Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
Vol.
4, No. 6, Decem
ber
2014, pp. 923~
930
I
S
SN
: 208
8-8
7
0
8
9
23
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
Clusteri
ng Al
gorithm Combined with Hill
Climbing for
Classi
fication of
Rem
o
te Sensing Image
B. Sai
Ch
an
d
a
n
a
*, K
.
Srini
vas
**,
R.
Kir
a
n Kum
a
r
*
*
Department of CSE,
GIT GITAM
University
, Visakhapatn
am, India
**
Dep
a
rtment o
f
CSE, VR
Sidd
hartha E
ngin
eer
ing College, Vijay
a
w
a
da, India
*
Depar
t
ment of
CSE, Krishna Un
ivers
i
t
y
,
M
a
chi
lipatn
a
m
,
Ind
i
a
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Aug 27, 2014
Rev
i
sed
No
v 7, 201
4
Accepted Nov 22, 2014
Clustering is an unsupervised cla
ssification
method widely used for
clas
s
i
fi
cat
ion of
rem
o
te s
e
nsing
i
m
a
ges. As the
spatial
resolu
tio
n of rem
o
te
sensing images getting high
er an
d higher,
the
co
m
p
lex s
t
ructure i
s
the s
i
m
p
le
objects becomes
obvious, which
makes th
e classification algorith
m
based
on
pixels b
e
ing
losing their adv
a
ntages. In
this pap
e
r, four
diff
eren
t clustering
algorithm
s
s
u
ch as
K-m
eans
,
Moving K-m
eans
,
F
u
zz
y
K-m
eans
and F
u
z
z
y
M
oving K-m
eans
are us
ed for
cl
as
s
i
fica
tion of r
e
m
o
te s
e
ns
ing im
ages
. In
all
the trad
ition
a
l cl
ustering algor
ith
m
s
, num
b
er
of clusters and initi
a
l
centro
i
ds
are random
l
y
s
e
lec
t
ed and oft
e
n
s
p
ecified b
y
th
e us
er. In this
p
a
per,
a hill
climbing algorithm for the
histogram of the in
put image will
generate th
e
number of clusters and init
ial
centroids requir
e
d
for cluster
i
ng. It overcomes
the shortage of
random in
itialization in
tr
aditio
nal
cluster
i
ng and ach
ieves
high computational speed b
y
reduc
ing the number
of
iter
a
tions. The
experimental results show that Fuzz
y
Moving
K-means has classified the
rem
o
te sensing
i
m
a
ge m
o
re a
ccu
rate
l
y
th
an o
t
her
three
algo
rithm
s
.
Keyword:
Im
age Classification
Im
age Clustering
Im
age Proce
ssing
Re
m
o
te Sen
s
ing
Copyright ©
201
4 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
:
B. Saicha
ndana
M
e
m
b
er IE
EE,
CSI,
I
A
E
N
G
a
n
d
Assistant P
r
ofess
o
r
Depa
rt
m
e
nt
of
C
o
m
put
er sci
e
nce a
n
d
E
ngi
n
eeri
n
g,
GITAM
In
stitute o
f
Techno
log
y
, GITAM Un
iv
ersity,
Vi
sak
h
a
p
at
na
m
-
530
04
5
, India
Em
a
il: b
s
ch
and
a
n
a
@g
m
a
i
l
.co
m
1.
INTRODUCTION
R
e
m
o
t
e
sensi
n
g ca
n
be
de
fi
ne
d as
any
p
r
o
c
e
ss w
h
e
r
eby
i
n
f
o
rm
at
i
on i
s
gat
h
ere
d
a
b
out
an
o
b
j
ect
, a
r
e
a
or
phe
n
o
m
e
non wi
t
h
out
m
a
ki
ng p
h
y
s
i
cal
cont
act
wi
t
h
t
h
e
ob
ject
[1]
.
T
h
e rem
o
t
e
sensing t
ech
n
o
l
o
gy
(aeri
a
l
sens
or technology
) is used to cla
ssify objec
ts on the Earth (bot
h on th
e s
u
rface, and in
the atm
o
sphe
re and
oceans) by
m
e
ans of propa
g
a
t
ed
sign
als.
Ne
w opportunities to use rem
o
te
sensi
ng data have
arise
n
, with
the
increase
of
spa
tial and spect
ra
l reso
luti
on
of
recently launc
hed
satellites. Re
m
o
te sensing im
age classification
is a key technology in rem
o
te sensing appl
ications
[2]. High res
o
luti
on
rem
o
te sensing has receive
d
m
u
c
h
attention
beca
use
of the
de
tailed inform
ation it pr
ovi
des of the
eart
h
s
u
rface. The problem
of im
age
classification is to assign label to each i
m
age pixe
l [3]. Rapid and
high accuracy
rem
o
te sensing im
age
classificatio
n
alg
o
rith
m
is th
e
p
r
econ
d
ition
o
f
k
i
nd
s
o
f
p
r
actical ap
p
licati
o
n
s
. In
rem
o
te
sen
s
ing
,
sen
s
ors are
av
ailab
l
e th
at can
g
e
n
e
rate m
u
ltisp
ectral d
a
ta, in
vo
lv
i
n
g fi
v
e
to
m
o
re th
an
hu
ndred b
a
nd
s.
B
a
sed o
n
t
h
e
cri
t
e
ri
a whet
he
r t
r
ai
ni
n
g
sam
p
l
e
s are
use
d
or
not
, i
m
age
cl
assi
fi
cat
i
on
m
e
t
hods a
r
e
classified into two categories. Th
ese cate
g
ories are dist
inguishe
d in
t
w
o m
a
i
n
way
s
as super
v
i
s
e
d
an
d
uns
u
p
er
vi
se
d cl
assi
fi
cat
i
on ap
proaches [4]
.
In supe
rvise
d
classifi
cation approaches la
nd c
ove
r cl
asses are
defi
ned. Suffic
i
ent refere
nce
data are available and
us
ed a
s
t
r
ai
ni
ng sam
p
l
e
s. The si
g
n
a
t
u
res ge
ne
rat
e
d fr
om
the training sam
p
les
are then
used to train the classifier to classify
th
e s
p
ectral d
a
ta in
to
th
em
at
ic
ma
p
[5
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJECE Vol. 4, No. 6, D
ecem
ber 2014
:
923 – 930
92
4
Exam
ples of s
upe
rvised clas
sification a
p
proache
s
a
r
e
Ma
x
i
mu
m l
i
k
e
l
i
h
o
o
d
,
mi
nim
u
m distance, artificial
neural net
w
ork,
decision tre
e
cla
ssifier etc. In
Uns
upe
rvised classi
fi
c
a
t
i
on ap
p
r
oac
h
es, cl
ust
e
ri
n
g
based
alg
o
rith
m
s
are u
s
ed
t
o
p
a
rtitio
n
t
h
e sp
ect
ral i
m
ag
e in
to
a n
u
m
b
e
r of sp
ectral classes based
on
th
e statistica
l
in
fo
rm
atio
n
inh
e
ren
t
in
th
e i
m
ag
e. No
prior d
e
fin
itio
ns
of th
e classes are u
s
ed
. Th
e an
alyst is resp
on
si
b
l
e fo
r
lab
e
lin
g
an
d
merg
ing
th
e sp
ectral classes in
to
m
ean
i
ngful classes. E
x
a
m
ples such as ISODAT
A
, K-m
eans
Clustering algorithm
etc bel
o
ng t
o
u
n
su
pe
rvi
s
e
d
cl
assi
fi
c
a
t
i
on a
p
pr
oach
es. Uns
u
pervis
ed
classification ha
s
evol
ved in t
w
o
basic strate
gies [6],
Iterative and Se
qu
en
ti
al. In
an iterativ
e pro
cedure
suc
h
as K-Me
ans or
ISODATA, an in
itial n
u
m
b
e
r of
d
e
sired
cl
u
s
ters are se
lected
, an
d
t
h
e
cen
tro
i
d
locatio
n
s
are t
h
en
m
o
v
e
d
aroun
d
un
til a statistical
ly o
p
t
i
m
al fit is o
b
t
ain
e
d. In
a
sequ
en
tial algo
rith
m
su
ch
as Classificatio
n
b
y
Progressiv
e
Gen
e
ralizatio
n, th
e larg
e
num
b
er of s
p
ectral com
b
inations is
grad
ual
l
y
red
u
ced t
h
ro
u
gh a
seri
es
of
st
eps
usi
n
g
vari
ous
p
r
oxi
m
i
t
y
m
easures.
In t
h
i
s
pa
per
,
we u
s
ed
f
o
u
r
d
i
ffere
nt
cl
ust
e
ri
ng al
go
rith
m
s
fo
r classi
ficatio
n
of
rem
o
te sen
s
ing
im
ag
e.
In
th
e cl
u
s
teri
n
g
al
g
o
rith
m
s
, p
a
ram
e
ters su
ch
as clu
s
ter
n
u
m
b
e
r and
initial cen
tro
i
d
p
o
s
ition
s
are ch
o
s
en
ran
d
o
m
l
y
and
oft
e
n s
p
eci
fi
e
d
by
t
h
e
use
r
.
I
n
t
h
e
p
r
op
ose
d
cl
ust
e
ri
n
g
al
g
o
r
i
t
h
m
s
, i
n
st
ead
of
ra
n
dom
l
y
in
itializin
g
th
e p
a
ram
e
ters in
th
e clu
s
tering
alg
o
rith
m
s
, th
e h
ill cli
m
b
i
n
g
alg
o
rith
m
o
n
th
e h
i
stogram
o
f
in
pu
t
i
m
ag
e will au
t
o
m
a
t
i
cally
d
e
term
in
e th
e clu
s
ter cen
ters and
th
e nu
m
b
er o
f
clu
s
ters in
th
e i
m
ag
e. Th
e Hill
cli
m
bing algorith
m
adaptively determin
es the initial clust
e
r centers a
nd
the num
ber of clusters according t
o
th
e ch
aracteristics o
f
th
e imag
e.
Using
hill cli
m
b
i
n
g
al
g
o
rith
m
as a p
r
elim
in
ary stag
e
with
clu
s
t
e
ring
alg
o
rith
m
s
red
u
ces th
e
nu
m
b
er of iteratio
ns for cla
ssificatio
n
and
costs less ex
ecu
tio
n ti
m
e
. Th
e qu
alitativ
e
an
d
q
u
a
n
titati
v
e
resu
lts sh
ow th
at Fu
zzy Mo
v
i
n
g
K-m
e
an
s clu
s
teri
n
g
alg
o
r
ith
m
h
a
s classified
th
e i
m
ag
e
b
e
tter th
an
o
t
her clu
s
tering
al
g
o
rith
m
s
.
Th
e
p
a
p
e
r is
o
r
g
a
n
i
zed
as fo
llo
ws:
Section
1 presen
ts
th
e Hill Cli
m
b
i
n
g
Alg
o
rith
m
,
Sectio
n 2
p
r
esen
ts t
h
e
K-
m
eans cl
ust
e
ri
ng al
go
ri
t
h
m
,
Sect
i
on
3
pres
ent
s
M
o
vi
n
g
K-m
eans cl
ust
e
ri
n
g
al
g
o
ri
t
h
m
,
Sect
i
on 4
prese
n
t
s
Fuzzy C-m
eans clustering algorithm
,
Section
5 prese
n
ts Fuzzy Movi
ng
K-m
eans Clustering algori
thm
,
Sect
i
on
6
p
r
ese
n
t
s
E
xpe
ri
m
e
ntal
resul
t
s
a
n
d fi
nal
l
y
Sect
i
o
n
7
re
po
rt
co
ncl
u
s
i
ons
.
2.
HILL CLI
M
B
I
NG
ALG
O
R
I
THM
Trad
ition
a
l h
ill
-cli
m
b
in
g
segmen
tatio
n
[7
]
[8
] is a
n
onp
ara
m
etric alg
o
r
it
h
m
th
at clu
s
ters th
e co
lors
of a
n
im
age. The idea is t
h
at each cl
uste
r is
represe
n
ted
by a hill in the
histogram
,
where the hill consi
s
ts of
ad
j
acen
t
co
l
o
rs. In
th
is p
a
p
e
r, an
ex
tend
ed
version
of h
ill cl
i
m
b
i
n
g
alg
o
rith
m
is p
r
esen
ted
.
Th
is Hill cli
m
b
i
n
g
alg
o
rith
m
wh
ich
is
u
s
ed
in th
e preli
m
in
ary stag
e
fo
r a cl
uste
ring algorit
h
m
is stated as
foll
ows:
In
p
u
t
:
Gl
obal
t
h
ree
di
m
e
nsi
onal
col
o
r hi
st
o
g
ram
of t
h
e im
age by the thre
e channels
of s
e
lected suitable color
space.
Ou
t
p
u
t: Th
e
num
b
e
r an
d v
a
l
u
es of
p
eaks=
Nu
m
b
er
of clusters an
d in
itial cen
tro
i
d
s
resp
ectiv
ely
Step
1: Start at
a non-ze
r
o bi
n of the
histogra
m
a
nd m
a
ke uphill
m
oves
until r
eachi
n
g a
pe
ak as follows:
1.
C
o
m
p
are t
h
e
n
u
m
b
er o
f
pi
xel
s
o
f
t
h
e c
u
r
r
ent
hi
st
o
g
ram
bi
n
wi
t
h
t
h
e
num
ber
of
pi
xel
s
of
t
h
e n
e
i
g
hb
ori
n
g
bi
ns
.
2.
If th
e n
e
i
g
h
b
o
r
in
g
b
i
n
s
h
a
v
e
d
i
fferen
t
n
u
m
b
e
r o
f
p
i
x
e
ls, the alg
o
r
ith
m
mak
e
an
uph
ill m
o
v
e
to
ward
s th
e
nei
g
hb
o
r
i
n
g bi
n wi
t
h
l
a
r
g
e n
u
m
ber
of pi
xel
s
.
3.
If t
h
e i
m
m
e
diat
e nei
g
h
b
o
r
i
n
g
bi
ns
ha
ve
t
h
e sam
e
n
u
m
b
er
o
f
pi
xel
s
,
t
h
e al
go
ri
t
h
m
chec
ks
t
h
e
n
e
xt
n
e
igh
boring
b
i
n
s
,
and
so
on
, u
n
til
two
n
e
ighb
oring
b
i
ns
with
d
i
fferen
t n
u
m
b
er
o
f
p
i
x
e
ls are foun
d.
Th
en,
an
u
p
h
ill m
o
v
e
is m
a
d
e
to
ward
s t
h
e
b
i
n
with larg
er
n
u
m
b
e
r
o
f
p
i
x
e
ls.
4.
The
uphill is c
ontinue
d
until reachi
n
g
a bin from
where
there
is no pos
sible hill m
ove
ment. That
is the
case whe
n
t
h
e
nei
g
h
b
o
ri
n
g
b
i
ns have sm
al
ler num
ber o
f
pi
xel
s
t
h
a
n
t
h
e curre
nt
bi
n
.
H
e
nce t
h
e cur
r
e
n
t
b
i
n
is id
en
tified
as p
e
ak
represen
ting
lo
cal m
a
x
i
m
u
m
.
5.
If
no
up
h
ill mo
v
e
is
do
n
e
, the stop
p
i
n
g
b
i
n is id
en
tified as a
p
e
ak
o
f
a
h
ill, and
all
b
i
n
s
lead
ing
t
o
t
h
is
peak are
ass
o
ciated with it.
St
ep 2:
Sel
ect
anot
he
r u
n
cl
i
m
bed bi
n as a st
art
i
ng bi
n a
nd
per
f
o
r
m
step 1 t
o
an
ot
h
e
r peak
. Thi
s
st
ep i
s
cont
i
n
ue
d
unt
i
l
al
l
t
h
e n
o
n
zer
o
bi
ns
o
f
t
h
e
hi
st
og
ram
are cl
i
m
bed.
St
ep
3:
Th
res
h
ol
di
n
g
:
Fi
nd t
h
e pea
k
s
wh
ose
val
u
e i
s
hi
g
h
e
r
t
h
an
o
n
e
perc
ent
o
f
t
h
e m
a
xi
m
u
m
peak (w
h
i
ch i
s
id
en
tified as l
o
cal
m
a
x
i
m
u
m
i
n
step
1
an
d 2).
Step 4: Re
m
o
ve the peaks which are
ve
ry
cl
ose. Thi
s
i
s
do
ne by
chec
k
i
ng t
h
e di
f
f
ere
n
ce bet
w
ee
n t
h
e gre
y
l
e
vel
s
of t
h
e t
w
o i
ndi
vi
d
u
al
peaks
.
I
f
t
h
e
di
ffe
rence
is
less th
an
20
, t
h
en
t
h
e p
e
ak
with
lowest valu
e is
rem
oved.
St
ep
5:
Nei
g
h
b
o
r
i
n
g
pi
xel
s
t
h
at
l
ead t
o
t
h
e
sam
e
peak are
gr
o
upe
d t
oget
h
er.
Step
6
:
Th
e iden
tified
p
e
ak
s
represen
t th
e i
n
itial n
u
m
b
e
r
o
f
clu
s
ters
o
f
t
h
e inpu
t im
ag
e. Th
u
s
th
e nu
mb
er and
values
of the
peaks a
r
e sa
ve
d.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Clu
s
terin
g
Algo
rithm Comb
ined
with
Hill Climb
i
ng
f
o
r Classifica
tio
n
o
f
Remo
te …
(B.
Sa
icha
nda
na
)
92
5
3.
K-
MEA
N
S C
L
USTERI
N
G
ALGO
RITH
M
K-m
eans i
s
on
e of t
h
e basi
c
cl
ust
e
ri
n
g
m
e
tho
d
s i
n
t
r
o
duce
d
by
Hart
i
g
an
[9]
.
T
h
i
s
m
e
t
hod i
s
use
d
t
o
gr
o
up
dat
a
t
o
t
h
e
nearest
ce
nt
re. T
h
e m
e
t
h
o
d
i
s
num
er
ical, un
sup
e
rv
ised
,
n
ond
eterm
i
n
i
st
ic an
d iterativ
e. The
K-m
eans clust
e
rin
g
alg
o
rit
h
m
for
classific
a
tion
of rem
o
te sensi
n
g im
age
is summ
arized as follows:
In
p
u
t
:
N:
num
ber o
f
pi
xel
s
t
o
be cl
ust
e
red;
x={x
1
, x
2
, x
3
, ……,
x
N
}:
pi
x
e
l
s
of rem
o
t
e
sensi
n
g im
age;
c = {c
1
,
c
2
, c
3
,….
,
c
j
}cl
u
sters
res
p
ectively.
Ou
t
p
u
t: cl: cluster of
p
i
x
e
ls
Step
1
:
Nu
m
b
er
o
f
cl
u
s
ters and
cluster cen
t
ro
id
s are
d
e
termin
ed
b
y
h
ill cli
m
b
i
n
g
algo
rit
h
m
.
Step
2: com
pute the cl
osest
cluster
for each
p
i
x
e
l an
d
classify it to
th
at clu
s
ter, ie: th
e obj
ectiv
e is to
m
i
nim
i
ze t
h
e s
u
m
of s
qua
res
of
t
h
e
di
st
ance
s gi
ven
by
t
h
e
fol
l
o
wi
n
g
:
∆
ij
= ||
x
i
-c
j
||
.
ar
g
mi
n
C
j
N
i
1
1
∆
ij
2
(1
)
Step 3: Com
p
ute new cent
r
oi
ds after all the pixels are
clustered.
The new centroids of
a cluster
is
calculated
b
y
th
e fo
llo
wi
ng
c
j
=
x
i
wh
ere x
i
bel
o
ngs
t
o
c
j
(2
)
Step
4
:
Rep
eat
step
s
2
-
3
till the su
m
o
f
squ
a
res g
i
v
e
n in
equatio
n
is m
i
n
i
mized
.
4.
MO
VING K-MEANS CL
USTERING AL
GORITHM
The M
o
vi
n
g
K
-
m
eans cl
ust
e
ri
ng al
g
o
ri
t
h
m
is t
h
e
m
odi
fi
ed
versi
o
n o
f
K-
m
eans pr
op
ose
d
i
n
[1
0]
. It
introduces the
conce
p
t of fitn
ess to ens
u
re t
h
at each cluste
r should ha
ve a
significa
nt num
ber of m
e
m
b
ers and
fin
a
l fitn
ess
valu
es
b
e
fo
re th
e
n
e
w po
sitio
n of cl
u
s
ter
is calcu
lated
.
Th
e M
o
v
i
n
g
K-m
ean
s clu
s
t
e
ring
alg
o
rith
m
fo
r classificatio
n
o
f
rem
o
te sen
s
ing
im
ag
e is su
mmarized
as
fo
ll
o
w
s:
In
p
u
t
:
N:
num
ber
o
f
pi
xel
s
t
o
be cl
ust
e
re
d;
x
=
{x
1
, x
2
, x
3
, ……,
x
N
}:
pi
xel
s
of
rem
o
t
e
sensi
n
g
i
m
age.
c = {c
1
, c
2
, c
3
, ….,
c
j
} : clu
s
ters resp
ectiv
ely.
Ou
t
p
u
t: cl: cluster of
p
i
x
e
ls
Step
1
:
Nu
m
b
er
o
f
cl
u
s
ters and
cluster cen
t
ro
id
s are
d
e
termin
ed
b
y
h
ill cli
m
b
i
n
g
algo
rit
h
m
.
Step
2: com
pute the cl
osest
cluster
for each
p
i
x
e
l an
d
classify it to
th
at clu
s
ter, ie: th
e obj
ectiv
e is to
m
i
nim
i
ze t
h
e s
u
m
of s
qua
res
of
t
h
e
di
st
ance
s gi
ven
by
t
h
e
fol
l
o
wi
n
g
:
∆
ij
= ||
x
i
-c
j
||
.
ar
g
mi
n
C
j
N
i
1
1
∆
ij
2
(3
)
Step
3: T
h
e fit
n
ess
for eac
h c
l
uster is calc
u
lated using
f (c
k
) =
k
c
t
( || x
t
-c
k
|| )
2
(4
)
Th
e
relatio
n
s
h
i
p
am
o
n
g
th
e
cen
t
ers m
u
st satisfy th
e
fo
llo
wi
n
g
cond
itio
n
:
f (c
s
)
≥
α
a
f(c
l
)
(5
)
whe
r
e
α
a
is s
m
all co
n
s
tan
t
v
a
l
u
e in
itially
with
v
a
lu
e in
range 0
<
α
a
<1/3, c
s
and c
l
are the centers that ha
ve the
sm
a
llest an
d
the larg
est
fitn
ess v
a
lu
es.
If
(5)
is n
o
t
fu
l
f
illed
,
th
e m
e
m
b
ers o
f
c
l
a
r
e assi
gned as m
e
m
b
ers of c
s
,
wh
ile th
e rest
are m
a
in
tain
ed
as th
e m
e
m
b
ers of c
l
.
The
p
o
s
i
t
i
ons
of c
s
and
c
l
are
recalcula
ted according t
o
:
C
s
=
1/n
cs
(
s
c
t
t
x
)
(6
)
C
l
= 1
/
n
cl
(
l
c
t
t
x
)
(7
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJECE Vol. 4, No. 6, D
ecem
ber 2014
:
923 – 930
92
6
The value
of
α
a
i
s
t
h
e
n
up
dat
e
d acc
or
di
n
g
t
o
:
α
a
=
α
a
-
α
a
/n
c
(8
)
Th
e abo
v
e
process are
rep
eated
u
n
til (5
) is fu
lfilled
.
Nex
t
all d
a
ta are
reassig
n
e
d
t
o
th
eir
n
earst cen
t
er an
d th
e
new cente
r
pos
itions are
recal
culated
using
(2).
Step
4
:
Th
e iteratio
n pro
c
ess i
s
rep
eated
un
til th
e
fo
llowing
co
nd
itio
n is sat
i
sfied
.
f (c
s
)
≥
α
a
f(c
l
)
(9
)
5.
FUZ
Z
Y
C-M
E
ANS
CL
US
TERING
AL
GOR
ITHM
The fuzzy c-means [11] is an
uns
up
er
vi
se
d cl
ust
e
ri
n
g
al
g
o
ri
t
h
m
.
Th
e
m
a
in
id
ea o
f
in
t
r
odu
cing
fu
zzy
conce
p
t in the
fuzzy c-m
eans algorithm
is that an object can bel
o
ng simu
ltan
e
ou
sly to
m
o
re th
an
on
e class
and
does s
o
by varying degrees called m
e
m
b
erships.
It
d
i
stribu
tes th
e
me
m
b
ersh
ip
valu
es in
a
no
rmalized
f
a
sh
i
o
n.
I
t
do
es no
t r
e
qu
ir
e
p
r
io
r
kn
ow
ledg
e
ab
ou
t th
e data
to
b
e
classif
i
ed. I
t
can
b
e
u
s
ed w
ith
an
y
n
u
m
b
e
r of
feature
s
and
num
b
er of class
e
s. The
fu
zzy
c-m
ean
s is an
iterativ
e
m
e
th
od
wh
ich tries to
sep
a
rate th
e
set o
f
d
a
ta in
t
o
a
num
b
e
r o
f
co
m
p
act clu
s
ters. It i
m
p
r
o
v
e
s t
h
e
p
a
rtitio
n
p
e
rforman
ce an
d rev
e
als th
e classificatio
n
o
f
o
b
j
ects m
o
re reason
ab
le. Th
e p
r
ed
efin
ed
p
a
ram
e
ters su
ch
as n
u
m
b
e
r o
f
clu
s
ters and
in
itial clu
s
terin
g
cen
ters
are
p
r
o
v
i
d
e
d
b
y
Hill clim
b
i
n
g
algo
rith
m
o
n
th
e h
i
stogra
m
o
f
rem
o
te sen
s
ing
im
ag
e. Th
e fu
zzy c-mean
s
alg
o
rith
m
is su
mmarized
as fo
llo
ws:
In
p
u
t
:
N=
num
ber
o
f
pi
xel
s
t
o
be cl
ust
e
re
d;
x
= {x
1
, x
2
, .
..,
x
N
}:
pi
xel
s
of
re
m
o
t
e
sensi
ng i
m
age;
c ={c
1
, c
2
, c
3
, ….,
c
j
}
: cluste
rs respectively;
m=2: the fuzzi
ness
pa
ram
e
ter
;
Out
put
:
m
e
m
b
ershi
p
val
u
es
o
f
pi
xel
s
a
n
d
cl
u
s
t
e
red
Im
age
Step
_1
: In
itiali
ze th
e
m
e
m
b
ersh
ip
m
a
trix
u
ij
is a v
a
lu
e in
(0
,1
) an
d
th
e
fu
zzin
ess p
a
ram
e
te
r m (
m
=2
). The su
m
of al
l
m
e
m
b
er
shi
p
val
u
es
of
a pi
xel
bel
o
n
g
i
n
g t
o
cl
ust
e
r
s
sh
oul
d sat
i
s
f
y
t
h
e const
r
ai
nt
ex
presse
d i
n
t
h
e
fo
llowing
.
c
j
1
u
ij
=1
(1
0)
for all i=
1
,
2
,
…….N, wh
ere c is th
e nu
mb
er of cl
u
s
ters and
N is t
h
e
n
u
m
b
e
r
o
f
p
i
xels in
rem
o
te sen
s
ing
im
age.
Step_2: Com
pute the cent
r
oi
d val
u
es for ea
ch cluster c
j
. Each
p
i
x
e
l should
h
a
v
e
a d
e
g
r
ee o
f
m
e
m
b
er
sh
ip
t
o
t
hose
desi
g
n
at
ed cl
ust
e
rs
. S
o
t
h
e goal
i
s
t
o
fi
n
d
t
h
e m
e
m
b
ershi
p
val
u
es
of
pi
xel
s
bel
o
n
g
i
n
g t
o
eac
h cl
ust
e
r.
Th
e al
g
o
rith
m
is an
iterativ
e op
ti
m
i
zatio
n
th
at
m
i
n
i
m
i
zes th
e co
st
fun
c
tion
d
e
fi
n
e
d as
fo
ll
o
w
s:
F=
c
i
N
j
1
1
u
ij
m
|| x
j
-c
i
||
2
(1
1)
whe
r
e u
ij
rep
r
esen
ts th
e m
e
mb
ersh
ip of
p
i
x
e
l x
j
in
t
h
e ith
cl
u
s
ter and
m
is th
e fu
zzin
e
ss
param
e
ter.
Step
_3
: Co
m
p
u
t
e th
e
u
p
d
a
ted
m
e
m
b
ersh
ip
valu
es u
ij
belonging to cl
usters
for each
pi
xel and cl
uster ce
ntroids
according t
o
the give
n
form
ula.
(1
2)
Step
_4
: Rep
eat step
s
2-3 un
til th
e co
st fun
c
tio
n is m
i
n
i
mize
d
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Clu
s
terin
g
Algo
rithm Comb
ined
with
Hill Climb
i
ng
f
o
r Classifica
tio
n
o
f
Remo
te …
(B.
Sa
icha
nda
na
)
92
7
6.
FUZ
Z
Y
MOV
I
NG K-
ME
A
N
S CLU
S
TERIN
G ALGO
RITH
M
In t
h
e Fuzzy
Movi
ng
K-m
eans clustering algorith
m
[11]
, t
h
e m
e
m
b
ershi
p
f
u
nct
i
o
n i
s
u
s
ed i
n
ad
d
ition
t
o
the Eu
clid
ian
d
i
stan
ce to con
t
ro
l t
h
e assi
g
n
men
t
o
f
th
e
me
m
b
ers to
t
h
e
p
r
op
er center. The
p
r
ed
efi
n
ed p
a
ra
m
e
ters
su
ch
as
nu
m
b
er o
f
clu
s
ters
and
in
itial clu
s
terin
g
cen
ters
requ
ired
for clusteri
ng
alg
o
rith
m
are p
r
ov
id
ed
b
y
ex
ecu
tin
g
Hill cli
m
b
i
n
g
m
ech
anis
m
o
n
th
e h
i
st
o
g
ram
o
f
th
e re
m
o
te sen
s
ing
i
m
ag
e.
The Fuzzy
M
o
ving K-m
eans clustering
al
g
o
rith
m
is su
mmarized
as fo
llows:
In
p
u
t
:
N
:
n
u
m
b
er o
f
pi
xel
s
t
o
be
cl
ust
e
red;
x={x
1
,x
2
,x
3
,……,x
N
}:
pi
xel
s
o
f
rem
o
t
e
sensi
n
g
i
m
age;
c
={c
1
,c
2
,c
3
,….
,
c
j
} : clusters
res
p
ectively; m
=
2: the
fuzzines
s
pa
ram
e
ter;
Out
put
:
m
e
m
b
ershi
p
val
u
es
o
f
pi
xel
s
a
n
d
cl
u
s
t
e
red
Im
age
Step
_1
: In
itiali
ze th
e
m
e
m
b
ersh
ip
m
a
trix
u
ij
is a v
a
lu
e in
(0
,1
) an
d
th
e
fu
zzin
ess p
a
ram
e
te
r m (
m
=2
). The su
m
of al
l
m
e
m
b
er
shi
p
val
u
es
of
a pi
xel
bel
o
n
g
i
n
g t
o
cl
ust
e
r
s
sh
oul
d sat
i
s
f
y
t
h
e const
r
ai
nt
ex
presse
d i
n
t
h
e
fo
llowing
.
c
j
1
u
ij
=1
(1
3)
for all i=
1
,
2
,
…….N,
wh
ere c (=2
)
is th
e nu
m
b
er of cl
u
s
ters an
d N is the nu
m
b
er of
p
i
x
e
ls in rem
o
te sen
s
i
ng
im
age.
Step_2: Com
pute the cent
r
oi
d val
u
es for ea
ch cluster c
j
. Each
p
i
x
e
l should
h
a
v
e
a d
e
g
r
ee o
f
m
e
m
b
er
sh
ip
t
o
t
hose
desi
g
n
at
ed cl
ust
e
rs
. S
o
t
h
e goal
i
s
t
o
fi
n
d
t
h
e m
e
m
b
ershi
p
val
u
es
of
pi
xel
s
bel
o
n
g
i
n
g t
o
eac
h cl
ust
e
r.
Th
e al
g
o
rith
m
is an
iterativ
e op
ti
m
i
zatio
n
th
at
m
i
n
i
m
i
zes th
e co
st
fun
c
tion
d
e
fi
n
e
d as
fo
ll
o
w
s:
F=
c
i
N
j
1
1
u
ij
m
|| x
j
-c
i
||
2
(1
4)
whe
r
e u
ij
rep
r
esen
ts th
e m
e
mb
ersh
ip of
p
i
x
e
l x
j
in
t
h
e i
th
cluster and
m
is the
fuzzi
ness
pa
ram
e
ter.
Step
3: T
h
e fit
n
ess
for eac
h c
l
uster is calc
u
lated using
f (
c
k
) =
k
c
t
( || x
t
-c
k
|| )
2
(1
5)
All cen
ters m
u
st satisfy th
e
follo
wing
co
nd
itio
n
:
f(c
s
)
≥
α
a
f(c
l
)
and
m(
c
sk
)>
m
(
c
lk
)
(1
6)
whe
r
e
α
a
is s
m
all co
n
s
tan
t
v
a
l
u
e in
itially
with
v
a
lu
e in
range 0
<
α
a
<1/3, c
s
and c
l
are the centers that ha
ve the
sm
a
llest
an
d
th
e larg
est fitn
ess v
a
lu
es, m
(
c
sk
) i
s
t
h
e
m
e
m
b
ershi
p
val
u
e
of
poi
nt
k acc
or
di
n
g
t
o
t
h
e sm
al
l
e
st
centre a
n
d m
(
c
lk
) is th
e m
e
mb
ersh
ip
v
a
l
u
e
o
f
po
in
t k acco
r
d
i
ng
to
t
h
e l
a
rg
est cen
t
re.
If
(16
)
is no
t fu
lfilled
,
t
h
e
me
mb
e
r
s
o
f
c
l
are assigned as m
e
m
b
er
s of c
s
, wh
ile th
e rest are m
a
in
tain
ed
as th
e
m
e
m
b
ers o
f
c
l
. The
p
o
s
ition
s
of
c
s
and c
l
are recal
culated acc
ordi
ng to:
C
s
=
1/n
cs
(
s
c
t
t
x
)
(1
7)
C
l
=1
/n
cl
(
l
c
t
t
x
)
(1
8)
The value
of
α
a
i
s
t
h
e
n
up
dat
e
d acc
or
di
n
g
t
o
:
α
a
=
α
a
-
α
a
/n
c
(1
9)
Th
e ab
ov
e
process are
rep
eated
u
n
til (1
6) is fu
l
f
illed
.
Ne
x
t
all d
a
ta are
reassig
n
e
d
t
o
th
eir n
e
arest cen
t
e
r and
th
e n
e
w cen
t
er
p
o
s
ition
s
ar
e recalcu
lated
u
s
ing
(2).
C
o
m
put
e t
h
e
u
pdat
e
d m
e
m
b
ershi
p
val
u
es
u
ij
bel
o
n
g
i
n
g t
o
c
l
ust
e
rs
fo
r eac
h
pi
xel
ac
co
rdi
n
g t
o
gi
ven
f
o
r
m
ul
a
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I
S
SN
:
2
088
-87
08
IJECE Vol. 4, No. 6, D
ecem
ber 2014
:
923 – 930
92
8
(2
0)
Step
4
:
Th
e iteratio
n pro
c
ess i
s
rep
eated
un
til th
e
fo
llowing
co
nd
itio
n is sat
i
sfied
.
f (c
s
)
≥
α
a
f(c
l
)
and
m(
c
sk
)>
m
(
c
lk
)
(2
1)
7.
E
X
PERI
MEN
T
AL RES
U
L
T
S
Qual
i
t
ati
v
e A
n
al
ysi
s
:
The p
r
op
ose
d
fo
ur cl
ust
e
ri
n
g
al
gori
t
h
m
s
are per
f
o
r
m
e
d on
a t
w
o rem
o
t
e
sensi
n
g i
m
ages, whi
c
h are
tak
e
n
fro
m
b
h
u
v
a
n
.
nrsc.g
ov
.i
n
[12
]
Clu
s
teri
n
g
algo
rith
m
s
with
an
d withou
t h
ill clim
b
i
n
g
are ex
ecu
ted
o
n
th
e
two
rem
o
te sen
s
ing
im
ag
es.
Th
e classificati
o
n resu
lt of
fuzzy
m
o
v
i
ng
k
-
mean
s clu
s
teri
n
g
algo
rith
m
with
h
ill
cli
m
b
i
n
g
on
t
w
o
im
ag
es is shown in
figu
re 1.
Th
e
h
ill cl
i
m
b
i
n
g
algo
rith
m
is ex
ecu
t
ed
on
the h
i
stog
ram
o
f
two
im
ages. For the first im
age the num
ber of
pe
aks =4 and
for the second imag
e, the num
b
er of
peaks =
3
. Then
th
e clu
s
teri
ng
alg
o
rith
m
is ex
ecu
ted
with
t
h
e
id
en
tified nu
mb
er of clusters
an
d in
itial cen
t
r
o
i
d
s
.
Qua
n
ti
t
a
ti
ve An
al
ysi
s
:
Qu
an
titativ
e an
alysis is a
n
u
m
erically o
r
ien
t
ed pro
c
edu
r
e to
figu
re ou
t th
e
p
e
rfo
r
m
a
n
ce of
alg
o
rith
m
s
with
ou
t an
y
h
u
m
an
erro
r.
In th
e
classifica
tion
map the class
e
s are
labe
led
with
d
i
fferen
t co
lors.
Tabl
e 1 sh
ow
s t
h
e cl
assi
fi
cat
ion acc
uracy
o
f
di
ffere
nt
cl
ust
e
ri
n
g
m
e
t
hods
on t
w
o rem
o
t
e
sensi
n
g i
m
ages. The
results confi
r
m that Fuzzy Moving K-
m
eans
al
go
ri
t
h
m
prod
uces hi
ghest
cl
a
ssification ac
curacy in class
i
fying
th
e rem
o
te sensin
g im
ag
e.
As t
h
e in
itial cen
t
ro
id
s
req
u
i
red
for cl
u
s
tering
algorith
m
s
are d
e
term
in
ed
by Hill cli
m
b
i
n
g
alg
o
rith
m
,
th
e nu
m
b
er of iterativ
e steps requ
ired
for classifyi
n
g
the o
b
j
ects is red
u
c
ed
.
While th
e in
itial cen
tro
i
ds
o
b
t
ain
e
d
b
y
h
ill cli
m
b
i
n
g
are
u
n
i
q
u
e
, th
e classified
resu
lt
is
m
o
re stab
le com
p
ared
with
trad
itio
n
a
l algo
ri
th
m
s
.
Tab
l
e
2
sh
ows th
e co
m
p
ariso
n
of iterativ
e step
s
nu
m
b
er
s fo
r cl
u
s
teri
ng
algorith
m
s
with
an
d witho
u
t
Hill
cl
im
bi
ng.
Tabl
e
2. C
o
m
p
ari
s
o
n
of
i
t
e
rat
i
v
e st
e
p
num
ber
s
Clustering
algorithm
Iterative steps
(without hill
clim
bing)
Iterative steps
(with hill
clim
bing)
IMA
G
E 1
K-
m
e
ans 33
16
M
oving K-m
eans
40
19
Fuzzy k-
m
eans
55
28
Fuzzy
M
oving
K-
m
e
ans
62
38
Clustering
algorithm
Iterative steps
(without hill
clim
bing)
Iterative steps
(with hill
clim
bing)
IMA
G
E 2
K-
m
e
ans 43
23
M
oving K-m
eans
58
32
Fuzzy k-
m
eans
72
41
Fuzzy
M
oving
K-
m
e
ans
89
49
Tabl
e 1.
C
l
assi
fi
cat
i
on Ac
c
u
racy in Pe
rcenta
ges
Method
(IMAGE 1)
(IMAGE 2)
K-means 81
84
Moving K-means
86
89
Fuzzy
K-means
89
92
Fuzzy
Moving
K-means
92
94
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Clu
s
terin
g
Algo
rithm Comb
ined
with
Hill Climb
i
ng
f
o
r Classifica
tio
n
o
f
Remo
te …
(B.
Sa
icha
nda
na
)
92
9
Im
age 1
Fuzzy M
ovi
ng
K-m
eans (Num
ber of cl
usters =4)
B
r
o
w
n:
Wat
e
r
,
B
l
ue:
Sa
nd
, O
r
an
ge:
Gree
n
a
r
ea, Sky
bl
ue:
Ho
uses
Im
age 2
Fuzzy M
ovi
ng
K-m
eans (Num
ber of cl
usters =5)
Orang
e
: Trees, Brown
:
W
a
ter,
Blu
e
:
Hill to
p, Sk
yb
lu
e:
Houses
, Gree
n:
Roadway
Fi
gu
re 1.
cl
assi
fi
cat
i
on res
u
l
t
s
8.
CO
NCL
USI
O
N
Thi
s
pa
pe
r has
prese
n
t
e
d
f
o
u
r
cl
ust
e
ri
ng al
go
ri
t
h
m
s
nam
e
l
y
K-m
eans, M
ovi
ng
K-m
eans, F
u
zzy
K-
mean
s
and
Fuzzy Mo
v
i
n
g
K-m
ean
s co
m
b
in
ed
with
h
ill
cli
m
b
i
n
g
for th
e classificatio
n
o
f
rem
o
te sen
s
ing
i
m
ag
e. Th
e qu
alitativ
e and qu
an
titativ
e
an
alysis do
n
e
prov
ed
th
at
Fu
zzy M
o
v
i
n
g
K-m
ean
s h
a
s h
i
gher
classificatio
n
q
u
a
lity th
an
oth
e
r clu
s
teri
n
g
alg
o
r
ith
m
s
. Clu
s
tering
alg
o
rith
m
co
m
b
in
ed
with
h
ill cli
m
b
i
n
g
o
v
e
rco
m
es th
e p
r
ob
lem
o
f
ran
d
o
m
selecti
o
n of
n
u
m
b
e
r o
f
clu
s
ters an
d in
itializatio
n
o
f
cen
t
ro
id
s. Th
e
pr
o
pose
d
m
e
t
hod
re
duce
s
t
h
e
n
u
m
b
er of
i
t
e
rat
i
ons
f
o
r cl
assi
fy
i
ng a
re
m
o
t
e
sensi
ng i
m
age an
d c
o
st
s l
e
ss
ex
ecu
tion
tim
e
.
REFERE
NC
ES
[1]
Yi Ma, Jie Zh
ang, Yufeng Gao
,
“High
Resolution Remote Sensing Image Clas
s
i
fication of Co
astal Zon
e
and its
Autom
a
tic Rea
l
i
zat
ion”,
International Conference on Computer
Scien
ce and Software Engineering,
pp. 827-829
2008 IEEE.
[2]
Xiaofang Liu, X
i
aowen Li, Ying
Zha
ng, Cunjian
Yang, Wenbo Xu, Min Li, Hu
an
min Luo, “Remote Sensing Imag
e
Classification U
s
ing Function Wei
ghted FCM Clustering Algorithm”,
Internation
a
l Geoscien
ce a
nd Remote S
e
nsing
Symposium
, pp.
2010-2013, 200
7 IEEE.
[3]
Penglin Zhang
,
Zhiy
ong Lv
, Lip
e
ng Gao and Li
Huang, “A
New Framework of the unsupervised
Classification fo
r
High-Resolution
Remote Sensing Image”,
Telko
m
nika Indonesia
n
Journal
of Electrical
Engineering
, Vol 10, No 7,
November 2012, pp. 1746-1755.
[4]
D. Lu, Q. W
e
ng, “
A
S
u
rvey of im
age clas
s
i
fica
ti
on meth
ods and techniques fo
r impro
v
ing classification
perform
ance
”,
I
n
ternational Jou
r
nal of
Remote s
e
nsing
, Vol 28,
No. 5, 10 Mar
c
h
2007, pp. 823-8
70.
[5]
J
o
s
e
f Cihlar, R
a
s
i
m
Latifov
ic,
J
ean Beaub
i
e
n
, “
A
Co
mparison of Clustering Stra
tegies f
o
r Unsupervised
Cla
ssifica
tion”
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Canadian Journ
a
l of Remote S
e
n
s
ing
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u
e
5, pp. 446-45
4.
[6]
A
y
kut AKGÜN
,
A.
Hüsnü ERONAT and Necdet TÜRKa,
“C
omparing different satell
ite image
classification
methods: an application in ay
v
a
lik di
strict, western, Turkey
”, ISPRS Arch
ives- V
o
lume XXXV
Part B4, 2004, pp
.
1091-1097.
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ecem
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0
[7]
Zhengji
a
n DING, Juanjuan JIA,
DIA LI, “Fast Clusteri
ng Segm
en
tation M
e
thod C
o
m
b
ining Hill C
lim
bing for Colo
r
Image”, Journal
of Information
and Com
putation
a
l Sciences, Vo
l
8, pp
. 2949-295
7.
[8]
Takumi OHASHI, Zah
e
r AGHBARI, Akifumi MAKINOUCHI,
“Hill Climbing
algorithm for
Ef
ficient Color
bas
e
s
Im
age S
e
gm
enta
tion”
,
Signa
l Processing, Patt
ern Recogn
ition
and
Appl
icat
ions
, 01
/2003.
[9]
J. A. Har
tig
an an
d M. A. Wong,
“
A
K-means clustering
algorithm”,
App
lied
Sta
tisti
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, 28
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100-108.
[10]
Siti Narain
i Sula
im
an, Nor Ashidi Mat Isa, “
D
enoising ba
sed Clu
t
ering Algori
t
hm
s for Segm
entati
on of Low level
of S
a
lt and
P
e
pper Noise Cor
r
upted Im
ages”
,
IEEE
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sa
ct
ions on Consum
er Elec
troni
cs, Vol. 56
, No
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November 2010, pp 2702-2710
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[11]
Nor Ashidi Mat Isa,
Sam
y
A.Sala
mah, Umi
Kalthum Ngah, “Adaptive
Fuzzy
Moving K-means Clusterin
g
Algorithm for I
m
age Segmentation”,
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umer
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tr
oni
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53.
[12]
www.bhuvan.nr
sc.gov.in
BIOGRAP
HI
ES OF
AUTH
ORS
B. Saichandan
a
received
B.Tech and
M.Te
ch
degree from JNTU H
y
der
a
bad and Andhra
University
in the
y
ear 2005 and 2007 respectively
.
She is currently
workin
g as Assi
stant
profes
s
o
r in the
Departm
e
nt of C
S
E, GIT, Gi
tam
Univers
i
t
y
. H
e
r
res
earch
int
e
res
t
includ
e im
age
classification, pattern
recognition
etc. Currently
s
h
e is
p
e
rsuing ph
d from JNTU Kakinada.
Dr. K. Srinivas receiv
e
d MCA, M.Te
ch a
nd Phd degrees from
Andhra Un
iversit
y
, JNTU
kakinad
a
and Achar
y
a Nagar
j
una
Univers
i
t
y
. His
res
earch
inter
e
s
t
include im
ag
e proces
s
i
ng and
bioinformatics.
Currently
he
is working as Pr
ofessor, Department of Compu
t
er science
and
Engineering, VR
Siddharth
a
Engi
neering
College, Vijay
a
w
a
da.
Dr. R. Kiran
ku
mar received M
C
A, M.Tech an
d Phd degrees f
r
om Andhra University
, JNTU
kakinad
a
and Achar
y
a Nagar
j
una
Univers
i
t
y
. His
res
earch
inter
e
s
t
include im
ag
e proces
s
i
ng and
bioinformatics.
Currently
he
is working as assist
ant Professor, d
e
partment
of Co
mputer science,
krishna Universi
t
y
, Ma
chil
ipa
t
na
m
.
Evaluation Warning : The document was created with Spire.PDF for Python.