Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l.
6, N
o
. 5
,
O
c
tob
e
r
201
6, p
p
. 2
188
~219
6
I
S
SN
: 208
8-8
7
0
8
,
D
O
I
:
10.115
91
/ij
ece.v6
i
5.1
068
2
2
188
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
Image S
e
gm
entation B
a
s
e
d on
Doubly Truncated Generalized
Laplace Mixture Model and K Means Clustering
T. Jyo
t
h
irmayi
1
,
K. Sriniva
s
a
Rao
2
, P. Sri
n
i
vas
a R
a
o
3
, Ch.
S
a
t
y
a
n
ar
ay
an
a
4
1
Department of Computer
Scien
ce a
nd
Engineering, GITAM University
, Vi
sakhapatnam, Andhra
Pradesh, Ind
i
a
2
Department of Statistics,
Andhr
a
Univers
ity
, Visakhapatnam, An
dhra Pradesh
,
In
dia
3
Department of Computer
Scien
ce and
S
y
s
t
ems
Engineering, An
dhra University
,
Vi
sakhapatn
am,
Andhra Pradesh, India.
4
Department of Computer
Scien
ce and Engineering,
JNTU-Kakin
ada, Andhra Pradesh, India
Article Info
A
B
STRAC
T
Article histo
r
y:
Received
Mar 30, 2016
Rev
i
sed
Ju
l 30
,
20
16
Accepted Aug 17, 2016
The pr
esent paper aims at p
e
r
f
orma
nce
evalu
a
tion
of Doubly
Truncated
Generalized Lap
l
ace Mixtur
e Mo
del
and K-Mean
s cluster
i
ng (DTGLMM-K)
for im
age an
al
ys
is
concerned
to
various
prac
tic
al app
lic
ations
l
i
ke s
ecur
i
t
y
,
surveillance, medical diagnostics
and other areas. Among the man
y
algorithms desig
n
ed and
develop
e
d for
image seg
m
entation
the do
minance of
Gaussian Mixture Model (GMM)
has been predo
m
inant which has the major
drawback o
f
suiting to
a par
ticu
l
ar ki
nd
of d
a
ta
.
Therefor
e
the
pr
es
ent work
aims at d
e
velop
m
ent of DTGLMM-K algorith
m which can
be suitable fo
r
wide variety
o
f
applications
and
data. Perf
ormance evaluation of the
develop
e
d algo
rithm has been done
throug
h various measures like
Probabilisti
c Rand index (PRI), Global Con
s
istenc
y Error
(GCE) and
Variat
ion of Inf
o
rm
ation (VOI). During the cur
r
ent work cas
e
s
t
udies
for
various differ
e
nt images having
pixel in
tensities
has been carried
out and the
obtain
e
d results
indicate
the s
uperi
ority
of th
e developed
algorithm for
improved image
segmentation
.
Keyword:
Double truncat
ed
gene
ralized
Laplace m
i
xture m
odel
Gene
ralized La
place
m
i
xture
m
odel
Im
age segm
entation algorithm
Perform
a
nce measure
s
Copyright ©
201
6 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
:
T. Jy
ot
hi
rm
ay
i
,
Depa
rt
m
e
nt
of
C
o
m
put
er Sci
e
nce a
n
d
E
ngi
n
eeri
n
g,
GIT
A
M
Uni
v
e
r
sity
,
Vi
sak
h
a
p
at
na
m
,
And
h
ra
Pra
d
es
h,
In
di
a.
Em
ail: koka.jy
o
thir
m
a
yi@gm
a
il.com
1.
INTRODUCTION
Im
ag
e seg
m
en
t
a
tio
n
aim
s
a
t
i
d
en
tifying
th
e
reg
i
o
n
s
o
f
in
terest in
an
im
ag
e o
r
anno
tatin
g th
e d
a
ta o
f
an im
age. It is the proces
s to
classify an
im
a
g
e in
to
sev
e
ral
clu
s
te
rs acc
ording to t
h
e feat
ure of im
age. Image
segm
ent
a
t
i
on t
echni
que
s are
base
d o
n
s
o
m
e
pi
xel
o
r
re
gi
on si
m
i
l
a
ri
ty
m
easures i
n
re
l
a
t
i
on t
o
t
h
ei
r
l
o
cal
nei
g
hb
o
r
h
o
o
d
.
Segm
ent
a
t
i
on t
echni
que
s are
br
oa
dl
y
cl
assi
fi
ed as regi
on
b
a
sed, e
dge
bas
e
d, t
h
resh
ol
d
b
a
sed
and m
odel
ba
sed [
1
]
-
[
4
]
.
A
m
ong t
h
ese
m
odel
base
d se
gm
ent
a
t
i
on algo
ri
t
h
m
s
are fou
n
d
t
o
be ef
fi
ci
ent
com
p
ared to other
[5].
In m
odel
base
d, e
n
tire im
age
is viewed as a
col
l
ection of im
a
g
e re
gions a
nd each
i
m
ag
e reg
i
o
n
is ch
aracterized b
y
a
prob
ab
ilit
y d
i
stribu
tio
n fu
n
c
tion
of
p
i
x
e
ls.
The pixel intensity
is conside
r
ed
as a feature com
pone
nt of the im
ag
e. The pixel intensities in im
age
may b
e
m
e
so
k
u
rtic, p
l
aty ku
rtic, lep
t
o
kurtic, sy
mm
et
ric and
asymme
tric. The e
ffici
ency of se
gm
e
n
tation
alg
o
rith
m
d
e
p
e
n
d
s on
prob
ab
ility d
i
strib
u
tio
n
fo
llowed
b
y
th
e p
i
x
e
ls
in
an
im
ag
e. Mu
ch
work
has b
e
en
repo
rted
co
nsid
eri
n
g th
e
p
i
x
e
l in
ten
s
ities fo
llo
w a Gau
ssian d
i
stribu
tion
and
v
a
riates
o
f
fi
n
ite GMM.
Zha
oxi
a F
u
et
al
[6]
p
r
op
ose
d
an i
m
age seg
m
ent
a
t
i
on m
e
tho
d
w
h
i
c
h
use
d
G
a
ussi
a
n
M
i
xt
u
r
e M
o
del
s
to
m
o
d
e
l th
e o
r
ig
in
al im
ag
e
an
d
tran
sform
s
th
e seg
m
en
tat
i
o
n
p
r
o
b
l
em
in
to
m
a
x
i
m
u
m li
k
e
lih
ood
p
a
rameter
estim
a
tion by
expectation-maxim
i
zat
ion(EM algorithm) a
n
d classify
th
e
p
i
x
e
ls in i
m
ag
e. Th
anh
Minh
Nguyen et al [7] propose
d a
mixture m
odel for im
age
segmen
tatio
n
wh
i
c
h
in
corpo
r
ated
sp
atial in
fo
rmation
b
e
tw
een
n
e
i
g
hb
or
ing
p
i
x
e
ls in
to
th
e
G
a
ussian
m
i
x
t
u
r
e
m
o
d
e
l b
a
sed
on
Mar
k
o
v
r
a
ndom f
i
eld
(
M
RF)
.
EM
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
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Im
ag
e
Seg
m
e
n
t
a
t
i
o
n
B
a
sed
o
n
D
o
u
b
l
y
T
r
u
n
c
a
t
e
d
Ge
ner
a
l
i
z
ed L
a
pl
ace
Mi
xt
ure M
odel
...
.
(
T
. Jy
ot
hi
rm
ay
i)
2
189
alg
o
rith
m
was ap
p
lied
t
o
opti
m
ize th
e p
a
ra
m
e
ters. Nag
e
sh V et al [8]
suggeste
d an approac
h
for
im
age
segm
ent
a
t
i
on o
f
m
e
di
cal im
ages based
on Fi
ni
t
e
Tru
n
cat
ed
Ske
w
Ga
ussi
a
n
di
st
ri
b
u
t
i
o
n.
Vam
s
i
Kri
s
hna
M
et
al
[9]
de
vel
o
pe
d a
segm
ent
a
t
i
o
n
m
odel
f
o
r
b
r
ai
n i
m
ages ba
sed
o
n
bi
va
ri
at
e Ga
ussi
an
di
st
ri
b
u
t
i
o
n
m
odel
wi
t
h
k-m
eans cluste
ring.
Howev
e
r app
licatio
n
o
f
fi
n
ite GMM is accu
rate
and
su
ccessfu
l
fo
r all k
i
nd
s of
p
i
x
e
l in
ten
s
ities
ex
cep
t lep
t
o
ku
rtic d
a
ta. Th
erefo
r
e an
altern
ativ
e i
m
ag
e seg
m
en
tatio
n
alg
o
rith
m
wh
ich can
b
e
app
licab
le to
al
l
ki
nds
o
f
dat
a
i
s
nee
d
ed
an
d t
h
e
p
r
ese
n
t
w
o
r
k
c
once
n
t
r
at
es m
a
inly in this aspect
by means
of
ge
neral
i
zation
o
f
GMM
with resp
ect to
kurto
sis. Jyo
t
h
i
rmayi et al
[10] devel
ope
d a
n
d analyzed a
n
im
age segmentation
algorithm
based on Ge
neraliz
ed Laplace Mixture Model
(GLMM) where the pixel in
tensities lie in ra
nge
of
(-
∞
,
∞
)
.
The
devel
ope
d m
odel
was i
n
t
e
gr
at
ed wi
t
h
hi
er
archi
cal
cl
ust
e
ri
n
g
m
e
t
hod a
nd
use
d
f
o
r i
m
age
segm
ent
a
t
i
on of i
m
ages w
h
i
c
h are
ha
vi
n
g
pl
at
y
k
u
r
t
i
c
an
d l
e
pt
o k
u
r
t
i
c
nat
u
re.
Hi
erar
chi
cal
cl
ust
e
ri
ng
a
n
d
m
o
men
t
m
e
th
od
o
f
esti
m
a
tio
n
was
u
s
ed
fo
r i
n
itializatio
n
o
f
p
a
ram
e
ters.
As an
ex
ten
s
ion
to
t
h
e prev
io
u
s
wo
rk
s, wit
h
in
t
h
e curren
t
work
an attem
p
t is
mad
e
to
ex
tend
th
e
G
L
MM as
D
o
u
b
l
y Tr
un
cated G
L
MM (D
TGLMM)
b
y
truncati
n
g
th
e ran
g
e o
f
p
i
x
e
l in
ten
s
ity v
a
lu
es
wi
th
in
a
sp
ecified rang
e. K-m
ean
s algo
rith
m
is u
s
ed
for in
itializatio
n
o
f
p
a
ram
e
ter
s
sin
ce it is si
m
p
le an
d
works well
for larg
e d
a
ta
sets wh
en
com
p
ared
with
hierarchical clustering. Pe
rf
or
m
a
nce eval
uat
i
on
of t
h
e
dev
e
l
o
p
e
d
m
odel
has
bee
n
ca
rri
ed
o
u
t
b
y
m
eans o
f
a
n
a
l
y
s
i
s
of
va
ri
ous
differe
n
t categories
of im
ages as case
studies.
2.
PROP
OSE
D
METHO
D
In t
h
i
s
pa
per a
n
al
g
o
ri
t
h
m
DTGLM
M
-
K ha
s been
p
r
o
p
o
se
d f
o
r i
m
age segm
ent
a
t
i
on. It
i
s
assum
e
d
that the whole im
age is collection of
im
age regions in which the pi
xel
intensity of each re
gion foll
ows
a
gene
ralized la
place distri
buti
o
n. T
h
e
parameters m
ean, va
riance
of
DT
GLMM are e
s
tim
a
ted through EM
alg
o
rith
m
.
In
it
ializatio
n
o
f
th
e p
a
ram
e
ters
is o
b
t
ain
e
d
by K-Mean
s clu
s
tering
. Im
age an
alysis wit
h
the
devel
ope
d al
g
o
r
i
t
h
m
i
s
perfo
r
m
ed on fi
ve i
m
ages fr
om
Berkeley im
age data set and com
p
ared with existing
alg
o
rith
m
s
av
ailab
l
e in
th
e literatu
re.
2.
1.
Doubly Trunc
ate
d
Ge
nerali
z
e
d Laplace
Distributi
o
n
Im
age seg
m
entation algorithm
s
conside
r
image as
a collection of im
age
regions where each im
age
reg
i
o
n
is represen
ted
b
y
p
i
x
e
l in
ten
s
ities. Fo
r a g
i
v
e
n
po
i
n
t p
i
x
e
l (x, y), th
e p
i
x
e
l in
ten
s
ity z=f(x,y) is
a
rando
m
v
a
riable. It is
g
e
n
e
rallyassu
m
e
d
that th
e p
i
x
e
l in
t
e
n
s
ities with
in th
e reg
i
o
n
lie
in
an infin
ite ran
g
e
.
Assu
m
i
n
g
th
at th
e
p
i
x
e
l in
ten
s
ity lie b
e
tween
‘a’ and
‘b’, t
h
e
p
r
o
b
a
b
ility d
e
n
s
ity fun
c
tion
o
f
t
h
e p
i
x
e
l
in
ten
s
ity is g
i
ven
b
y
f
x,
μ,
σ2
|
|
∑
|
|
w
h
er
ea
,
μ
,
0
(1
)
or
fx,
μ,
σ
2
r
xμ
σ
e
2σ
∑
r
k
r
γ
2k
1
,
aμ
σ
γ
2k
1
,
bμ
σ
Here it is assumed
th
at en
tire i
m
ag
e is co
lle
ctio
n
of
seve
ra
l im
age regions. In eac
h im
ag
e region the
pixel inte
nsities are c
h
a
r
ac
terized
by doubly trun
cated gene
ralized
Laplace probability
m
ode
l.
The
p
r
ob
ab
ility d
e
nsity fu
n
c
tion
of p
i
x
e
l i
n
ten
s
ities in
wh
o
l
e imag
e is
o
f
th
e
form
px
∑
α
f
x
,μ
,σ
(2)
whe
r
e k i
s
t
h
e
num
ber
of re
gi
ons
, 0
≤α
i
≤
1 are weights suc
h
that
Σ
α
i
=1 and
α
i
is the weight associated
with i
th
regi
on i
n
t
h
e
wh
ol
e i
m
age and
f
x,
μ
,
σ
2
)
is the p
r
o
b
ab
ility d
e
nsity fu
n
c
ti
o
n
o
f
Gen
e
ral
i
zed
Lap
l
ace
d
i
str
i
bu
tio
n of
i
th
im
age regi
o
n
a
n
d i
s
as
gi
v
e
n i
n
eq
uat
i
o
n
(1
).
The m
ean of t
h
e distribution i
s
Evaluation Warning : The document was created with Spire.PDF for Python.
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08
I
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Vo
l. 6
,
N
o
. 5
,
O
c
tob
e
r
20
16
:
218
8
–
21
96
2
190
E(X)=
x
f
x
dx
=
μ
+
∑
,
,
∑
,
,
(3)
The
vari
a
n
ce
o
f
t
h
e
di
st
ri
but
i
o
n
i
s
var
(
x
)
=
var
∑
X
=
∑
,
,
,
,
∑
,
,
(4
)
2.
2.
Estima
tion
Of
The
Mo
del P
a
rameters
By EM Algorithm
The estim
a
t
es
of the m
odel param
e
ters are obtained
t
h
rough EM algorithm
.
To obtai
n accurate res
u
lt
it is conside
r
ed that the ra
nge
of
pi
xel inte
nsi
ties is finite in nature
and doubly
truncated generalized Laplace
d
i
stribu
tio
n is
well su
ited.
Its prob
ab
ility d
i
strib
u
tion
fun
c
ti
o
n
is
g
i
v
e
n
in eq
u
a
tion
2
.
Th
e
lik
elihoo
d fun
c
tion
o
f
ob
serv
ation
s
x1
,x2
…
.xn
is
L(
θ
)=
∏
px
,θ
)
(i.e) L(
θ
∏
∑
α
f
x
,μ
,σ
(5
)
Log L
(
θ
∑
log
|
|
∑
|
|
(6)
The
u
pdat
e
d e
quat
i
o
ns
o
f
E
M
al
go
ri
t
h
m
fo
r est
i
m
at
i
ng t
h
e m
odel
param
e
t
e
rs are
∂
∂μi
T
x
,
θ
log
r
x
μ
σ
e
|
|
2σ
∑
r
k
r
x
e
|
|
dx
l
o
g
α
0
Th
is im
p
lies
∑
T
x
,θ
|
|
0
∑
T
x
,θ
|
|
∑
T
x
,θ
=0 (7)
whe
r
e
T
x
,θ
,
∑
,
Fo
r upd
ating
σ
d
i
ffere
ntiate Q
(
θ;
θ
w.
r.t
σ
a
nd
equa
t
e
to
0
Q
(
θ;
θ
0
∂
∂σ
T
x
,
θ
log
r
x
μ
σ
e
|
|
2σ
∑
r
k
r
x
e
|
|
dx
l
o
g
α
0
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Im
ag
e
Seg
m
e
n
t
a
t
i
o
n
B
a
sed
o
n
D
o
u
b
l
y
T
r
u
n
c
a
t
e
d
Ge
ner
a
l
i
z
ed L
a
pl
ace
Mi
xt
ure M
odel
...
.
(
T
. Jy
ot
hi
rm
ay
i)
2
191
x
μ
r
σ
x
μ
σ
x
μ
2σ
1
2σ
∑
r
k
r
bμ
σ
.
b
μ
σ
.e
|
|
aμ
σ
.
a
μ
σ
.e
|
|
∑
r
k
r
x
e
|
|
dx
T
x
,θ
0
whe
r
e
T
x
,θ
,
∑
,
(8
)
sol
v
i
n
g
t
h
e e
q
u
a
t
i
ons
7 a
n
d
8
we ca
n
get
t
h
e
fi
nal
est
i
m
at
es
of
t
h
e
param
e
t
e
rs
μ
and
σ
.
2.
3.
Initia
liza
t
io
n
Of The Pa
ramet
ers B
y
K
Means
Algorithm
Fo
r EM algorith
m
th
e p
a
ram
e
ter
α
an
d t
h
e m
odel
pa
ram
e
t
e
rs
μ
and
σ
h
a
v
e
to b
e
in
itialized
wh
ich
are u
s
u
a
lly consid
ered
as
k
nown. Th
e in
itial v
a
lu
e
for
α
i
=
1/k whe
r
e k
is the
num
b
er
of im
age
regions
.
The k
v
a
lu
e is in
itialized
with
n
u
m
b
er o
f
p
eaks in
h
i
stogr
am o
f
im
ag
e. After
ob
tain
ing
“k
” v
a
l
u
e in
dou
b
l
y
truncated
gene
ralized La
place m
odel the estim
a
tion of
m
odel param
e
ters is done
by EM algorit
hm
. The
initial estim
a
tes of m
odel param
e
ters are obtaine
d
t
h
rough K-Means
a
l
gorith
m
and m
o
m
e
nt
m
e
thod of
estim
a
tors for doubly truncated ge
neralized Laplace m
i
xture m
odel. The
sha
p
e pa
ram
e
ter r ca
n be esti
mated
by
sam
p
l
e
ku
rt
osi
s
usi
n
g t
h
e f
o
l
l
o
wi
ng
eq
uat
i
on
β
∑
∑
,
,
∑
∑
,
,
∑
r
k
r
γ
2k
1
,
γ
2k
1
,
(9
)
The m
ean of t
h
e distribution i
s
x
μ
∑
,
,
∑
,
,
(1
0)
and
σ
2=
∑
,
,
,
,
∑
,
,
(
1
1)
wi
t
h
k
n
o
w
n va
l
u
es of a an
d b
sol
v
i
n
g eq
uat
i
ons
9,
10 a
nd 1
1
sim
u
l
t
a
neo
u
s
l
y
by
Newt
on
R
a
phs
o
n
M
e
t
hod t
h
e
param
e
ters
μ
and
σ
ar
e
o
btained
. W
i
t
h
th
ese in
i
tial esti
mates
fin
a
l esti
m
a
tes
are ob
tain
ed
th
ro
ugh
EM
alg
o
rith
m
as g
i
v
e
n in
sectio
n
3
.
2.
4.
Segme
n
t
a
ti
on Al
g
o
ri
thm
After
refi
n
i
ng
th
e p
a
ram
e
ters
th
e n
e
x
t
step
is to
seg
m
en
t th
e im
ag
e b
y
allo
catin
g
th
e
pix
e
ls to
the
segm
ent
s
. Thi
s
ope
rat
i
on i
s
perf
o
r
m
e
d by
segm
ent
a
ti
on al
go
ri
t
h
m
.
The i
m
age segm
ent
a
t
i
on al
go
ri
t
h
m
co
nsists of
f
our
steps.
St
ep
1:
U
s
i
n
g
K-M
e
a
n
s al
go
r
i
t
h
m
at
t
a
i
n
t
h
e
num
ber
of
i
m
age
regi
ons
.
Step
2
:
Acqu
ire th
e in
itial estimates o
f
th
e mo
d
e
l
p
a
ram
e
ter
s
u
s
i
n
g K-Mean
s al
g
o
rith
m
.
St
ep 3:
Usi
n
g t
h
e EM
al
gori
t
hm
wi
t
h
updat
e
d eq
uat
i
o
n
s
, f
i
nd t
h
e re
fi
ne
d
est
i
m
a
t
e
s of t
h
e m
odel
para
m
e
t
e
rs
α
i,
μ
i,
σ
i2
fo
r
i=
1
,
2
…
.k
.
Step
4: Alloc
a
te each
pi
xel into the c
o
rres
pondi
ng j
th
r
e
g
i
on
acco
r
d
i
ng
t
o
th
e m
a
x
i
m
u
m
lik
elih
o
od of
t
h
e
j
t
h
com
pone
nt
L
j
.
That is z
s
is
assig
n
e
d
to th
e j
th
regi
on
f
o
r
w
h
i
c
h L
i
s
m
a
xim
u
m
.
Lm
a
x
∑
|
|
(1
2)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE
Vo
l. 6
,
N
o
. 5
,
O
c
tob
e
r
20
16
:
218
8
–
21
96
2
192
3.
RESULTS
A
N
D
DI
SC
US
S
I
ON
For c
o
nd
uct
i
n
g
t
h
e expe
ri
m
e
nt
at
i
on ran
d
o
m
l
y
fi
ve
im
ages were take
n from Berkeley image dataset
(www.eecs.be
r
keley.edu/Rese
arch/P
rojects/
CS/vision/
bs
ds
/BSDS300/h
tml/dataset/images.htm
l
). Image
co
nsists of
K
i
m
ag
e reg
i
o
n
s and
i
n
itial v
a
lu
e of
K is obtain
e
d
b
y
h
i
sto
g
ram
o
f
p
i
x
e
l in
ten
s
ities. Th
e
five
im
ages and the
i
r res
p
ective
hi
stog
r
a
m
s
ar
e sh
own
in Figur
e 1
.
Im
age
Histo
g
ram
Figure
1. Im
ages and c
o
rres
ponding
Histogra
m
s
Based
o
n
h
i
stog
ram
s
th
e in
itial esti
m
a
tes fo
r five im
ag
es h
a
v
e
b
een
ob
tain
ed. Th
e m
o
d
e
l p
a
ram
e
ters
considere
d
are
α
i
,
μ
i
and
σ
i
f
o
r
i=1,2…K
w
h
er
e
K
is the nu
m
b
er
of
r
e
gi
o
n
s a
n
d t
h
e
y
are
obt
ai
ne
d
by
t
h
e
meth
o
d
g
i
v
e
n
in
section
2
.
3
.
Fin
a
l
p
a
ram
e
ters fo
r th
e fi
v
e
im
ag
es h
a
ve b
e
en
d
e
ri
v
e
d
u
s
ing
t
h
ese
in
itial
param
e
t
e
rs and
up
dat
e
d eq
uat
i
ons i
n
sect
i
o
n 2.
2 an
d t
h
e
fi
n
a
l
param
e
t
e
rs and
prese
n
t
e
d i
n
Tabl
es 1
,
2
,
3
,
4 an
d
5.
Tabl
e
1. E
s
t
i
m
a
t
i
on
of
pa
ram
e
t
e
rs f
o
r
Im
age 1
Esti
m
a
t
e
d
Valu
es
o
f
th
e Para
m
e
t
e
rs f
o
r I
m
ag
e1
Nu
m
b
er
o
f
reg
i
o
n
s
(K=3
)
Para
m
e
ters
Esti
m
a
tion of Initi
al Para
m
e
t
e
rs B
y
K Me
ans
E
s
tim
a
tion of Final Par
a
m
e
ter
s
by EM
Algor
ith
m
Region1
Region2
Region3
Region1
Region2
Region3
α
i
0.
33
0.
33
0.
33
0.
0
0.
0499
0.
9501
μ
i
19.
34
85.
56
173.
93
15.
5
63.
23
107.
89
σ
i
15.
86
19.
45
30.
37
8.
53
17.
30
27.
26
a=0 b=255
Tabl
e
2. E
s
t
i
m
a
t
i
on
of
pa
ram
e
t
e
rs f
o
r
Im
age 2
Esti
m
a
t
e
d
Valu
es
o
f
th
e Para
m
e
t
e
rs f
o
r I
m
ag
e2
Nu
m
b
er
o
f
reg
i
o
n
s
(K=3
)
Para
m
e
ters
Esti
m
a
tion of Initi
al Para
m
e
t
e
rs B
y
K Me
ans
E
s
tim
a
tion of Final Par
a
m
e
ter
s
by EM
Algor
ith
m
Region1
Region2
Region3
Region1
Region2
Region3
α
i
0.
33
0.
33
0.
33
0.
19
0.
35
0.
45
μ
i
198.
65
165.
48
113.
61
173.
61
142.
16
93.
80
σ
i
13.
96
12.
77
18.
88
13.
53
18.
3
18.
2
a=34 b=254
Tabl
e
3. E
s
t
i
m
a
t
i
on
of
pa
ram
e
t
e
rs f
o
r
Im
age 3
Esti
m
a
t
e
d
Valu
es
o
f
th
e Para
m
e
t
e
rs f
o
r I
m
ag
e3
Nu
m
b
er
o
f
reg
i
o
n
s
(K=3
)
Para
m
e
ters
Esti
m
a
tion of Initi
al Para
m
e
t
e
rs B
y
K Me
ans
E
s
tim
a
tion of Final Par
a
m
e
ter
s
by EM
Algor
ith
m
Region1
Region2
Region3
Region1
Region2
Region3
α
i
0.
33
0.
33
0.
33
-
0
.
08
-
0
.
12
1.
2
μ
i
103.
69
52.
32
122.
42
110.
55
49.
37
134.
80
σ
i
6.
66
15.
36
6.
88
8.
53
8.
3
8.
26
a=7 b=187
Tabl
e
4. E
s
t
i
m
a
t
i
on
of
pa
ram
e
t
e
rs f
o
r
Im
age4
Esti
m
a
t
e
d
Valu
es
o
f
th
e Para
m
e
t
e
rs f
o
r I
m
ag
e4
Nu
m
b
er
o
f
reg
i
o
n
s
(K=3
)
Para
m
e
ters
Esti
m
a
tion of Initi
al Para
m
e
t
e
rs B
y
K Me
ans
E
s
tim
a
tion of Final Par
a
m
e
ter
s
by EM
Algor
ith
m
Region1
Region2
Region3
Region1
Region2
Region3
α
i
0.
33
0.
33
0.
33
0.
05
0.
32
0.
62
μ
i
113.
39
172.
35
241.
02
193.
86
180.
16
129.
80
σ
i
16.
42
18.
72
14.
30
10.
09
13.
7
10.
27
a=30 b=255
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Im
ag
e
Seg
m
e
n
t
a
t
i
o
n
B
a
sed
o
n
D
o
u
b
l
y
T
r
u
n
c
a
t
e
d
Ge
ner
a
l
i
z
ed L
a
pl
ace
Mi
xt
ure M
odel
...
.
(
T
. Jy
ot
hi
rm
ay
i)
2
193
Tabl
e
5. E
s
t
i
m
a
t
i
on
of
pa
ram
e
t
e
rs f
o
r
Im
age 5
Esti
m
a
t
e
d
Valu
es
o
f
th
e Para
m
e
t
e
rs f
o
r I
m
ag
e5
Nu
m
b
er
o
f
reg
i
o
n
s
(K=3
)
Para
m
e
ters
Esti
m
a
tion of Initi
al Para
m
e
t
e
rs B
y
K Me
ans
E
s
tim
a
tion of Final Par
a
m
e
ter
s
by EM
Algor
ith
m
Region1
Region2
Region3
Region1
Region2
Region3
α
i
0.
33
0.
33
0.
33
0.
3570
0.
6037
0.
0394
μ
i
193.
36
125.
28
53.
88
142.
57
62.
28
34.
80
σ
i
10.
28
19.
88
20.
26
10.
53
18.
30
18.
22
a=5 b=231
Sub
s
titu
tin
g
the fin
a
l esti
m
a
t
e
s o
f
th
e m
o
d
e
l p
a
ram
e
ters
th
e p
r
ob
ab
ility d
e
n
s
ity fu
n
c
tion o
f
th
e p
i
x
e
l
in
ten
s
ities in
each
im
ag
e are
esti
m
a
ted
.
Th
e estim
ated
p
r
ob
ab
ility d
e
nsity fu
n
c
tion
of th
e
p
i
x
e
l i
n
tensities o
f
t
h
e imag
e1 is f(x
,
θ
1
34
.12
1
x
15.
5
8.53
e
.
.
1
69.2
1
x
6
3
.
2
3
17.30
e
.
.
1
109.
04
1
x
107
.89
27
.26
e
.
.
Th
e estim
ated
p
r
ob
ab
ility d
e
nsity fu
n
c
tion
of th
e
p
i
x
e
l i
n
tensities o
f
t
h
e imag
e2 is f(x
,
θ
1
27
.06
1
x
173
.61
13.53
e
.
.
1
36
.6
1
x
142
.16
18
.30
e
.
.
1
36.4
1
x
9
3
.
8
0
18.2
e
.
.
Th
e estim
ated
p
r
ob
ab
ility d
e
nsity fu
n
c
tion
of th
e
p
i
x
e
l i
n
tensities o
f
t
h
e imag
e3 is f(x
,
θ
1
17
.06
1
x
110
.55
8.53
e
.
.
1
16
.6
1
x
49.
37
8.3
e
.
.
1
16.52
1
x
134
.80
8.
26
e
.
.
Th
e estim
ated
p
r
ob
ab
ility d
e
nsity fu
n
c
tion
of th
e
p
i
x
e
l i
n
tensities o
f
t
h
e imag
e4 is f(x
,
θ
1
20
.18
1
x
193
.86
10.09
e
.
.
1
27
.4
1
x
180.
16
13
.7
e
.
.
1
20.54
1
x
129
.80
10
.27
e
.
.
Th
e estim
ated
p
r
ob
ab
ility d
e
nsity fu
n
c
tion
of th
e
p
i
x
e
l i
n
tensities o
f
t
h
e imag
e5 is f(x
,
θ
1
21
.06
1
x
142
.57
10.53
e
.
.
1
36
.60
1
x
6
2
.
2
8
18.30
e
.
.
1
36.44
1
x
3
4
.
8
0
18.
22
e
.
.
Using
th
e prob
ab
ility d
e
n
s
ity fu
n
c
tion
and seg
m
en
tatio
n
alg
o
rith
m
,
seg
m
en
tatio
n
is perfo
r
m
e
d
o
n
following im
ages. T
h
e
ori
g
ina
l
im
ages and
se
gm
ent
e
d i
m
ages are
sh
ow
n
i
n
Fi
gu
re
2.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
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:
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08
I
JECE
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l. 6
,
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o
. 5
,
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c
tob
e
r
20
16
:
218
8
–
21
96
2
194
Fi
gu
re
2.
O
r
i
g
i
n
al
Im
age and
Segm
ented Im
age
Once
t
h
e i
m
age se
gm
ent
a
t
i
on
has
bee
n
per
f
o
r
m
e
d, i
t
s
per
f
o
rm
ance has
bee
n
m
easure
d
by
calcu
latin
g
th
e p
e
rform
a
n
ce metrics
lik
e Prob
ab
ilistic Ra
n
d
Ind
e
x
(PR
I
) g
i
v
e
n
b
y
Un
n
i
k
r
ish
n
a
n
R
et a
l
(2
0
0
7
)
,
Gl
o
b
al
C
onsi
s
t
e
ncy
Err
o
r
(
G
C
E
)
g
i
ven
by
M
a
rt
i
n
D. a
n
d
et
al
and
Va
ri
at
i
on
o
f
I
n
f
o
rm
at
i
on (
V
O
I
)
g
i
v
e
n
b
y
Meila M (2
005
). The stand
a
rd
criteria fo
r m
e
tric
s is th
at PR
I an
d GCE v
a
l
u
es m
u
st lie in
rang
e
0
to
1. T
h
e
per
f
o
r
m
a
nce m
e
t
r
i
c
s fo
r i
m
age seg
m
ent
a
t
i
on m
e
tho
d
base
d o
n
do
u
b
l
y
t
r
u
n
cat
ed ge
ne
ral
i
zed
m
i
xt
ure
m
odel
usi
ng
k-m
eans i
s
co
m
p
ared wi
t
h
GM
M
,
GLM
M
using Hierarchical cl
ust
e
ri
n
g
(
G
LM
M
-
H), a
n
d
GLM
M
usi
n
g
K-M
eans cl
u
s
t
e
ri
ng
(GLM
M
-
K) a
nd s
h
o
w
n i
n
Fi
gu
re 3. It
i
s
obse
r
v
e
d t
h
at
t
h
e pr
op
ose
d
m
e
t
hod sat
i
s
fi
es t
h
e st
an
da
rd
cri
t
e
ri
on
as t
h
e
PR
I a
n
d
GC
E
val
u
es
f
o
r
fi
ve
im
ages are i
n
r
a
nge
0 t
o
1 a
n
d t
h
e
pr
o
pose
d
m
e
t
hod
o
u
t
p
e
r
f
o
rm
s t
h
e a
b
o
v
e m
e
t
h
o
d
s.
Fi
gu
re 3.
C
o
m
p
ari
s
on
of Perform
ance
Meas
ures
Using t
h
e
deve
lope
d al
gorithm
the im
age can als
o
be
reconstructed. Once the
im
ag
e is reco
nstru
c
ted
d
i
fferen
t
qu
ality
m
e
trics can
be co
m
p
u
t
ed
t
o
stu
d
y
th
e p
e
rform
a
n
ce o
f
im
a
g
e
q
u
a
lity. Th
e qu
ality
m
e
tric
s lik
e
i
m
ag
e fid
e
lity, mean
squ
a
re error an
d im
ag
e q
u
a
lity h
a
v
e
b
e
en
calcu
lated
an
d shown in Tab
l
e 6 as
fo
ll
ows.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
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8-8
7
0
8
Im
ag
e
Seg
m
e
n
t
a
t
i
o
n
B
a
sed
o
n
D
o
u
b
l
y
T
r
u
n
c
a
t
e
d
Ge
ner
a
l
i
z
ed L
a
pl
ace
Mi
xt
ure M
odel
...
.
(
T
. Jy
ot
hi
rm
ay
i)
2
195
Tab
l
e 6
.
Seg
m
en
tatio
n
Qu
ality
Metrics
Im
age M
e
thod
Im
age Quality
Met
r
ics
Im
age
Fidelity
Signal to Noise Ra
tio
Im
age
Quality Index
Im
age1
GM
M
0.
99
0.
24
1.
0
GL
MM
-H
0.
99
0.
24
0.
988
GL
MM
-K
0.
99
0.
419
0.
988
DT
GLMM
-
K
.
99
0.
34
.
99
Im
age2
GM
M
0.
99
2.
01
0.
99
GL
MM
-K
0.
99
0.
41
0.
99
GL
MM
-H
0.
99
2.
03
0.
99
DT
GLMM
-
K
.
99
3.
34
.
99
Im
age3
GM
M
0.
98
1.
45
0.
98
GL
MM
-K
0.
99
0.
03
0.
99
GL
MM
-H
0.
99
1.
45
0.
99
DT
GLMM
-
K
0.
99
2.
25
.
98
Im
age4
GM
M
.
99
2.
23
1.
0
GL
MM
-K
.
98
4.
4
.
998
GL
MM
-H
.
99
2.
69
1.
0
DT
GLMM
-
K
1.
0
4.
5
.
99
Im
age5
GM
M
.
99
1.
09
0.
99
GL
MM
-K
.
99
2.
67
.
99
GL
MM
-H
.
99
1.
13
.
997
DT
GLMM
-
K
.
99
3.
77
.
99
From
Table
6,
it is obse
r
ved that the
im
ages recons
tructed
using c
u
rre
n
t
m
e
thod a
r
e cl
ose to
reality.
Th
e im
ag
e fid
e
lity is al
m
o
st sa
m
e
fo
r all m
e
th
od
s. Th
e sign
al to no
ise
ratio
and im
ag
e q
u
a
lity in
d
e
x
is
larger
t
h
an
ot
he
r m
e
tho
d
s.
T
h
e
ori
g
i
n
al
im
ages an
d re
co
nst
r
uct
e
d i
m
ages usi
n
g
devel
ope
d
se
gm
ent
a
t
i
on al
g
o
ri
t
h
m
are
prese
n
ted in Fi
gure
4.
Fi
gu
re
4.
O
r
i
g
i
n
al
an
d R
e
c
o
ns
t
r
uct
e
d
Im
ages
4.
CO
NCL
USI
O
N
Thi
s
pa
per di
s
c
usses t
h
e de
vel
o
pm
ent
and anal
y
s
i
s
of
im
age segm
en
t
a
t
i
on al
go
ri
t
h
m
based on
Doubly Trunc
ated Ge
ne
ralized La
pl
ace
Mi
xture distribution. In
m
a
ny
image segm
entation al
gorithm
it is
cu
sto
m
ary to
assu
m
e
th
at p
i
x
e
l in
ten
s
ities asso
ciated
with
i
m
ag
e reg
i
on
s
are m
e
so
k
u
r
ti
c an
d
h
a
v
i
ng
in
fi
n
ite
rang
e. Bu
t in
reality
in
m
a
n
y
i
m
ag
es p
i
x
e
l in
ten
s
ities associated
with
i
m
ag
e reg
i
on
s may n
o
t
b
e
m
e
so
ku
rtic
and
ha
ve i
n
fi
n
i
t
e
range
. T
h
es
e t
w
o
dra
w
bac
k
s
of e
x
i
s
t
i
ng
m
odel
based i
m
age segm
ent
a
t
i
on al
g
o
ri
t
h
m
s
are
avoi
ded i
n
t
h
i
s
pape
r
by
charact
eri
z
i
ng
pi
xel
i
n
t
e
n
s
i
t
y
associ
at
ed
w
i
t
h
im
age reg
i
on f
o
l
l
o
ws
D
o
u
b
l
y
Truncated Ge
neralized
Lapl
ace distribution. T
h
e
Doub
l
y
Truncated
Gene
ralized
L
a
place distri
bution i
s
capabl
e
o
f
p
o
r
t
r
ay
i
ng t
h
e i
m
age r
e
gi
ons
w
h
i
c
h a
r
e
havi
n
g
sy
m
m
e
t
r
i
c
or s
k
ewe
d
a
n
d
pl
at
y
or m
e
so
ku
rt
i
c
pi
xel
i
n
t
e
nsi
t
y
di
st
ri
but
i
o
ns.
The m
odel
par
a
m
e
t
e
rs
are
o
b
t
ai
ned
deri
vi
n
g
u
pdat
e
d e
q
uat
i
ons
f
o
r
t
h
e
d
o
ubl
y
truncated
gene
ralized La
place mixture m
odel of EM al
gorithm
.
The initializa
tion of
m
odel param
e
ter is
carri
ed
usi
n
g
K M
eans an
d
m
o
m
e
nt
m
e
t
hod o
f
est
i
m
a
t
i
o
n. T
h
e im
age segm
ent
a
t
i
on al
go
ri
t
h
m
i
s
devel
ope
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE
Vo
l. 6
,
N
o
. 5
,
O
c
tob
e
r
20
16
:
218
8
–
21
96
2
196
usi
n
g m
a
xim
u
m
l
i
k
el
i
hoo
d
u
nde
r B
a
y
e
si
an
fram
e
. The
p
e
rf
orm
a
nce o
f
t
h
e al
g
o
ri
t
h
m
i
s
eval
uat
e
d t
h
r
o
ug
h
expe
ri
m
e
nt
at
i
o
n wi
t
h
fi
ve
ra
nd
om
l
y
im
ages fr
om
B
e
rkel
y
dat
a
set
an
d
fo
u
nd t
h
at
t
h
i
s
m
e
t
hod
o
u
t
p
e
r
f
o
rm
s
exi
s
t
i
ng i
m
age segm
ent
a
t
i
on m
e
t
hod
wi
t
h
i
m
age
m
e
t
r
i
c
s
PR
I, GC
E a
n
d
VO
I. T
h
i
s
se
gm
ent
a
t
i
on i
s
m
u
ch
useful
for im
a
g
e a
n
alysis of
several
im
ages
. T
h
e im
age s
e
gm
ent
a
t
i
on m
e
t
h
o
d
s ca
n
be
fu
rt
he
r e
x
t
e
n
d
e
d
by
consideri
ng
doubly
truncated m
u
ltivariate gene
ralized
laplace mixture
m
odel whic
h are useful for col
o
r
i
m
ag
es. Th
is
will b
e
tak
e
n
u
p
in
ou
r
fu
rt
her inv
e
stig
ation
s
.
It is also
ob
serv
ed
th
e trun
catio
n of
p
r
ob
ab
ility
m
odel
si
gni
fi
c
a
nt
l
y
i
n
fl
ue
nce
t
h
e se
gm
ent
a
t
i
on
pe
rf
o
r
m
a
nce
.
REFERE
NC
ES
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n
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,
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u
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t appro
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e
dica
l Im
age s
e
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entat
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on Bas
e
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k
ew Gaus
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i
an
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.,
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Evaluation Warning : The document was created with Spire.PDF for Python.