TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 12, No. 8, August 201
4, pp. 6230 ~ 6237
DOI: 10.115
9
1
/telkomni
ka.
v
12i8.571
6
6230
Re
cei
v
ed
Jan
uary 10, 201
4
;
Revi
sed Fe
brua
ry 24, 20
14; Accepted
March 10, 20
14
Infrared Image Segmentation using Adaptive FCM
Algorithm Based on Potential Function
Jin Liu*
1
, Haiy
ing Wang
2
, Shaohua
Wa
ng
3
Schoo
l of Elect
r
onic En
gin
eer
i
ng, Xidi
an U
n
iv
ersit
y
,
2 South T
a
ibai
Roa
d
, Xi
’an, S
han
n
x
i, Chi
n
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: jinli
u@
xi
di
an.
edu.cn
1
, hai
yi
n
g
w
a
ng@stu.ci
dia
n
.ed
u
.cn
2
A
b
st
r
a
ct
T
r
aditio
nal
F
u
zz
y
C-
mea
n
s s
e
gmentati
o
n
al
g
o
rith
m re
qu
ires
to set c
l
usteri
n
g
n
u
m
ber
i
n
a
d
v
ance,
and
to ca
lcul
at
e i
m
a
g
e
cluste
ring c
enter
by t
he it
erativ
e
arit
hmetic. So
the
traditio
nal
al
go
rithm is s
ensiti
v
e
to the
initi
a
l v
a
lu
e a
n
d
the c
o
mputat
i
on c
o
mp
lexity
is
hig
h
. In or
der to
i
m
pr
ove t
he tra
d
itio
nal
F
u
zz
y
C
-
me
ans
al
gorith
m
, this
pa
per
prese
n
ts an
in
frared
i
m
ag
e s
e
g
m
e
n
tatio
n
method
usi
n
g
a
daptiv
e F
u
zz
y
C-
me
ans a
l
gor
ith
m
bas
ed o
n
p
o
tentia
l functio
n
. T
he pr
esent
ed al
gorith
m
c
an dir
e
ctly det
ermine th
e opti
m
a
l
clusteri
ng n
u
m
ber a
nd c
l
uster
i
ng c
enter for
i
n
frared
i
m
ag
e t
o
be s
e
g
m
ente
d
by the
pot
ent
ial fu
nction. Aft
e
r
calcul
atin
g the me
mbers
h
ip
matrix of
pixels i
n
the infrare
d
ima
ge by
the fu
zz
y
theory, the
final seg
m
e
n
t
e
d
imag
e is obtai
ned thro
ug
h the fu
zz
y
cluster
i
ng. T
he exper
i
m
e
n
ts show
that the presente
d
alg
o
rith
m in the
pap
er co
ul
d d
e
termin
e
the
o
p
timal c
l
uster
i
ng
nu
mb
er
of
the i
n
frared
i
m
age
ad
aptiv
ely
,
and
ens
ure
the
accuracy of s
e
g
m
e
n
tatio
n
, w
h
ile sig
n
ifica
n
tly reduc
in
g the co
mp
utatio
n spee
d an
d
compl
e
xity of the
alg
o
rith
m.
Ke
y
w
ords
:
infr
ared i
m
age se
gmentati
on, po
tential functi
on,
optimal cl
uster
i
ng n
u
m
ber, F
C
M alg
o
rith
m
Copy
right
©
2014 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
As the
ba
sis
of the inf
r
are
d
targ
et reco
gni
tion
and
tracking, i
n
fra
r
ed ima
ge
se
g
m
entation
techni
que i
s
one of th
e
key tech
nolog
ies to i
m
pro
v
e the infrared warning
system
and
the
infrared guid
ance system
perfo
rman
ce
[1].
In view of the inf
r
ared i
m
age
s
with l
o
w
co
ntra
st, l
o
w
SNR
and
ed
ge bl
ur
ch
aracteri
st
ics, traditional
infrared
ima
ge segm
entation
method
s m
a
inly
inclu
de the
edge m
e
thod
, thresh
old
method, r
egi
on growi
ng
method a
nd
feature
clu
s
terin
g
algorith
m
, etc.
The FCM
se
gmentation al
gorithm [2-4]
as an un
su
pe
rvised
clu
s
tering algo
rithm, is one
of the mo
st
perfe
ct in th
eory a
nd the
most
wid
e
ly use
d
clu
s
tering alg
o
rithm
s
b
a
se
d o
n
t
h
e
obje
c
tive function. Its gre
a
test co
ntrib
u
tion lies
in t
hat the fuzzy
theory is int
r
odu
ce
d into
the
membe
r
ship
degree
of im
age
pixels. B
u
t the alg
o
rit
h
m requi
re
s t
o
set the
clu
s
tering
numb
e
r in
advan
ce, an
d
to cal
c
ul
ate i
m
age
clu
s
teri
ng
cente
r
by
the
iterative a
r
ithmetic, so
t
he
alg
o
rithm
i
s
sen
s
itive to the initial value and the comp
utation com
p
l
e
xity is high.
In gene
ral, the traditional F
C
M cl
uste
ring
al
gorithm h
a
s
slo
w
e
r
conv
erge
nce sp
ee
d, and
bigger sensiti
v
ity
to initial
value [5], resear
che
r
s hav
e prop
osed
a numbe
r of improve
d
FCM
algorith
m
. Literatu
re [6] uses the stati
s
tical hi
stogram
of the image
instead of th
e image pixel
in
cal
c
ulatin
g th
e clu
s
te
ring
center. It al
so
cited th
e
pote
n
tial functio
n
neigh
borhoo
d
informatio
n a
s
weig
hts to determin
e
the
value of th
e fuzzy
me
mbershi
p
of the current
pixel for image
segm
entation
.
Though thi
s
algorith
m
imp
r
oves th
e
ima
ge se
gmentat
ion quality, it
still requi
re
s to
set the cl
ustering
num
ber i
n
advance, and i
s
still sens
itive to the initial val
ue. Besides, Literat
u
re
[7] and Lite
rature [8]
ha
ve improve
d
the F
C
M al
gorithm
a
cco
rding
to thei
r o
w
n
are
a
s of
appli
c
ation f and a
c
hieve
d
certain
re
sult
s.
This pa
pe
r prese
n
ts a met
hod to ada
ptivel
y determin
e
the maximum potential
resi
dual
height an
d di
rectly dete
r
mi
ne the optim
al clu
s
te
ri
ng
numbe
r an
d
clu
s
terin
g
ce
nter for inf
r
ared
image
seg
m
entation by t
he pote
n
tial functio
n
cl
ust
e
ring
metho
d
,
and then th
roug
h the fu
zzy
clu
s
terin
g
to
obtain the
segm
ented
infrare
d
im
age. Experi
m
ental re
sul
t
s sho
w
tha
t
the
pre
s
ente
d
al
gorithm i
n
th
e pap
er
can
real
i
z
e inf
r
a
r
ed im
age
segmentatio
n
adaptively, a
nd
ensure
the
a
c
cura
cy of
se
gmentat
ion,
while significantly reduci
n
g
the com
put
ation spe
ed and
compl
e
xity of
the algorith
m
. It is condu
cive to
achieve real-time p
r
o
c
es
sing of infrared im
age
s.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Infrare
d
Im
age Segm
entation usi
ng Ada
p
tive F
C
M Algorithm
Base
d on Potential
…
(Jin
Liu)
6231
2. The Adap
tiv
e
FCM Algorithm Ba
se
d on Poten
t
ial Function
2.1. Potentia
l Function Cl
usterin
g
Alg
o
rithm
[9
]
Define the hi
stogram probability function of the image
I
:
1
-
0
1
-
0
)
(
1
)
(
M
i
N
j
ij
p
k
MN
k
H
(1)
Whe
r
e,
）
（
j
i
I
I
,
is a digital image, the si
ze of the
image to be segm
ented i
s
N
M
, and:
255
,
,
1
,
0
0
)
,
(
1
)
(
k
else
k
j
i
I
if
k
ij
，
(2)
The proba
bility of the appearan
ce of pix
e
l gray value
k
in the image
I
is represented
by
)
(
k
H
P
approximatel
y. The normal
i
zed hi
stog
ra
m prob
ability function of th
e image
I
is:
))
(
(
max
)/
(
)
(
g
H
k
H
k
H
P
g
P
N
(3)
The ba
sis fu
nction of pot
ential functio
n
gene
rally a
dopts the form of
)
1
/(
1
)
(
2
x
x
C
.
When the normali
z
ed hi
st
ogram probability function
)
(
k
H
N
interpol
ates
o
v
er the ba
si
s function
)
(
x
C
, the histogra
m
potential function of the i
m
age
I
can b
e
got:
255
,
,
2
,
1
,
0
)
(
1
)
(
)
(
255
0
2
k
k
i
i
H
k
P
i
N
，
(4)
Usi
ng an ap
prop
riate
con
t
rol
fa
ctor
can
ma
ke t
h
e
p
eak
v
a
lley
ch
ara
c
t
e
ri
st
ic
s
of
t
h
e
histog
ram p
o
t
ential functio
n
be very clo
s
e to
the one
s of the normalize
d
histo
g
ram p
r
ob
abi
lity
function.
Define the n
o
r
mali
zed hi
st
ogra
m
potenti
a
l function of
the image
I
:
255
,
,
1
,
0
,
255
,
,
1
,
0
)),
(
(
max
)/
(
)
(
g
k
g
P
k
P
k
P
g
N
(5)
Let
)
(
)
(
0
k
P
k
P
N
, which i
s
the normali
zed histo
g
ra
m
potential fun
c
tion of the image
I
,
and defin
e
C
ord
e
r histo
g
ram remai
n
ing pot
ential functio
n
as follo
ws:
255
,
,
1
,
0
,
,
2
,
1
)
(
1
1
)
(
)
(
4
*
1
k
C
c
x
k
r
P
k
P
k
P
c
d
c
c
c
，
，
(6)
Whe
r
e,
}
)
(
|
{
},
255
,
,
1
,
0
),
(
max{
*
1
1
*
c
c
c
c
c
P
k
P
k
x
k
k
P
P
(7)
d
r
is the
facto
r
t
o
control
the
radiu
s
of atte
nuation,
and
C
is the
num
ber of cre
s
ts i
n
t
h
e
histog
ram. E
x
perien
c
e
ha
s sho
w
n that
if the pixel
g
r
ay level ran
ge of the i
n
frared
imag
e to be
segm
ented
is bigg
er, the
radiu
s
of
atten
uation
sh
ould
be l
a
rg
er, a
n
d
the
co
rresp
ondin
g
value
of
the factor
d
r
sh
o
u
ld be smalle
r; if the cre
s
ts of the infra
r
ed image to
be se
gmente
d
are mo
re,
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 8, August 2014: 623
0 –
6237
6232
the radiu
s
of
attenuation
should
be
sma
ller,
a
nd th
e
correspon
ding
value
of the
factor
d
r
sh
oul
d
be larg
er. Define the factor
d
r
as
follows
:
2
5
)
1
(
H
d
D
C
r
(8)
Whe
r
e,
is a consta
nt in the experim
ent
, and
H
D
means
the gray de
p
t
h of image
I
, w
h
ose
value is the di
fference between the maxi
mum and min
i
mum value
s
of image
I
.
Based o
n
hi
stogram re
m
a
ining p
o
tent
ial f
unction d
e
fine functio
n
grou
ps div
i
ded by
potential as follows:
255
,
,
1
,
0
,
,
,
2
,
1
,
||
||
1
1
)
(
)
(
4
*
k
C
c
x
k
r
k
P
k
F
c
d
c
c
(9)
As can be
se
en from the expre
ssi
on, functio
n
gro
u
p
s divided by
potential is actually a
quarti
c ba
sis
function who
s
e center i
s
c
x
and who
s
e h
e
i
ght is
)
(
*
k
P
c
. So wh
en the value of
C
is
kno
w
n, dividi
ng histog
ram
potential function is a
pro
c
ess wh
ere th
e quarti
c ba
si
s functio
n
is the
best fitting of
the given
histogram
poten
tial function,
and the
fitting functio
n
s a
r
e
C
F
F
F
...,
2
1
，
，
in
Equation (9).
Acco
rdi
ng to the above alg
o
rithm, use the func
tion g
r
o
ups divid
ed b
y
potential to divide
the histo
g
ra
m potential f
unctio
n
, and
the clu
s
te
ri
ng
ce
nter i
s
o
b
t
ained. Howe
ver, due
to the
influen
ce of the radi
us of a
ttenuation pa
ramete
r, some
potential whi
c
h should n
o
t be divided in
to
is likely to a
p
pear in th
e p
r
oce
s
s of divi
sion,
and
the
p
o
tential shoul
d be
eliminat
ed i
s
na
med
as
pse
udo
-pote
n
t
ial [10]. Idea
lly, each
cre
s
t in the
hi
stogra
m
fun
c
tion divide
d b
y
potential i
s
in
uniform
di
stri
bution, a
n
d
the inte
rval
be
tween
the
two cre
s
ts shou
ld be
C
D
H
/
. Though in reality
this condition
is gen
erally
not met, accordin
g
to the
ideal interva
l
we can defi
ne an a
dapti
v
e
fuzzy p
s
eu
do
-potential fa
ctor
p
f
as
follows
:
C
D
f
H
p
3
2
(10)
Whe
r
e,
C
is the
num
ber of
categ
o
rie
s
,
H
D
mean
s the
g
r
ay d
epth
of image
I
, and
is
a
con
s
tant i
n
t
he exp
e
rim
e
nt. Set
i
x
and
j
x
are
two
ab
sci
ssas
of the
adj
ace
n
t pe
ak p
o
ints i
n
the
function g
r
ou
ps divide
d by potential, thei
r va
lue ca
n b
e
cal
c
ulate
d
by the type (7), if:
p
j
i
f
x
x
|
|
(11)
Then eithe
r
must be a pseudo
-pote
n
tia
l
. Extr
act the two extremu
m
values of the both
histog
ram
fu
nction
divide
d by
potentia
l re
sp
ectively
, and
compa
r
e the
s
e
two
extremum
val
ues
to obtain the maximum. Then add the
two cu
rves
o
f
the both histogram fun
c
tion divided by
potential tog
e
t
her, an
d giv
e
the sum fu
nction
a fitting acco
rdin
g t
o
the follo
win
g
equ
ation, a
n
d
then the histogram fun
c
t
i
on divided
by potential,
)
(
'
k
F
,after mergin
g pse
udo
-po
t
entials is
obtaine
d:
4
'
)
(
1
)
(
x
k
r
y
k
F
d
(12)
Whe
r
e,
y
repre
s
ent
s the ma
ximum of the two hist
o
g
ra
m function di
vided by pot
ential above,
and
x
mean
s extremum value
point of the sum function.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Infrare
d
Im
age Segm
entation usi
ng Ada
p
tive F
C
M Algorithm
Base
d on Potential
…
(Jin
Liu)
6233
2.2. The Ada
p
tiv
e
Determine of the Ma
ximum Remaining Height of Potential
The alg
o
rith
m de
scribe
d
above
still requi
re
s to
be set the n
u
mbe
r
of ca
tegory
C
artificially, which makes
the algorithm reduce
s its versatility, so a
thre
shold val
ue to make t
h
e
iteration
stop
sh
ould
be
set in the
alg
o
rithm. Th
e t
h
re
shol
d val
u
e
h
R
is called t
he maximu
m
remai
n
ing h
e
i
ght of potenti
a
l, and its ra
nge is
1
0
h
R
. If the
value of
h
R
co
uld
be determin
e
d
adaptively, the value of
C
ca
n
also be o
b
tai
ned ad
aptivel
y.
In the cu
rve
of potential
function, th
e gr
ayscale
every ab
sci
ssa of the
pe
ak p
o
int
rep
r
e
s
ent
s ha
s the po
ssi
bili
ty to be a clusterin
g
ce
nter. This is be
ca
use:
(1) In a n
e
i
ghbo
rho
od in
terval, the correspon
ding
grayscal
e
k
to the c
r
es
t has
the
highest probability;
(2) The gray
scale
s
a
r
ou
nd the
grayscale
k
has th
e lea
s
t
varian
ce
with
the grayscal
e
k
,
whi
c
h a
c
cord
s with the cl
u
s
terin
g
thoug
ht.
Since
the ma
ximum
remai
n
ing heig
h
t
o
f
potential
h
R
is
a va
lu
e g
r
e
a
t
er
th
an
0 an
d
le
ss
than 1, if the least cre
s
t value of the norma
lize
d
histo
g
ram p
o
tentia
l function of the image
I
is as
the referen
c
e
standa
rd, the
value of
h
R
coul
d be set in th
e three
situations:
(1) T
he value
is greate
r
tha
n
the least crest value an
d
less tha
n
1;
(2) T
he value
is equal to th
e least cre
s
t value;
(3) T
he value
is less than the lea
s
t cre
s
t
value and greater than
ze
ro.
Figure 1. The
Relation
ship
of
h
R
and the Normalize
d
Hi
sto
g
ram Potenti
a
l Functio
n
As sho
w
n in
Figure 1, if th
e value
of
h
R
is
set a value
greater th
an th
e lea
s
t cre
s
t
value
and l
e
ss th
a
n
1, the
pote
n
tial informati
on of th
e sm
allest crest will
be
lo
st in
the process
of
comp
uting. M
ean
while, in t
he curve
of
potential
fun
c
tion, the grayscale
eve
r
y
absci
ssa of t
he
peak point represent
s
has the possibility
to be a clust
e
ring
c
enter, whi
c
h means that if
the value
of
h
R
is
set
duri
n
g the
interval
, a
clu
s
terin
g
ce
nter could
be
lo
st; Assume th
at the
value of
h
R
is
set a value less than the
least crest value
and g
r
e
a
ter than zero. As during
the descen
d
i
ng
rang
e from th
e lea
s
t cre
s
t
value to the
value of
h
R
, there
is n
o
crest in
the curve
of
norm
a
lized
histogram
potential funct
i
on, that i
s
to
say,
the possibility to exi
s
t a category in the
corre
s
p
ondin
g
g
r
ayscale
d
u
ring
the
interval is ve
ry
sm
all. So it i
s
n
o
t
meanin
g
ful t
o
set the val
u
e
of
h
R
in the interval.
In summa
ry, the value of
h
R
should be
set as the se
co
n
d
ca
se, in wh
ich the cre
s
t value
in the curve
of the normal
i
zed
histo
g
ra
m potential f
unctio
n
is th
e
most rea
s
on
able. Define t
h
e
h
R
as
follows
:
}
,...,
,
min{
2
1
n
h
P
P
P
R
(13)
gra
y
scal
e
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TELKOM
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6234
Whe
r
e,
n
P
P
P
,
,
,
2
1
rep
r
ese
n
t the
crest valu
es i
n
the
cu
rve
of the
no
rmalize
d
hi
st
ogram
potential fun
c
tion, and
n
is t
he num
ber
o
f
the cre
s
ts i
n
t
he cu
rve
of the histog
ram pote
n
tial
function.
2.3. The Principle of the
Adap
tiv
e
FCM Algorithm
Bas
e
d on Po
ten
t
ial Function
The tradition
al FCM al
gori
t
hm
[11] is a
method
whi
c
h u
s
e
s
the
g
r
ay value
of i
m
age
and
the distan
ce
information
betwe
en the
pixels to
calcul
ate ima
ge clu
s
te
ring
cente
r
and
the
membe
r
ship matrix
of pixels by
the
iterat
ive
arith
m
etic, a
nd t
hen i
m
age
segmentatio
n
is
achi
eved. Ho
wever, th
e co
mplexity of the iterative
a
r
ithmetic i
s
hi
g
her, a
nd it is
not co
ndu
civ
e
to
achi
eve re
al-t
ime segme
n
tation of infrared imag
es
. T
he pote
n
tial functio
n
cl
ust
e
ring
algo
rith
m
can
calculate
the p
o
tential
inform
ation
of ever
y g
r
ay
scale
duri
ng
the imag
e g
r
ay ran
ge, a
n
d
throug
h me
rging the
pseudo
-pote
n
tia
l
determi
ne the
optimal clu
s
terin
g
nu
mber and
t
he
clu
s
terin
g
ce
nter for the in
frare
d
image
to be segm
en
ted adaptivel
y.
This p
ape
r introdu
ce
s the p
o
tential functi
on clu
s
te
ring
algorith
m
into
the traditiona
l FCM
segm
entation
algorithm, a
nd presents
an infra
r
ed i
m
age
seg
m
e
n
tation meth
od u
s
ing a
d
a
p
tive
FCM alg
o
rith
m based on
potential fun
c
tion. The pr
e
s
ente
d
algo
rithm ca
n dire
ct
ly determine t
he
optimal clu
s
te
ring num
be
r and clu
s
te
rin
g
cente
r
for infrare
d
image
segm
entation
by the potential
function, in
stead of the traditional FCM
segm
entat
ion
algorithm setting the clust
e
ring n
u
mbe
r
in
advan
ce a
nd
cal
c
ulatin
g im
age
clu
s
terin
g
ce
nter
by the iterative arithm
etic. And
then obtai
n th
e
final segm
ent
ed image by the fuzzy clu
s
tering. Th
e ste
p
s are as foll
ows:
1)
Cal
c
ulate t
he hi
stog
ram
potential fun
c
tion for inf
r
ared ima
g
e
I
by the formula
(4
),
k
is
the gray se
ri
es, and obtai
n the cre
s
t value
s
n
P
P
P
,
,
,
2
1
of the n
o
rmali
z
e
d
histogram p
o
ten
t
ial
function. The
n
cal
c
ulate th
e maximum remainin
g hei
ght of potential
h
R
by the form
ula (13
)
.
2) Let the initial numbe
r of categ
o
rie
s
2
C
, and the numb
e
r
of pse
udo
-p
otential
0
K
.
3)
Cal
c
ulate
the fa
ctor
d
r
by the formula
(8
), the
fu
zzy p
s
eu
do-potenti
a
l
facto
r
p
f
by the
formula (10), the
c
ord
e
r
hist
ogra
m
re
mai
n
ing p
o
tential
function
)
(
k
P
c
by the formul
a (6),
whe
r
e
K
C
c
,...,
2
,
1
, and the co
rresp
ondi
ng
c
x
.
K
is the numbe
r of pseu
do-pot
ential.
4) Cal
c
ul
ate the crest valu
e of
)
(
k
P
c
, and obtain the value of
*
1
c
P
. If
h
c
R
P
*
1
, then go
to step 5; Otherwi
se, repe
a
t
step 3.
5) Cal
c
ul
ate the function
grou
ps divid
e
d
by potential
K
C
F
F
F
,
,
2
1
by the formula (9),
and orde
r
c
x
in the ord
e
r of a
s
cendi
ng. Th
en
the co
rrespondi
ng so
rti
ng re
sult of
K
C
F
F
F
,
,
2
1
is
'
'
2
'
1
,
,
K
C
F
F
F
.
6) If
0
K
, the pseu
do-p
o
tential e
x
ists. Cal
c
ula
t
e the fitting functio
n
by the formula
(12
)
,
and th
en o
b
tain the fin
a
l f
unctio
n
g
r
ou
p
s
divide
d by
potential
s
s
2
1
,...,
,
C
s
F
F
F
, in whi
c
h the
val
ue of
c
x
is the clu
s
teri
ng ce
nter, an
d the final value of
C
is the cl
usteri
ng nu
m
ber.
7)
Cal
c
ulate
t
he Eu
clide
an
distan
ce
bet
wee
n
e
a
ch pi
xel and
the
cl
usteri
ng
ce
nt
er i
n
the
infrared imag
e,
)
,
,
(
c
j
i
D
.
|
)
(
)
,
(
|
)
,
,
(
c
Center
j
i
I
c
j
i
D
(14)
8) Defin
e
the membe
r
ship
of each pixel
belon
ging to the clu
s
teri
ng
cente
r
as foll
ows:
C
c
m
c
j
i
D
c
j
i
D
c
j
i
U
1
1
2
'
'
)
)
,
,
(
)
,
,
(
(
1
)
,
,
(
(15)
9) Cla
s
sify the pixels, and
comp
are the membe
r
ship
s of each pixel
)
,
(
j
i
in the infrare
d
image,
)
,
,
(
c
j
i
U
C
c
,...,
1
. The pixel
)
,
(
j
i
belo
n
g
s
to the cl
ass who
s
e
mem
bership
is th
e
large
s
t, and the final imag
e segm
ented
is gotten by cl
usteri
ng.
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TELKOM
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046
Infrare
d
Im
age Segm
entation usi
ng Ada
p
tive F
C
M Algorithm
Base
d on Potential
…
(Jin
Liu)
6235
3. Results a
nd Discu
ss
To validate
th
e alg
o
rithm
th
is p
ape
r p
r
e
s
ents,
the
cl
ustering
num
be
r
set in
the tra
d
itional
FCM
segm
en
tation algo
rith
m wa
s eq
ual
with the opti
m
al clu
s
te
rin
g
numb
e
r o
b
tained a
daptiv
ely
by the
algo
rithm in
this p
aper.
Compa
r
e th
e
seg
m
entation re
su
lts
an
d effici
ency of
the
two
algorit
h
m
s in
t
h
is cir
c
u
m
st
a
n
ce.
Four inf
r
ared
image
s were
adopte
d
in th
e ex
perim
ent, of which the
singl
e-m
an in
frare
d
image
sh
own
in Fig
u
re
2 i
s
fro
m
the i
n
frare
d
data
made
by lab
o
rato
ry, with
320
240
pixels.
The ship inf
r
ared ima
g
e
sho
w
n in F
i
gure
3 is from a dom
e
s
tic resea
r
ch
institutes,
with
320
240
pixels. The
d
ouble
ped
estrians i
n
fra
r
ed i
m
age
sho
w
n
in Figu
re 4 i
s
from an
infra
r
e
d
databa
se in t
he Internet, with
320
240
pixels.
(a) the o
r
igin
al image
(b) the
re
sult of FCM (
C
=
3
)
(c) the re
sult
of the improv
ed
algorith
m
(C=3)
Figure 2. The
Single-ma
n Infrared Imag
e
(a) the o
r
igin
al image
(b) the
re
sult of FCM (
C
=
2
)
(c) the re
sult
of the improv
ed
algorith
m
(C=2)
Figure 3. The
Ship Infrared
Image
(a) the o
r
igin
al image
(b) the
re
sult of FCM (
C
=
4
)
(c) the re
sult
of the improv
ed
algorith
m
(C=4)
Figure 4. The
Doubl
e Pede
strian
s Infra
r
e
d
Image
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6236
From
Figu
re
2 to Fig
u
re
4,
the Fig
u
re
(a
)
is the
origi
n
al infra
r
ed
im
age to
be
se
g
m
ented,
the Figure (b) is the se
gmentation
result of
the
infrare
d
image by the traditional F
C
M
segm
entation
algorithm, a
nd the Figu
re
(c) i
s
t
he se
gmentation
result of
the infrared imag
e by
the improve
d
algorithm
propo
sed in thi
s
pap
er. As
can be
see
n
from the figure
s
, the pro
p
o
s
ed
algorith
m
ca
n a
c
hieve
th
e same
results a
s
th
e tra
d
itional
FCM
se
gme
n
tatio
n
alg
o
rithm
e
v
en
better. Table
1 sho
w
s the compa
r
ison of the two meth
ods in
comp
u
t
ation time.
Table 1. The
Comp
ari
s
o
n
of the Two M
e
thod
s in Co
mputation Ti
me
Simulation ima
g
e The
clusterin
g
nu
mber C
T
he time of F
C
M
(
s
)
The time of the i
m
prove method
(
s
)
the sin
g
le-man
3
12.4641
1.5772
the tank
3
20.1532
1.6524
the double pedes
trians
4
18.7104
1.9106
We
ca
n
see
that when
their
clu
s
te
rin
g
num
be
r i
s
set
equ
ally, the effici
en
cy of the
algorith
m
propo
sed in th
is pap
er i
s
sup
e
rio
r
to
one of the tradition
al FCM segm
entat
ion
algorith
m
.
In addition, the traditional F
C
M algo
rithm
is sen
s
itive to the initial value. So after setting
the clu
s
terin
g
numbe
r, though ea
ch
clu
s
terin
g
re
sult
is the sam
e
, there i
s
a visu
al differen
c
e i
n
the image, which i
s
not
co
ndu
cive to pe
ople'
s s
ubje
c
t
i
ve evaluatio
n. The imp
r
o
v
ed algo
rithm
in
this pa
per
ad
aptively determines th
e cl
u
s
terin
g
num
b
e
r an
d the
clusteri
ng
cent
er, so th
ere i
s
no
influen
ce
of i
n
itial value
o
n
the
se
gme
n
tation result, and
the
re
su
lt is u
n
iqu
e
.
Figure 5
a
r
e
the
segm
entation
results of
the single
-
man infra
r
e
d
image th
roug
h the tradition
al F
C
M
segm
entation
algorithm
si
mulating several time
s. Le
t cluste
ring n
u
mbe
r
3
C
.
As ca
n be
seen from th
e
figure ab
ove
,
the
Figure
6 are the
si
mulating resu
lts of the
same i
n
fra
r
e
d
image
by the sam
e
meth
od and th
e cl
usteri
ng n
u
m
ber
wa
s set e
qually. Althou
gh
the final clust
e
ring
re
sults
are three categori
e
s,
the result
s displayed in the ima
ge are diffe
re
nt
in vision. Afte
r many time
s
simulatio
n
to
the
sa
me
sin
g
le-m
an infra
r
ed im
age
by the algo
rithm
in
this p
ape
r, the result is
uniqu
e an
d i
s
the
sa
me
as Fi
gu
re 2
(
c).
We
ca
n
con
c
lu
de tha
t
the
improve
d
al
g
o
rithm i
n
thi
s
pape
r ove
r
co
mes the
def
e
c
t of tradition
al FCM al
gori
t
hm sen
s
itive to
the initial value.
4. Conclusio
n
Traditio
nal F
C
M
seg
m
ent
ation al
gorith
m
re
quires to
set
clu
s
teri
n
g
num
be
r in
advan
ce,
and to cal
c
ul
ate image clu
s
terin
g
ce
nter by the iter
ative arithmetic.
So the traditional algo
rith
m is
sen
s
itive to the initial valu
e and the
co
mputation
co
mplexity is hi
gh, and it is
not co
ndu
cive to
achi
eve re
al-t
ime se
gment
ation of infra
r
ed imag
es. T
he propo
se
d algorith
m
in this pa
pe
r ca
n
adaptively d
e
termin
e the
optimal clu
s
terin
g
num
b
e
r and
clu
s
tering
cente
r
by the potential
function
clu
s
tering
algo
rith
m, calculate t
he memb
er
ship matrix of
pixels u
s
ing t
he fuzzy theo
ry,
and th
en
obt
ain the
final
segmente
d
re
sult by th
e
fu
zzy clu
s
teri
ng
.
The
exp
e
ri
ments sh
ow
that
the propo
se
d
algo
rithm
ca
n en
su
re the
accu
ra
cy
of segm
entation
,
while signifi
cantly
redu
ci
ng
Figure 5. The
Segmentatio
n Re
sults of th
e S
ingle
-
ma
n by FCM
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Infrare
d
Im
age Segm
entation usi
ng Ada
p
tive F
C
M Algorithm
Base
d on Potential
…
(Jin
Liu)
6237
the com
putati
on spee
d an
d com
p
lexity of the algo
rithm. In additi
on, it overco
mes the
defe
c
t of
traditional F
C
M algorithm
sensitive to the initial value.
Ho
wever, im
age noi
se
ha
s a g
r
eat infl
uen
ce
on th
e
infrared ima
ge segme
n
ta
tion. The
prop
osed alg
o
rithm do
es n
o
t perform well in the noise sup
p
re
ssio
n pro
c
e
ssi
ng,
so the re
duct
i
on
noise part will
be one of the
future re
sea
r
ch in this al
go
rithm.
Ackn
o
w
l
e
dg
ements
This
wo
rk was
sup
p
o
r
ted
in pa
rt by
Nation
al Natural S
c
ien
c
e
Foun
dation
for youn
g
schola
r
s
of Chin
a und
er grant No. 6110
1246
(“
Re
sea
r
ch on
IR obje
c
t segmentatio
n
and
recognitio
n
b
a
se
d on G
r
a
ph and ISA”),
and the Fu
n
damental
Re
sea
r
ch Fun
d
s for the Cen
t
ral
Universitie
s
u
nder G
r
ant
s
No. K50
511
0
2001
9 (“
Research
on o
b
j
e
ct d
e
tection
and
re
cog
n
ition
for IR image”).
Referen
ces
[1]
Jian
hua
Sh
en,
Sha
ngq
ia
n L
i
u, Yan
x
ua
n M
a
.
F
a
st infrar
e
d
ima
g
e
segm
entatio
n
alg
o
rit
h
m.
Jour
nal
of
infrare
d
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