects starting from th
e p
e
rsp
e
ctive of p
a
rtic
l
e
sw
arm and fu
zz
y
me
mb
ersh
ip restrictions
and g
e
ts a
PSO-F
C imag
e seg
m
e
n
tatio
n
al
gorith
m
so as
to
effectively av
oi
d bei
ng tra
ppe
d into the
loca
l
opti
m
u
m
a
nd i
m
pr
ove the sta
b
ility a
nd re
lia
b
ility of clusteri
n
g
alg
o
rith
m. T
he experi
m
enta
l
results sho
w
that
this new
PSO-F
C
alg
o
rith
m has
excelle
nt ima
g
e
se
gm
en
ta
ti
on
effects.
Ke
y
w
ords
: image se
g
m
e
n
tation, fu
zz
y c
l
ust
e
rin
g
, particle s
w
arm opti
m
i
z
a
t
ion
1. Introduc
tion
Image segm
entation is
n
o
t only one
of t
he study
hotsp
ots of i
m
age p
r
o
c
e
s
sing
and
comp
uter vi
si
on, but it is
also th
e si
gn
ificant
foun
da
tion of imag
e
re
cognitio
n
.The p
u
rp
ose
of
image
segme
n
tation i
s
to
segment
the
o
b
jective
re
gio
n
pe
ople
ne
e
d
from
the
ba
ckgro
und
[1].
As
a commo
n
d
a
ta an
alysi
s
tool,
clu
s
tering a
nalysi
s
is the
process to
divid
e
data
sets
into
enormou
s
cl
usters con
s
tituted by similar dat
a.Cl
ustering an
alysis has b
een
widely use
d
in
image
se
gm
entation, d
a
ta minin
g
, p
a
ttern
cla
ssif
i
cation, m
edi
cal
diag
no
sis a
nd
mach
ine
learni
ng [2
]. Among numerou
s image
segm
entation
algorithm
s, the image
segm
entation
a
lgorith
m
ba
sed on
cl
uste
ri
ng an
alys
i
s
i
s
an extremely
impo
rtant an
d wid
e
ly u
s
e
d
algorith
m
in image segme
n
tation. The tradition
al cl
u
s
terin
g
algo
rithm is a kind
of determini
st
ic
clu
s
terin
g
alg
o
rithm. One o
f
the many sa
mples b
e
lon
g
s
to a ce
rtain
cla
ss to a certain extent and
it can
al
so
be
long to
an
oth
e
r
cla
s
s o
r
ot
her
cla
s
se
s a
t
the same
time du
e to
th
e un
ce
rtainty
and
f
u
zzi
ne
ss
of
it
s cla
s
s,
t
her
efore, it is
difficult to divid
e
it into the
only cla
s
s ex
actly. The m
o
st
gene
rally-u
se
d alg
o
rithm i
s
fu
zzy
clu
s
t
e
ring
alg
o
rith
m and
it ha
s excell
ent
co
nverge
nce a
s
an
unsupe
rvise
d
cluste
ring al
gorithm [3].
Fuzzy set is
suitabl
e to proce
s
s the rel
e
vant
pro
b
le
ms to un
ce
rta
i
nty and fuzzi
ness an
d
it has be
en
extensively
appli
ed. F
u
zzy
clu
s
te
rin
g
come
s i
n
to bei
ng
by
integratin
g f
u
zzy
clu
s
t
e
rin
g
a
n
d
t
he
con
c
e
p
t
of
f
u
zzi
ne
ss
.
Fuz
z
y
clu
s
t
e
ring
ma
ke
s
it
pos
sible
f
o
r t
he
clu
s
t
e
ri
ng
sampl
e
s tobe
long to m
u
ltip
le cla
s
se
s a
n
d
it uses
me
mbershi
p
to refer to th
e si
ze of th
e d
e
g
r
ee
of memb
ershi
p
. As
a
widel
y use
d
m
e
tho
d
, FC alg
o
rith
m ha
s
bee
n
succe
ssfully
a
pplied
in i
m
a
ge
analysi
s
, me
dical
diag
no
sis, ta
rget i
dentif
icatio
n
and im
age
segm
entation
.
FC al
gorit
hm
perfo
rms fu
zzy clusteri
ng o
n
the con
s
ist
ent pixels in the image through mem
b
e
r
shi
p
matrix and
segm
ents th
e image thro
ughthe iterat
ive optimizati
on of the obj
ective functio
n
. However,
FC
algorith
m
also has ma
ny shortcomin
gs [
4
]. For inst
an
ce, it is greatl
y
affected by noise. It is ve
ry
sen
s
itive to
th
e initial
value
and it
de
pend
s g
r
e
a
tly on
the
sele
ction
of the i
n
itial
cl
usteri
ng
cent
er.
When the initial clustering cent
e
r
seve
re
ly deviates from the gl
oba
l optimal clustering center,
it
may cau
s
e th
e alg
o
rithm
trappe
d in
lo
ca
l optimum,
especi
a
lly in th
e
ca
se
of
num
erou
s clu
s
te
ri
ng
sampl
e
s.
The
r
efore, this
ki
nd of p
r
o
b
le
ms
can
be
so
lved by imp
r
o
v
ing the m
e
m
bership
fun
c
tion
in FC algo
rith
m and intro
d
u
c
ing PSO wit
h
stron
g
glob
al optimizatio
n ability [5].
Comp
ared
wi
th FC
algo
rith
m, PSO ca
n
see
k
th
e glo
b
a
l optimal
sol
u
tion at
a sho
r
t time;
it allows sele
cting initial v
a
lue
rand
oml
y
and it
can obtain
the op
timal
solu
tio
n
;
therefore, it can
greatly red
u
c
e the pre
-
p
hase wo
rk [6]. By us
ing
such
cha
r
a
c
teri
stics as ergodi
city and
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Fuzzy Clu
s
tering Im
age Segm
entation Base
d on Parti
c
le Swa
r
m
Optim
i
zation (Z
han
she
n
Fen
g
)
129
rand
omn
e
ss
of PSO and i
n
tegratin
g th
e optimizatio
n
ch
ara
c
te
rist
ic of pa
rticle
swarm, thi
s
p
aper
prop
oses
a PSO-F
C algo
ri
thm, namely the fuzzy clu
s
terin
g
alg
o
rit
h
mba
s
ed
on
particl
e swa
r
m
optimization
with global
optimization ability by
integrating PSO algorithm and F
C
al
gori
t
hm.
PSO-FC
ca
n
not only search the
optim
al sol
u
tion wi
thin the glo
b
a
l ran
ge, but
it can al
so
exert
the a
c
cura
cy
of the l
o
cal
optimization
ability
of F
C
al
gorith
m
and
obtain
the gl
obal
op
timal
solutio
n
. Thi
s
pape
r firstly introd
uces the ap
plic
atio
n analy
s
is of
image
segm
entation. Th
e
n
it
discu
s
ses th
e fundam
ent
al theori
e
s of
fuzzy cl
us
te
ring a
nd pa
rt
icle swa
r
m al
gorithm. Next, it
prop
oses the
image se
g
m
entation al
gorithm b
a
se
d on parti
cle
swa
r
m and
fuzzy clu
s
te
ring.
Finally, it is the experim
ent
al analysi
s
.
2. Image Segmenta
tion
So far, it is v
e
ry difficult t
o
find an
effective comm
on imag
e
se
gmentation
method to
make va
riou
s imag
es
re
ach the
opti
m
al se
gment
ation quality. Many imag
e seg
m
entati
on
algorith
m
s a
r
e meant for
certain type of
image o
r
ce
rtain spe
c
ific
segm
entation
.
From the type
of image, image se
gme
n
tation inclu
d
e
s
gray imag
e
segme
n
tatio
n
, color ima
g
e segm
entati
o
n
and texture i
m
age
segm
e
n
tation. Acco
rding to t
he
d
e
finition of image segm
ent
ation, the image
segm
entation
algo
rithm
s
a
r
e
divided
int
o
two
type
s:
one i
s
ba
sed
on
re
gion
a
nd it
use
s
th
e
regio
nal
simil
a
rity, namely
assumi
ng th
at the n
e
igh
borh
ood
pixe
ls in
the
sa
me regio
n
h
a
ve
simila
r ch
ara
c
teri
stics such as g
r
ay, col
o
r or te
xture
while the oth
e
r is b
a
sed o
n
boun
dary a
nd it
use
s
the di
scontinuity between re
gion
s [7].
In the image
study and appli
c
ation, peopl
e
name
the part they are interested in
obje
c
tive or f
o
reg
r
o
und a
n
d
the re
stba
ckgroun
d.
Image se
gme
n
ta
tion is to exp
r
ess the im
a
g
e
into
the sets meeting unifo
rmity,
conn
ectivity
and con
s
iste
ncy, na
mely to mark and
positio
n
the
obje
c
tive and
backg
ro
und i
n
the ima
ge
and the
n
se
g
m
ent the
obj
ective fro
m
th
e ba
ckgroun
d
or
other p
s
eu
do
-obje
c
tives a
c
cordi
ng to the prio
r kn
o
w
led
ge of objective and
backg
rou
nd.T
he
regio
nal u
n
ifo
r
mity refers t
o
ce
rtain
sim
ilarity
crite
r
io
n ba
sed
on
gray, texture,
colo
r an
d ot
her
cha
r
a
c
teri
stics that all
pix
e
ls in
this re
gion m
eet. Conne
ctivity mean
s that thi
s
regio
n
h
a
s the
path to lin
k
a
n
y two p
o
ints.
And
con
s
i
s
te
ncy i
s
t
he to
p
o
logy a
c
cura
cy of the
se
g
m
entation
sh
ape
in medi
cal im
age segm
ent
ation. In othe
r wo
rd
s, it
needs to
con
s
id
ernot o
n
ly the local
pro
p
e
r
ty,
but also the
con
n
e
c
tivity
of the global geomet
rical shape. Peopl
e
have come
up with different
descri
p
tion
s on image
se
gmentation a
nd they hav
e given image
segme
n
tatio
n
the followi
ng
definition wit
h
the con
c
e
p
t
of set:use
set Rto refer to the entire
image re
gio
n
; divide R i
n
to
Cno
n
-e
mpty sub
-
regio
n
s (sub
-sets), na
mely
12
,,
C
RR
R
and me
et the followin
g
five conditio
n
s:
(1)
1
C
i
i
RR
.
(2)If
1,
2
,
,
,
i
iC
R
are co
nn
ected regio
n
s.
(3) T
o
all
i
and
j
,
ij
，
ij
RR
.
(4)If
1,
2
,
,
iC
, then
()
i
PR
T
r
u
e
.
(5) If
ij
, then
()
ij
P
RR
F
a
l
s
e
.
Among the
s
e con
d
ition
s
,
()
i
PR
is the logic predicate to the eleme
n
ts in set
i
R
.Conditio
n
(1
)
requi
re
s that the unio
n
set
of all su
b
-re
gi
on in the seg
m
entation result shall in
clu
de
all the pixels of the original
image; Cond
ition(2
)
req
u
ires that the pixels
of the sa
me sub
-
regio
n
in the
se
gme
n
tation result are
conn
ect
ed; Conditi
o
n
(
3) re
qui
re
s t
hat any
pixel
of the
ori
g
in
al
image
can’t
belon
g to two differe
nt sub-regi
on
s;
Con
d
ition(4)
requi
re
s that
the pixels
whi
c
h
belon
g to the
same
regi
on
have ce
rtain
same
cha
r
a
c
teristics a
nd
Con
d
ition(5)
requires th
at the
different su
b-regio
n
s in the
segme
n
tatio
n
result have different ch
aracteri
stics [8].
In one
wo
rd
, image
se
g
m
entation i
s
to segme
n
t the regio
n
s with
ce
rtain
simila
r
prop
ertie
s
int
o
the sam
e
regio
n
and
segment th
o
s
e with different pro
pertie
s
into differe
nt
regio
n
s. An e
ffective segm
entation sh
all
preserve
the
important ch
ara
c
teri
stics
of the image in a
possibly
sho
r
t time and
g
e
t the con
s
istent outline
or compl
e
te area
of
the obje
c
tive
in
t
he
image [9].
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 13, No. 1, March 2
015 : 128 – 1
3
6
130
3. Fundame
ntal Theorie
s of Fuzz
y
Clusteri
n
g
and
Particle S
w
arm Optimization
3.1. Fundam
e
ntal Princip
l
e of Fuzz
y
C
l
ustering (F
C)
FC algo
rithm
is a metho
d
to automatically cla
ssify
the sample
s. It determines the
membe
r
ship
of every sam
p
le to the cla
ss
cente
r
by minimizi
ng th
e obje
c
tive function
so a
s
to
determi
ne th
e cla
ss of the
sample. FC
divides the set
Z
in a fuzzy manne
r and
determi
ne
s the
degree eve
r
y
data poi
nt b
e
long
s to eve
r
y cla
s
s with t
he mem
b
e
r
ship value
bet
wee
n
0 a
nd
1
.
In
line with the i
n
trodu
ction
of fuzzy divisio
n
, membe
r
shi
p
matrix allo
ws the
circu
m
stan
ce
s wit
h
the
value of
0 an
d 1; h
o
wever, one m
e
mb
e
r
shi
p
u
n
ific
ati
on rest
rictio
n
sh
all b
e
ad
d
ed, that i
s
, th
e
sum of the m
e
mbe
r
ship
s that one data
point bel
o
n
g
s
to different cl
asse
s sh
all b
e
1.
1
1,
1,
,
c
ij
i
uj
n
(1)
Then, the obj
ective functio
n
of FC is a
s
follows:
2
11
(,
)
cn
m
mi
j
i
j
ij
J
UP
u
d
(2)
In this
formula,
ij
u
can
be
any real
nu
mber
betwee
n
0 an
d 1 a
nd
1,
m
is a
weigth
ed ind
e
x called fu
zziness ind
e
x, fuzzy cont
rol para
m
eter a
n
d
weig
hted p
a
ram
e
ter [10]
.
Con
s
tru
c
t
ne
w o
b
je
ctive fu
nction
throug
h lag
r
an
gian
multiplier an
d
acco
rdi
ng to
Formul
a
(1) a
nd(2) a
n
d
get the necessary
conditi
ons to
ma
ke
Formul
a (2
) g
e
t the minimu
m value [11].
1
1
1
(,
,
,
,
)
(
,
)
(
1
)
c
n
nj
i
j
j
i
JU
P
J
U
P
u
2
11
1
1
(1
)
cn
n
c
m
ij
ij
j
i
j
ij
j
i
ud
u
(3)
In this
formula,
,1
,
,
j
j
n
, is the lagran
gian m
u
l
t
iplier of
n
co
nstrai
nt form
ulas i
n
Formula (1).It c
an be
s
e
en from lagrangian multiplie
r
that the s
o
lutions
of
Formula (1), (2) and
(3)
are
equiv
a
lent. Seek th
e partial
deriv
atives of
all in
put paramete
r
s a
nd ma
ke t
he re
sult 0
an
d
get the ne
ce
ssaryconditio
n
s to ma
ke
Formul
a (2
)
get the mini
mum by inte
grating
co
nst
r
aint
con
d
ition Fo
rmula (1
).
1
1
n
m
ij
j
j
i
n
m
ij
j
ux
c
u
(4)
and
2/
(
1
)
1
1
m
ij
m
c
ij
k
kj
u
d
d
(5)
3.2. Basic F
C
Flo
w
The co
re of FC algo
rithm is the estima
tions of the clustering center
matrix
[]
i
cxd
Pc
and
f
u
zzy
mem
b
e
r
shi
p
mat
r
ix
[]
ij
c
x
n
Uu
.
The e
s
timation of FC pa
rameters can
be dete
r
mine
d by
Formul
a (4
)
and (5) an
d they are mut
ually int
egrat
ed; therefo
r
e,
perform esti
mation solution
throug
h alternative iterative algorith
m
s [
12].
Step 1: Initialize the
pa
ram
e
ters of the
cl
us
teri
ng ce
nter
mat
r
ix.
As for
the given numbe
r
of
clu
s
t
e
ri
ng
cla
s
s
e
s
(2
)
cc
n
,
n
is t
he s
a
mpl
e
si
ze.
A
s
sumi
n
g
that the ite
r
ative sto
ppi
ng
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Fuzzy Clu
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d on Parti
c
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r
m
Optim
i
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han
she
n
Fen
g
)
131
threshold i
s
,
whi
c
h ra
nge
s from 0.001 to 0.01. Set th
e maximum iteration
s
a
s
a
nd initialize th
e
c
l
us
tering c
e
nter matrix
()
t
P
with
0
t
.
Step 2:
Upd
a
t
e the fu
zzy
d
i
vision m
a
trix. Cal
c
ul
ate th
e di
stan
ce
s
()
t
ij
d
from eve
r
y sa
mple
j
x
to the cluste
ring ce
nter
i
c
through the
clu
s
tering cente
r
matrix
()
t
P
, updat
e the fuzzy di
vision
matrix
()
t
U
accord
ing to Formul
a (5) a
nd get
()
2/
(
1
)
()
()
1
1
t
ij
m
t
c
ij
t
k
kj
u
d
d
(6)
Step 3: Upda
te the
cluste
ring
cente
r
m
a
tr
ix, update
the cl
uste
ring
ce
nter
matri
x
(1
)
t
P
according to
Formul
a (4
) a
nd get:
()
1
(1
)
()
1
n
m
t
ij
j
j
t
i
n
m
t
ij
j
ux
c
u
(7)
Step 4: Judg
e the th
re
sh
old. Fo
r the
given thresh
old
, if
(1
)
(
)
tt
PP
, or
the
numbe
r of iteration
s
is la
rge
r
than or
equal to the maximum iterative cou
n
ts
()
tl
, stop the
iteration; othe
rwi
s
e, ma
ke
1
tt
and turn to Step 2.
Whe
n
a
ce
rta
i
n sa
mple
j
x
overlap
s
with
a certai
n clu
s
te
ring ce
nter
i
c
,
0
ij
j
i
dx
c
.
In orde
r to avoide
0
ij
d
; specify that when
0
ij
d
, the membe
r
shi
p
that this sa
mple belo
n
g
s
to
this
cla
s
s is
1
and
the m
e
mbershi
p
it b
e
long
s to
oth
e
r
cla
s
ses is
0. Wh
en th
e i
t
eration
process
stop
s, get th
e fuzzy clu
s
t
e
ring
ce
nter
and t
he e
s
ti
mation value
of the par
a
m
eter
s of fu
zzy
division m
a
tri
x
. The judgm
ent eviden
ce
FC al
gorit
h
m
determi
ne
s th
e clu
s
te
ring
class of
sampl
e
j
x
is
1,
,
arg
m
a
x
ij
ic
ku
(8)
As for the a
bove iterative
algorithm
s, pre
-
initialize the fuzzy division mat
r
ix and then
impleme
n
t the iteration p
r
o
c
e
ss [13],[14]
.
3.3. Fundam
e
ntal Princip
l
e of PSO
The fu
ndam
e
n
tal pri
n
ci
ple
of PSO
com
e
s
by stim
ula
t
ing g
r
oup
fe
eding.
They
perfo
rm
simple b
ehav
iors o
n
acco
unt of the followin
g
three
rule
s: (1) mo
vement towa
rds the n
earest
comp
anio
n
; (2) moveme
nt towards the d
e
stinatio
n;
(3) movement towards the g
r
o
up ce
nter [15]
.
A
ssu
me t
hat
12
(,
,
)
ii
i
i
n
X
xx
x
,
12
(,
,
)
ii
i
n
Vi
v
v
v
,
12
(,
,
)
ii
i
i
n
Pp
p
p
are th
e
c
urre
nt
positio
n, flying spe
ed an
d
global o
p
tima
l position of
particl
e ire
s
p
e
ctively. In order to ma
ke t
h
e
particl
e to fin
d
food at th
e
sho
r
te
st time, it need
s to
find a
soluti
on in the
qu
estion
domai
n to
minimize the
value
of the
obje
c
tive fu
nction,
name
l
y that the o
b
jective fu
nct
i
on
()
F
x
is the
bigge
st an
d
then the
current optim
al po
sition
o
f
the ith pa
rticle
ca
n b
e
dete
r
mine
d by
Formul
a (9
).
()
(
(
1
)
)
(
()
)
(1
)
(
1
)
(
(
1
))
(
(
))
ii
i
i
ii
i
p
ti
f
F
x
t
F
p
t
pt
x
ti
f
F
x
t
F
p
t
(9)
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015 : 128 – 1
3
6
132
Assu
me that
the numb
e
r
of individual
s in the group
is
S
and the o
p
timal po
sitio
n
all
individual
s ca
n find is
()
g
P
t
,as in
dicate
d by Formula (10
)
:
01
0
1
(
)
(
)
,
(
)
,
(
)
(
(
))
mi
n
(
(
)),
(
(
)),
(
(
))
gs
g
s
p
t
pt
p
t
p
t
f
p
t
f
pt
f
p
t
f
p
t
(10)
Acco
rdi
ng to
the definition
of PSO, the s
peed
and p
o
s
ition u
pdate
of every pa
rticle
can
be de
scribe
d by Formula
(11) an
d (1
2):
11
2
2
(
1
)
(
)
(
)
(
()
()
)
(
)
(
()
(
)
)
ij
ij
j
i
j
i
j
j
g
j
ij
vt
vt
c
r
t
p
t
x
t
c
r
t
P
t
xt
(11)
(1
)
(
)
(
1
)
ij
ij
i
j
xt
x
t
vt
(12)
In these form
ulas: the su
b
s
cript "
i
" means pa
rticle
I
, "
j
" refers
to the
jt
h
dimensio
n
of the pa
rticl
e
;
t
is the
n
u
mbe
r
of iterations
wh
ere
the group i
s
lo
cated;
1
c
and
2
c
are
accele
ration
con
s
tant
s, which
are
withi
n
[0,2] and
12
1
cc
and
1
r
and
2
r
are two
ran
d
o
m
numbers
within [0,1].
It can be see
n
by analyzin
g Formul
a (1
1) and (12
)
that
1
c
are
2
c
the param
eters to be
use
d
to adj
u
s
t the po
sitio
n
of the pa
rticle a
nd the
global
optima
l
positio
n re
spectively. In the
mean
while, i
n
ord
e
r to a
v
oid the pa
rticle fro
m
devi
a
ting from th
e se
arch
spa
c
e, it need
s
to
con
s
trai
n
ij
v
and
ij
x
in the group
evolution, na
mely
ma
x
m
a
x
,
ij
vv
v
,
ma
x
m
a
x
,
ij
xx
x
.
The
parti
cle
speed
up
date
in Fo
rmula
(1
1) i
s
divided
i
n
to three
part
s
: the
first
pa
rt is its
curre
n
t spee
d; the
se
con
d
part i
s
it
s o
w
n expe
rien
ce
and th
e third
part i
s
the
so
cial
re
cog
n
ition.
If the particle
update
s
its speed o
n
ly through its o
w
n
experie
nce, as indi
cated in
Formul
a (1
3).
11
(
1
)
(
)
(
)
(
()
()
)
ij
ij
j
i
j
i
j
vt
vt
c
r
t
p
t
x
t
(13)
In this
way, t
he p
e
rfo
r
man
c
e
of PSO
w
ill be ve
ry b
a
d
be
ca
use
without exchan
ge of
grou
p info
rm
ation am
ong
different
pa
rticles,
it
will l
ead to
the i
n
depe
ndent
m
o
vement of
N
particl
es in
a
grou
p a
nd it i
s
e
a
sy to
be
trappe
d into
l
o
cal
optimu
m
. If only so
cia
l
re
cog
n
ition i
s
adde
d, see F
o
rmul
a (14
)
:
22
(
1
)
(
)
(
)
(
()
()
)
ij
ij
j
g
j
i
j
vt
vt
c
r
tP
t
x
t
(14)
Then the mo
vement of the particl
e will
becom
e a social be
havio
r with self-re
c
ognition.
Although it can expan
d th
e se
arch
ran
ge of the pa
rticle an
d imp
r
ove the
con
v
ergen
ce
sp
e
ed,
the algorithm will be easy to be trapped i
n
to local optimum [16],[17].
The follo
win
g
is th
e fun
d
a
m
ental p
r
in
ci
ple of
pa
rticle
moveme
nt in
PSO, a
s
in
dicated
in
Figure 1.
Figure 1. Particle movem
e
nt sch
ematic
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Fuzzy Clu
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tering Im
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d on Parti
c
le Swa
r
m
Optim
i
zation (Z
han
she
n
Fen
g
)
133
The gen
eral pro
c
e
ss of P
S
O is indicated in Figu
re 2
[18].
Figure 2. Basic flowcha
r
t of PSO
4. Image Segmenta
tion Al
gorithm Ba
s
e
d on Particl
e
S
w
a
r
m an
d Fuzz
y
Clus
tering
4.1. Theore
t
ical Idea of PSO-F
C Algor
ithm
Whe
n
the
st
anda
rd F
C
al
gorithm
se
g
m
ents th
e g
r
ay image, it
divides th
e cl
asse
s of
pixels
acco
rdi
ng to
the
gra
y
cha
r
a
c
teri
st
ics of
im
age
and co
ntinuo
usly
u
pdate
s
the
mem
b
e
r
ship
matrix an
d
cl
usteri
ng
ce
nter u
n
til the
al
gorithm
conv
erge
nce th
ro
ugh
gra
d
ient
desce
nt so a
s
to
reali
z
e the segmentatio
n of gray imag
e. However,
in daily life, the pixels p
o
ints of a com
m
o
n
image
are
en
ormo
us. F
o
r
example, a
common
256
×256 g
r
ay ima
ge ha
s 6
5
,53
6
pixels
point
s
and the pixel
s
point
s to be
classified a
r
e
65,536 a
c
cording to the st
anda
rd F
C
al
gorithm. Fo
r the
stand
ard
F
C
algorith
m
to
d
i
vide a
c
cordi
n
g to
pixel
po
in
ts
, th
e n
u
m
be
r
o
f
ite
r
a
t
io
ns
an
d th
e
time
it
take
s are un
doubte
d
ly very huge. Th
e
r
efore, the
sta
ndard FC
alg
o
ri
thm is
not suitabl
e for real-
time application [19].
4.2. Flo
w
o
f
PSO-FC
Step 1: Rea
d
in the o
r
ig
inal imag
e to be
segm
e
n
ted. Assum
e
that the n
u
mbe
r
of
c
l
us
te
r
i
ng
is
c
, the popul
atio
n si
ze is
N
, the learni
ng fa
ctors
are
1
c
and
2
c
,the inertia
weight
fac
t
or
ma
x
m
i
n
max
ma
x
t
ite
r
; the maximum in
ertia weight
factor i
s
ma
x
an
d the minim
u
m
weig
hted fact
or is
mi
n
；
the ma
ximum iterations
ma
x
it
e
r
and the m
a
ximum sp
ee
d is
ma
x
V
[20].
Step 2:Initialize the p
a
rti
c
le wa
rm. Ra
ndomly ge
ne
rate
12
,,
,
N
zz
z
. The nu
mber
of
d
i
me
ns
io
ns
is
D
dimension a
nd the vector
1
1
,1
1
,
2
1
,D
()
zz
z
z
，，
，
with every co
mpone
nt value is
within 0~1. Take the valu
ation ran
ge o
f
every comp
onent ca
rri
er and particl
e
swa
r
m of
i
z
as
,,
1,
2
,
,
1
,
2
,
.
.
,
ij
i
j
x
ab
a
z
j
D
i
N
,,
, and cal
c
ulat
e the objective function[21],[22].
Step 3: Evalu
a
te the fitness of every
particle and up
d
a
te the individual extremu
m
i
p
and
the global ext
r
emum
g
p
acco
rding to Form
ula (9
) and (1
0).
Step 4: Ran
domly gen
erate a
D
-dim
ensi
onal ve
ctor
00
,
1
0
,
2
0
,
D
(
s
,s
,
.
.
.
,s
)
s
with every
comp
one
nt value withi
n
0
~
1.
Step 5: Upd
a
t
e its own
sp
eed a
c
cordin
g to Form
ula
(11
)
in PSO
and restri
ct i
t
within
mi
n
m
a
x
[,
]
VV
.
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93-6
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TELKOM
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Vol. 13, No. 1, March 2
015 : 128 – 1
3
6
134
Step 6: Accordin
g to
Fo
rmula
(5
)
an
d (6
), u
pdat
e the
memb
ership
matrix
ij
u
and
c
l
us
te
r
i
ng
c
e
n
t
e
r
1
,
t
id
Z
. In the
mean
while,
u
pdate th
e
sp
eed
and
po
si
tion of eve
r
y parti
cle
and
gene
rate the
next-gen
eration parti
cle swarm [23].
Step7: Ju
dge
wh
ether it h
a
s
rea
c
h
ed t
he iter
ation t
e
rmin
ation
co
ndition. If the
iteratio
n
terminate
s
, jump out fro
m
circulation
and output the global o
p
timal solutio
n
g
p
, namely th
e
clu
s
terin
g
ce
nter and o
u
tp
ut the segme
n
ted image, o
t
herwi
se, turn
to Step 3.
5. Experimental Re
sult & Analy
s
is
In order to v
e
rify the
effectivene
ss of t
he
al
gorith
m
prop
osed
i
n
t
h
is pap
er, co
mpare
it
with fuzzy cl
usteri
ng al
go
rithm an
d m
u
lti-thre
sh
old
Otsu im
age
seg
m
entatio
n method. T
h
e
algorith
m
of this p
ape
r do
esn’t n
eed to
determi
ne th
e numb
e
r
of cla
s
ses i
n
ad
vance
and it
ca
n
self-a
daptivel
y divide into several cl
asses in t
he clu
s
terin
g
proce
ss. Comp
arat
ive
experime
n
ts
need
to d
e
termine the
nu
m
ber of
cla
s
se
s in
adva
n
ce
and th
e n
u
m
ber of
cla
s
se
s a
r
e
dete
r
mi
ned
according to the numb
e
r of
classe
s
of the algorith
m
in
this pape
r.
Simulate this experime
n
tal
result and d
a
ta in the en
vironme
n
t of Wind
ows 7
with Intel
(R) Co
re
2CP
U
1.33G
an
d a memo
ry of 2.5G
through M
a
tlab
R201
2a. Set the algorit
hm
para
m
eters a
s
follows: the
size of the p
a
rticle
swarm
is 100; the maximum iterations i
s
200;
the
learni
ng fa
cto
r
s
are:
11
.
9
c
&
21
.
8
c
, the numbe
r of
clu
s
ters
3
c
,
the ma
ximum inertia
weig
ht
fac
t
or is
max
0.9
, the
minimum ine
r
tia weight fact
or is
mi
n
0.
1
, and the fuzzy index i
s
3
m
.
Figure 3 is th
e segm
entati
on effects by
different algo
rithms.
(a)Origin
a
l image
(b
)Fu
zzy cl
uste
ring alg
o
rithm
(c) Multi-th
reshold Ot
su
method
(d) Algo
rithm of this p
aper
Figure 3. Segmentation result
s by differe
nt algorithm
s
Figure 3 (a
) is the origi
nal
image to be
pro
c
e
s
sed while Figu
re 3
(b), (c) a
nd (d) are the
results to
se
gment
(a) by
usi
ng fu
zzy
clu
s
terin
g
al
g
o
rithm, multi
-
threshold
Otsu algo
rithm
a
n
d
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Fuzzy Clu
s
tering Im
age Segm
entation Base
d on Parti
c
le Swa
r
m
Optim
i
zation (Z
han
she
n
Fen
g
)
135
PSO-FC
seg
m
entation al
gorithm.
It can
b
e
see
n
throug
h com
pari
s
on
that with
d
e
termi
ned
numbe
r of cl
a
s
ses, the
s
e t
h
ree
se
gment
ation meth
o
d
s
can segme
n
t the tree in t
he middl
e of the
image; ho
we
ver, as fo
r th
e tree
s an
d pl
ants in th
e ba
ckgro
und, the
segm
entatio
n effect by fu
zzy
clu
s
terin
g
al
g
o
rithm i
s
the
wo
rst
sin
c
e
the ori
g
inal t
r
ee
can’t b
e
i
dentified. Ne
xt come
s mu
lti-
threshold Otsu
method, which can se
g
m
ent
so
me
trees. Th
e alg
o
rithm of thi
s
pape
r ha
s t
h
e
best se
gmen
tation
effect and
it ca
n segment ev
ery obje
c
tive completely. T
o
sum
up, t
h
e
improve
d
alg
o
rithm propo
sed in this pa
p
e
r ha
s better i
m
age segm
e
n
tation effect
s.
6. Conclusio
n
Since ima
ge
has m
any un
certai
nties
an
d i
naccu
ra
cy, people fin
d
that fuzzy theory ha
s
excelle
nt de
scriptio
n a
b
ility on
su
ch
un
certaintie
s. Im
age
seg
m
ent
ation i
s
to
cla
ssify the
ima
g
e
pixels. Apply fuzzy cl
uste
ri
ng into imag
e seg
m
entati
on to get better effect
s tha
n
the traditio
nal
image processing
metho
d
s.However FC algorith
m
h
a
s bad
anti-noi
se ability o
r
ro
bustn
ess
and
it
is ea
sy to be converged t
o
local minim
u
m. T
herefo
r
e, this pape
r integrate
s
PSO and FC
and
applie
s it into image se
gm
entation to g
e
t excell
ent segmentatio
n effects throu
gh com
p
a
r
ati
v
e
study of the experime
n
tal result
s.
Ackn
o
w
l
e
dg
ments
This wo
rk
wa
s sup
porte
d by
the
Sci
e
n
c
e and
te
ch
n
o
logy research
proj
ect
s
i
n
Henan
provin
ce de
p
a
rtment of ed
ucatio
n (g
rant
No.12A52
00
38).
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