TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol.12, No.6, Jun
e
201
4, pp. 4250 ~ 4
2
5
7
DOI: 10.115
9
1
/telkomni
ka.
v
12i6.426
8
4250
Re
cei
v
ed Au
gust 30, 20
13
; Revi
sed
De
cem
ber 2
1
, 2013; Accepte
d
Jan
uary 24,
2014
Magnetic Resonance Imaging Fusion by 3D Compactly
Supported Shearlet Transform
Chan
g Dua
n
*
1,2
, Qihong
Huan
g
3
, Shuai Wang
1
, Xuegang
Wang
1
, Hong Wan
g
1
1
School of Elec
tronic Eng
i
n
eer
ing, Un
iversit
y
of Electronic S
c
ienc
e an
d T
e
chno
log
y
(UEST
C)
2
Researc
h
Institute of Electron
ic
Scienc
e an
d T
e
chnolog
y, U
EST
C
3
Electronic En
g
i
ne
erin
g Col
l
e
g
e
, Chen
gd
u Un
iversit
y
of Information T
e
chno
log
y
(CUIT
)
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: pertinn
a
x
@1
63.com
A
b
st
r
a
ct
T2* an
d q
u
a
n
ti
tative susce
pti
b
ility
mapp
in
g
(QSM) of
mag
netic res
o
n
anc
e ima
g
in
g
(MRI) im
ages
provide different
type inner
st
ructur
e
infor
m
ation
of scanned or
gans. If t
hey can be pr
operly fused into
one
set, the details
of the scaned
organ c
an be
revea
l
ed
mo
r
e
clearly. In this
paper, a 3
D
MRI ima
ge fus
i
o
n
meth
od
bas
ed
on 3D c
o
mp
a
c
tly supp
orted
shearl
e
t trans
form (3
D-CSS
T
) and 3D
du
al tree c
o
mpa
c
tly
supp
orted sh
e
a
rlet transfor
m
(3D-DT
-CSST
)
,
is propos
ed,
w
h
ich can ov
er
come the l
i
m
ita
t
ion, loss of i
n
ter
layer c
o
rrel
a
tiv
e
infor
m
ation,
of conve
n
tio
nal
2D i
m
age fus
i
on
meth
ods. 3
D
-DT
-
CSST
is
our
mo
dificati
o
n
of
3D-CSST
, w
h
i
c
h is a
ppr
oxi
m
ate shift i
n
vari
ant. It can i
m
prove th
e p
e
rformanc
e of fu
sion
metho
d
. T
h
e
prop
osed
meth
od is
eval
uate
d
by 4
grou
ps
of MRI im
ages
of hu
ma
n bra
i
ns. T
he
resu
lts sugg
est that th
e
prop
osed
meth
od h
a
s
a b
e
tter perfor
m
a
n
ce
than c
onve
n
tio
nal
2D w
a
ve
let
,
2D DT
-CW
T
and
3D w
a
v
e
le
t
,
3D DT
-CW
T
b
a
sed
fusio
n
methods,
an
d 3
D
-DT
-
CSST
b
a
sed
meth
od
i
s
better th
an
3D-CSST
bas
e
d
meth
od.
Ke
y
w
ords
:
me
dic
a
l i
m
a
g
e
fusion, co
mp
actly supp
orte
d s
hear
let tra
n
sform, q
u
a
n
ti
tative susce
pti
b
ility
ma
pp
ing
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
Medical im
ag
e fusi
on
is a
sp
eci
a
l
ca
se of im
age
f
u
sio
n
, an
d
h
a
s
bee
n
stu
d
ied fo
r
decade
s. It h
a
s
wid
e
ly ap
plied i
n
me
di
cal
diag
no
sis [1, 2]. It ref
e
rs to
extract
and
me
rge
the
feasibl
e
information from
different source ima
ges, whi
c
h
were captu
r
ed
by different
ki
nd
s
of
devic
es
,
s
u
c
h
as
CT, MRI,
PET etc
., or different
c
onfig
uration
s
of th
e same
devi
c
e, su
ch
a
s
M
R
I
T2* and qu
an
titative susce
ptibility mapping (QSM
). S
peci
a
l device
s
or spe
c
ial configuration
s
of
the sam
e
dev
ice reveal diff
erent a
s
p
e
ct
of scann
ed o
r
gan
s. The inf
o
rmatio
n of source im
age
s is
correl
ated or,
more likely, compl
e
me
nta
r
y. For in
sta
n
c
e, CT im
age
s provi
de the
details of de
n
s
e
hard
tissue
s,
MRI imag
es
provide
the in
ner
structu
r
e
of soft tissue
s: T2*
provid
e the
cont
ra
st of
the tissue rel
a
xation time, QSM provide susceptibilit
y contrast information, such
as caused by
a
rang
e of en
doge
nou
s m
agneti
c
biom
arkers a
nd
contrast a
g
e
n
ts e.g. iro
n
,
calci
u
m a
nd
gadoli
n
ium
(Gd). If
differe
nt data
can
b
e
p
r
op
erly
fu
sed,
th
e fuse
d data contai
ns all the sail
ent
informatio
n o
f
the scan
ne
d organ,
whi
c
h
can
reve
a
l
the detail
s
of inne
r st
ru
cture mo
re
cle
a
rly
than ea
ch
si
ngle
sou
r
ce.
Previou
s
ly, all sou
r
ce
d
a
ta
need
to be
registe
r
ed.
3D T2* ma
gnitu
de
image
s an
d
QSM imag
es are
getting from the
same
scan, an
d th
erefo
r
e,
have
alre
ady exa
c
tly
regi
stered.
Curre
n
tly many re
sea
r
che
s
on
medi
cal
fusion m
e
tho
d
only con
s
id
er the
2D
ca
se. While
many dia
gno
stic
devices can p
r
ovide
3
D
ima
g
e
s
,
an
d the val
ue of
ea
ch voxel i
n
the
3D ima
g
e
s
is
co
rrel
a
ted
not only to
th
e adj
acent p
o
i
nts in
same
l
a
yer, b
u
t al
so
to the
poi
nts in n
e
igh
b
o
r
in
g
layers. Th
ere
f
ore, it’s ne
cess
ary to de
velop the 3D image fusi
o
n
method in
stead of 2D i
m
age
fusion meth
o
d
whi
c
h cau
s
e the loss of the co
nsi
s
ten
cy in the third dimen
s
ion.
Fusio
n
meth
o
d
s
can
be
pe
rforme
d in
sp
atial
domai
n or certai
n
tra
n
sformed do
main.
In
spatial d
o
mai
n
, the intuitive fused im
ag
e is se
lecte
d
as the
weight
ed average i
m
age of sou
r
ce
image
s [3]. This ki
nd of method
s is rel
a
tively easy to implement, b
u
t its perform
ance is lo
w a
n
d
alway
s
cau
s
e
the decre
ase or even loss of some
fea
s
ible info
rmat
ion. The tran
sform
ed dom
ain
based fusio
n
methods a
r
e
usually follo
wing the ste
p
s: 1) pe
rforming the forward tran
sform to
sou
r
ces i
m
ag
es, 2)
acquiri
ng the fused
coeffici
ent
s f
r
om
coeffici
e
n
ts of source
image
s un
d
e
r
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Magneti
c
Re
sonan
ce Im
aging Fusi
on b
y
3D Com
pactl
y Suppo
rted
Shearl
e
t… (Chang
Dua
n
)
4251
fusion
rule
s, 3) pe
rformi
ng
backward transfo
rm to
fus
ed
c
oeffic
i
ents
to get the fus
ed image. I
n
this type of method
s, the rese
ar
ch w
o
rk
s u
s
ually
f
o
cu
sed o
n
two point
s: the choi
ce of the
transfo
rm an
d the desi
gn
of fusion rul
e
.
Many multi
scale t
r
an
sforms a
r
e
appli
ed in fu
sio
n
method
s, such a
s
DWT
[4
], lifting
wavelet [5],
compl
e
x wavelet [6], cu
rvelet [7], sh
ea
rlet [8], etc.
Shearl
e
ts
em
erge
d in
re
cent
years a
m
on
g the most succe
ssful
framewor
ks
for the effic
i
ent repres
entation of
multidimen
sio
nal data. Ind
eed, many transfo
rm
s
are
introdu
ced t
o
overcome t
he limitation of
traditional
m
u
lti-scale
tra
n
sforms of
poor abilit
y
of ca
pturin
g
edg
es an
d
othe
r a
n
iso
t
ropic
feature
s
. Ho
wever,
sh
earlet tran
sform
stan
ds
out
sin
c
e it h
a
s
many adva
n
tage
s uni
quel
y: a
singl
e o
r
fin
i
te set
of g
enerating
fu
nction
s;
o
p
timally sparse
re
pre
s
e
n
tations for mul
t
i-
dimen
s
ion
a
l data; a unified treatment
of the
contin
uum and di
gi
tal realm
s
; and a com
p
a
c
tly
sup
porte
d tra
n
sform etc.
With so ma
n
y
advant
age
s above, shea
rlet tran
sfo
r
m
has
bee
n wi
dely
utilized i
n
to
many imag
e
pro
c
e
s
sing
tasks
su
ch
as d
e
-noi
sing [9], edge
detectio
n
[10],
enha
ncement
[11], etc. In this pa
per,
the co
nventi
onal 3
D
Co
mpactly Sup
ported S
hea
rlet
Tran
sfo
r
m
(3
D-CSST) is i
m
prove
d
to
o
v
erco
me it
s
la
ck
in
g o
f
s
h
ift in
va
r
i
an
c
e
pr
o
p
e
r
t
y, th
r
oug
h
the Du
al Tre
e
(DT)
struct
ure, a
nd the
n
bot
h 3
D
-CSST and 3
D
-DT-CSST a
r
e sel
e
cte
d
a
s
the
transfo
rm
s fo
r the 3D me
di
cal imag
e fusi
on.
Thre
e fusio
n
rule
s are utilized in thi
s
p
aper: maxim
u
m point
s’ modulu
s
(MPM
), whi
c
h
con
s
id
ers onl
y the value of single poi
nt; maximum re
g
i
onal ene
rgy
(MRE
), whi
c
h
con
s
ide
r
s the
informatio
n fo
r lo
cal
re
gion
[12], and t
r
ea
ts ea
ch
poi
nts of th
e
regio
n
eq
ually an
d
maximum
su
m
of modified lapla
c
ian [13], which al
so
con
s
id
ers
the
information i
n
local re
gio
n
, but treats the
cente
r
point of
the regi
on
and
the poin
t
s
a
r
ou
nd
it
d
i
f
f
e
rent
ly
.
Th
ese
t
h
r
ee
cla
ssi
c f
u
sio
n
ru
les
are expa
nde
d into 3 dime
nsio
ns. In ord
e
r to ev
aluate
the performa
n
ce of p
r
op
osed metho
d
, the
quality indice
s also are ex
pand
ed into 3
dimensi
o
n
s
.
The
re
st of th
e pa
per i
s
o
r
gani
zed
a
s
fo
llowing
s. In
section
2, the
i
m
pleme
n
tatio
n
of
3D-
CSST a
nd th
e mo
dificatio
n
of 3
D
-DT
-
CSST are
in
tro
duced. In
se
ction 3, fu
sion
metho
d
b
a
sed
on 3
D
-CSST
and 3
D
-DT
-
CSST with th
ree fu
sion
rul
e
s i
s
p
r
op
osed. Fro
m
the
experim
ents of
se
ction 4, the comp
ari
s
o
n
of 2D and
3D
method
s and the perf
o
rma
n
ce abo
ut the propo
sed
methods are illustrated
and discussed. Finally, we draw
concl
u
si
ons in section 5.
2. 3D Comp
a
c
tly
Supported Shearle
t Trans
f
orm
Figure 1. Steps of Forw
a
r
d
and Backward 3D-CSST
In [14], Lim propo
se
d the
prin
ciple a
nd
the det
ails
ab
out the co
nst
r
uctio
n
of Co
mpactly
Suppo
rted S
hearl
e
t Tra
n
sform (CSST).
His
wo
rk is
mainly focu
s
on 2
D
case. We first expa
nd
this impl
eme
n
tation into 3
D
case. The
step
s of forward
and
ba
ckward 3
D
-CS
S
T are
given
in
Figure 1. Th
e input
sign
al
()
f
x
is first p
r
ocesse
d by
she
a
r
ope
ration in th
re
e pyrami
ds,
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 6, June 20
14: 4250 – 4
257
4252
r
e
pr
es
e
n
t
ed
b
y
P
,
P
, and
P
, whi
c
h a
r
e a
r
ound x, y an
d z axi
s
re
sp
ectively. The
n
th
e
A
n
isot
r
opi
c
D
i
sc
ret
e
W
a
v
e
let
Tra
n
sf
o
r
m
(A
D
W
T
)
i
s
perfo
rmed
on
every
sh
eared versio
ns
of
input si
gnal.
The o
u
tputs
of ADWT,
1
k
CC
,
1
k
CC
and
1
k
CC
, are the
coeffici
ents
of thre
e
pyramid
s
of the tran
sform
whe
r
e the pa
rameter
k
is the numbe
r of directio
ns.
Figure 2. Shear Ope
r
atio
n of 2D and 3
D
-CSST
Shear o
peration ha
s an int
eger
cont
rol p
a
ram
e
ter
[,
]
nN
N
stands the offset that the
first poi
nt of first row are shifted alon
g
one di
re
ction,
whe
r
e
N
is th
e si
ze
of ima
ge an
d min
u
s
refers to i
n
ve
rse
directio
n. The illu
strati
on of
shea
r
operation
with
nN
is
given in
Figure 2.
With su
ch scheme,
m
any dire
ction
s
ca
n
be re
pr
e
s
e
n
ted
without
resampli
ng th
e ori
g
inal
dat
a.
And finally, the sh
ea
red
da
ta are
emb
e
d
ded into
a
re
ctangl
e with
the same
si
ze
s of the
ori
g
in
al
image
s, whi
c
h guarantee
s no more extra memo
ry
is need
ed to st
ore the
she
a
red image
s. T
he
backward sh
ear op
eration
just has th
e same
step
s b
u
t in an inverse o
r
de
r. She
a
r ope
ratio
n
can
be fu
rther ex
pand
into
3D ca
se,
as in
Figure 2.
The
2D shea
r
op
eration
is p
e
rformed
layer
by
layer alon
g x-axis and the
n
y-axis con
s
e
quently.
Figure 3. Re
constructio
n
of 2D-CSST an
d 2D-DT
-
CS
ST
(
a
)T
h
e
re
co
ns
tr
uc
te
d
image
s
,
(
b
)
th
e
r
e
c
o
ns
tr
uc
ti
on
by low frequenc
y
c
o
effic
i
ents
, (c
)~(e) the
recon
s
tru
c
tio
n
by three sin
g
le scale of hi
gh frequ
en
cy coeffici
ents
3D ani
sotro
p
i
c DWT
is perfo
rmed
n
e
xt
to
sh
ear ope
ration.
Anisotropi
c
DWT i
s
necessa
ry, b
e
ca
use it
sa
tisfies th
e d
e
finition
of shearl
e
t
tra
n
sf
orm, whi
c
h requires
opti
m
al
rep
r
e
s
entioin
to curve-li
ke singul
aritie
s. In
the application of image fusi
on, the optimal
rep
r
e
s
entatio
n of curve
-
like sing
ularitie
s ha
s littl
e impact to the
performan
ce
of fusion re
sults.
And from exp
e
rime
nts, the
value of performa
n
ce
indi
ce
s of anisotropic
DWT
we
re inde
ed le
ss
than that of
DWT. So the
req
u
ire
m
ent
of aniso
tro
p
ic DWT is rel
e
ase
d
to
com
m
on
DWT.
DWT
has its o
w
n
dra
w
ba
ck: the shift varian
t prope
rty, which
cau
s
e
s
distortio
n
s in
fused ima
g
e
s.
Fortun
ately, the shift varia
n
t prope
rty ca
n be
red
u
ced
throug
h the st
ructu
r
e of Du
al Tree.
Usi
ng the sa
me method i
n
[15] whi
c
h
Kingsb
u
ry
wa
s usi
ng to illu
strate the
shif
t-variant
of DWT an
d shift-inva
riant
of dual tree complex
wavel
e
t transfo
rm (DT CW
T), th
e comp
ari
s
on
of
recon
s
tru
c
tio
n
re
sults b
e
twee
n traditio
nally CSST a
nd DT
CSST
were given i
n
Figure 3. T
h
e
input image
wa
s a white
circle lo
cated
at the cent
er of a black b
a
ckgroun
d. The image
s in
first
row were
the
recon
s
tru
c
tio
n
imag
es alo
ng on
e di
re
ction of
DT
CS
ST and th
e i
m
age
s in
second
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Magneti
c
Re
sonan
ce Im
aging Fusi
on b
y
3D Com
pactl
y Suppo
rted
Shearl
e
t… (Chang
Dua
n
)
4253
row
we
re th
e recon
s
tru
c
t
i
on image
s
along the
sa
me dire
ction
of CSST. And it shoul
d
b
e
observed fro
m
pictures in
(a) that both
CSST
and DT CSST ca
n recon
s
tru
c
t
the input image
s
pre
c
isely. But in lo
w frequ
ency
co
effici
ents
(b
) a
nd
different
scal
es
of hig
h
co
efficients (c)~(e),
the recon
s
tru
c
tion i
m
age
s of
DT
CSST were
mu
ch smooth
e
r t
han th
ose of
CSST. T
h
e
s
e
differen
c
e
s
sugge
sted tha
t
CSST was shift-varia
n
t and DT CSS
T
wa
s (ap
p
roximately) sh
ift-
invariant. An
d in 3
D
ca
ses, DT st
ru
cture
co
uld al
so effectively
redu
ce
the
shift-varian
ce
of
CSST.
3. Proposed
Fusion Meth
od
Figure 4. Steps of Prop
osed Medi
cal V
o
lume Fu
sio
n
Method
The p
r
o
p
o
s
e
d
fusi
on m
e
thod i
n
thi
s
pape
r b
e
lon
g
s
to th
e vox
e
l-level fu
sio
n
, with
averag
e rul
e
for low frequ
ency coefficie
n
ts
m
ean
(
,
)
ll
l
f
ab
CC
C
, and thre
e different fu
sion
rule
s for
high freq
uen
cy coefficient
s:
a)
Max modulu
s
of Points’ Modulu
s
(MPM)
,
,
aa
b
f
ba
b
CC
C
C
CC
C
(1)
The fu
sed
hig
h
coefficient
s are
tho
s
e h
a
v
e the
la
rge
r
modulu
s
as
in
equ
ation (1
),
wh
ere
,{
,
,
}
t
Ct
a
b
f
mean
s th
e h
i
gh fre
que
ncy
co
efficient
s,
,
ab
label t
w
o
so
urce d
a
ta
re
spectively,
f
refers
the
fus
ed
res
u
lt.
This
fus
i
on rule
co
nsi
d
ers only
sin
g
le poi
nt’s i
n
formatio
n of
coeffici
ents.
b)
Max Regio
n
Energy (M
RE
)
The fused hig
h
freque
ncy coefficient
s are acq
u
ire
d
according to (2) [12],
,
,
aa
b
f
ba
b
CE
E
C
CE
E
(2)
Whe
r
e
2
1
()
,
{
,
}
tt
t
p
EC
p
C
t
a
b
N
,
is a l
o
cal
regi
on,
t
C
,
is the me
an o
f
all
t
C
in
,
N
is the
numb
e
r of co
efficient
s in
. The fu
sed hig
h
coefficient
s a
r
e the
coeffici
ents that have th
e
large
r
lo
cal e
nergy. Thi
s
fu
sion
rule
con
s
ide
r
s
all the
informatio
n of points
whi
c
h
are in the l
o
cal
regio
n
.
c)
Max Sum of Modified La
pl
acia
n (MSML
)
The fu
sed
hi
gh fre
quen
cy
coeffici
ents
are
acquired
acco
rding
to (3
). 3
D
ve
rsio
n of
Modified La
pl
acia
n index i
s
cal
c
ul
ated throu
gh eq
uat
ion (5
), and t
he su
m of them is calcula
t
ed
as (4
), whe
r
e
,,
ij
k
exhaust every point in source imag
es and
is a local regio
n
aro
und the
cente
r
point
(,
,
)
ij
k
. The paramet
er
s
equals 1 i
n
this pap
er.
This fu
sion rule also co
nsiders
all the info
rm
ation of p
o
int
s
whi
c
h a
r
e i
n
the lo
cal
re
gion
, and
wh
at’s mo
re, th
e center poi
n
t
and othe
r poi
nts are treate
d
differently.
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TELKOM
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Vol. 12, No. 6, June 20
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257
4254
,
,
aa
b
f
ba
b
CS
M
L
S
M
L
C
CS
M
L
S
M
L
(3)
2
,,
(,
,
)
[
(
,
,
)
]
,
{
,
}
tt
pq
t
SM
L
i
j
k
ML
i
p
j
q
k
t
t
a
b
(4)
(
,
,
)
2
(
,,
)
(
,,
)
(
,,
)
2
(
,
,
)(
,
,
)(
,
,
)
,
{
,
}
2
(
,,
)
(
,,
)
(
,,
)
tt
t
t
tt
t
tt
t
M
L
ij
k
C
ij
k
C
i
s
j
k
C
i
sj
k
Ci
j
k
Ci
j
s
k
C
i
j
s
k
t
a
b
Ci
j
k
Ci
j
k
s
C
i
j
k
s
(5)
The
step
s
of
prop
osed
fusi
on m
e
thod
a
r
e given
in F
i
gu
r
e
4
.
F
i
r
s
tly,
fo
r
w
ar
d 3D
-CSST
o
r
3D-DT
-
CSST
are p
e
rfo
r
m
ed to
both
so
urce im
age
s,
the l
o
w freq
uen
cy is the
averag
e of
b
o
th
sou
r
ce coefficient
s, the fused hi
gh fre
q
uen
cy
fused by
Equation (1~3).
Fin
a
lly, the backwa
r
d
3D-CSST
or 3D-DT-CSST are p
e
rfo
r
med to fu
se
d coefficie
n
ts, and th
e ou
tput is th
e fu
sed
image
s as
re
pre
s
ente
d
by
f
V
.
4. Results a
nd Analy
s
is
In this
se
ctio
n, the p
e
rfo
r
mances of
p
r
opo
se
d
m
e
thod
s were
e
v
aluated on 4
hu
man
brain
subje
c
t
s
, an
d
comp
ared
with
2
D
, 3D-DWT [4]
and
2
D
, 3
D
-DTCWT
[5] b
a
se
d meth
od
s.
The hum
an study wa
s a
pprove
d
by
our Institutio
nal Revie
w
Board. MR e
x
amination
s
were
perfo
rmed
wit
h
a 3.0T M
R
system
(Sign
a
HDx
t, GE,
USA), usi
ng
an 8-ch
ann
el
head
coil. A 3D
T2* weig
hted
multi echo gradi
ent ech
o
sequ
en
ce
wa
s use
d
wi
th the following paramete
r
s:
FA=20
°
; TR=57m
s; num
ber of TEs=8; fi
rs
t TE=
5
.7ms
; uniform TE s
p
ac
ing (
∆
TE)=6.
7ms;
BW=±41.6
7
kHz;
field
of view (FOV)=24cm;
a ran
g
e
of re
solutio
n
s we
re
test
ed:
0.57
0.7
5
2
mm
3
. The 3
D
T2* ma
gnitu
de an
d QSM
image
s, whi
c
h ar
e
re
co
nst
r
ucte
d by the
tools of [16],
are
interpol
ated t
o
12
8
1
28
1
2
8
. In QSM
pro
c
e
s
sing,
the mag
net
ic field
s
o
u
tside th
e b
r
ai
n
pare
n
chyma were co
rru
pted
by noi
se, therefo
r
e,
QS
M re
gion
s
were
crop
ped
by ma
sks,
which
were obtain
e
d
by brain e
x
traction tool
(BET
) of [17]. Consequ
ently, the experim
ents
were
evaluated by
the valid data
in all masks.
Figure 5. Inter Fram
e Diffe
ren
c
e
s
for 2
D
and 3D Fu
si
on Method
s
Firstly, we ev
aluated
the
consi
s
ten
c
y in
the third dim
ensi
on b
e
twe
en 2
D
m
e
tho
d
s
and
3D m
e
thod
s.
2D m
e
thod
s f
u
se
d source
i
m
age
s laye
r by
layer,
3
D
method
s
di
re
ctly
fused all 3
D
image
s a
s
a
whol
e. Con
s
i
s
ten
c
y alon
g the thir
d axi
s
can
be eval
uated by
bot
h the pe
rspe
ctive
impre
s
sion o
f
inter frame
difference (IFD) ima
g
e
s
, as sho
w
n i
n
Figure 5,
and their mu
tual
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TELKOM
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Magneti
c
Re
sonan
ce Im
aging Fusi
on b
y
3D Com
pactl
y Suppo
rted
Shearl
e
t… (Chang
Dua
n
)
4255
informatio
n (I
FD_MI
)
[18,
19]. Fro
m
Fi
gure
5, it
ca
n be
noti
c
ed
that the fu
sed ima
g
e
s
b
y
2D
method
s hav
e several ob
vious disto
r
ti
ons which
re
sembl
e
s to n
e
ither of the sou
r
ce imag
es.
While
in the
results
by 3
D
meth
od
s, the IDF
ima
g
e
s
of were
much
con
s
ist
ent to the
IDF of
sou
r
ce d
a
ta, sug
g
e
s
ted th
at the IDF i
m
age
s were hi
ghly co
rrelate
d
to the I
D
F o
f
sou
r
ce ima
g
e
s.
The differe
nce among the
3D metho
d
s
can h
a
rdly
be
noticed. Thi
s
con
c
lu
sion
can be comfirmed
by IFD_MI, as listed in Ta
ble 1. Only the first su
bject
s
are li
sted fo
r the limitation of the pape
r. In
this expe
rim
ent, only the
voxels in th
e com
m
on
region
of two
masks
we
re cal
c
ul
ated
b
y
equatio
n
(6
). Suppo
se con
v
entional
IFD_MI
without
mask is
re
prese
n
ted by
(,
,
)
ii
i
ia
b
f
M
ID
D
D
,
whe
r
e
,,
ii
i
ab
f
D
DD
ar
e
the
in
te
r fr
ame d
i
ffe
r
e
nc
e ima
g
e
s
for
both
s
o
u
r
c
e
s
,
ii
ab
VV
a
nd
i
f
V
fus
e
d
image
s,
1
,{
,
,
}
ii
i
tt
t
DV
V
t
a
b
f
,
i
repre
s
ent
s that the current l
a
yer is the
i
-t
h lay
e
r,
N
ref
e
rs
to the whole
numbe
r of l
a
yers alo
ng th
e
third axi
s
, an
d
refers to
point-wi
se mult
iplication. The
quality indice
s of The m
e
thod of 3
D
-DT
-
CSST
with
MSML rule
h
a
s the hi
ghe
st value of IFD_MI,
and all the va
lues for 3
D
m
e
thod
s are hi
gher tha
n
the
2D method
s
with sam
e
rul
e
.
1
1
1
1
ID
F
_
M
I
(
,
,
)
(
)
1
N
ii
i
i
i
ia
b
f
i
M
I
D
D
D
Mas
k
Mask
N
(6)
Table 1. IFD_
MI for the First Subject
IFD_MI
2D DWT
2D DTCW
T
3D DWT
3D DTCW
T
3D CSST
3D DT
CSST
MPM
1.8443
1.7659
1.8905
2.2147
2.0943
2.5409
MRE
1.7349
1.7650
1.8989
2.1558
2.0257
2.3809
MSML
1.7274
1.7503
2.0965
2.3432
2.0374
2.5899
One
laye
r of
each co
ronal, axial
and sa
gittal
imag
es are sel
e
cte
d
as
th
e
rep
r
e
s
entatio
ns, the
sou
r
ce an
d
re
sult
image
s a
r
e
shown in
Figu
re
6 to
Figu
re 8. F
r
om
th
e
perspe
c
tive i
m
pre
s
sion, it
wa
s ha
rd to t
e
ll whi
c
h fu
si
on meth
od
was b
e
tter, be
cau
s
e th
e re
sult
image
s were
much
simila
r
to each othe
r. The dist
in
cti
ons
amon
g th
em ca
n be
no
ticed o
n
ly after
carefully ob
servation. Thi
s
ph
eno
men
on sugg
es
te
d that both
the p
r
op
osed
method
s
an
d all
conve
n
tional
method
s co
ul
d fulfill the ta
sk. T
w
o pe
rforma
nce indi
ce
s, Mutual Informatio
n (MI)
and Q
AB|F
[20], were sele
cted to evaluat
e the pr
op
osed method
s,
and were ex
pand
ed into
3D
versio
n. They
were li
sted in Table 2. It
sho
u
ld
be no
ticed that the quality indices of pro
p
o
s
ed
method
s were larg
er tha
n
the method
s t
hat ba
s
ed o
n
DWT
or
DT
CWT. And in
the ca
se of 3
D
-
CSST an
d 3
D
-DT-CSST,
the rul
e
of M
S
ML ha
d the
high
est in
di
ce
s. The
sa
me ph
enom
e
na
coul
d also be
noticed in ot
her subje
c
ts
whi
c
h
were o
m
itted for the limitation of the pap
er.
Figure 6. Coronal Sou
r
ce and Result Image
s
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TELKOM
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Vol. 12, No. 6, June 20
14: 4250 – 4
257
4256
Figure 7. Axial Source an
d Re
sult Images
Figure 8. Sagittal Source a
nd Re
sult Image
s
Table 2. Perf
orma
nce of the First Subje
c
t
First subject
2D DWT
2D DTCW
T
3D DW
T
3D DTCW
T
3D CSST
3D DT
CSST
MPM
MI 1.1652
1.2168
1.1615
1.2404
1.2574
1.2718
Q
AB
|
F
0.1824
0.1985
0.1820
0.2109
0.2182
0.2264
MRE
MI 1.1596
1.2323
1.1471
1.2561
1.3054
1.3112
Q
AB
|
F
0.1987
0.2185
0.1975
0.2351
0.2442
0.2568
MSML
MI 1.1566
1.2339
1.2043
1.2617
1.3062
1.3132
Q
AB
|
F
0.1977
0.2158
0.2257
0.2402
0.2534
0.2656
5. Conclusio
n
Conve
n
tional
2D i
m
age
fu
sion
metho
d
can
only fu
se
the 3
D
M
R
I i
m
age
s laye
r
by layer,
whi
c
h l
ead
s t
o
the l
o
ss
of inter l
a
yer correlatio
n
of
3D im
age
s. I
n
this pa
per,
the 3
D
m
edi
cal
image
fusio
n
metho
d
s ba
sed
on
3
D
-CSST and
its
shift inva
riant
version,
3D-DT-CSST,
were
prop
osed. F
r
om the
prin
ci
ples of meth
o
d
s
and th
e ex
perim
ents the
followin
g
con
c
lu
sion
s
can
be
dra
w
n:
1) the
3D-tra
nsfo
rm ba
se
d m
e
thod
s h
ad
a
b
e
tter
con
s
i
s
te
ncy al
ong
th
e third axi
s
t
han
conve
n
tional
2D-t
ran
s
form based m
e
thod
s. 2)
F
r
om b
o
th pe
rsp
e
ctive im
pre
ssi
on a
n
d
the
perfo
rman
ce
indices, the
prop
osed m
e
dical fu
si
o
n
method
s were
better
than
3D-DWT or 3D-
DTCWT.
3)
Among the
fusio
n
rule
s o
f
3D-CSST o
r
3
D
-DT-CSS
T
ba
sed
met
hod
s, the M
S
ML
rule ha
d a bet
ter perfo
rma
n
c
e than oth
e
r
two rule
s.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
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ISSN:
2302-4
046
Magneti
c
Re
sonan
ce Im
aging Fusi
on b
y
3D Com
pactl
y Suppo
rted
Shearl
e
t… (Chang
Dua
n
)
4257
Ackn
o
w
l
e
dg
ements
This
wo
rk
wa
s supp
orted i
n
part by the
Nation
al Nat
u
re S
c
ien
c
e
Found
ation o
f
Chin
a
(No.6
113
900
03). T
he
aut
hors al
so
wo
uld li
ke to
th
ank Dr. Yi
Wang fo
r
data
providin
g a
n
d
Dr.
Tim Varta
n
ia
n, Dr. Jai Pe
rumal, a
nd
Dr. Nan
c
y
Neal
on fo
r d
a
ta
collectio
n, a
s
well
as to tho
s
e
reviewers an
d editors for their de
dicate
d works.
Referen
ces
[1]
CR Hatt, AK Jain, V Parthasarathy
, A Lang, AN Ra
val. MRI-3D ultrasound-
X
-ray
image fusion
w
i
t
h
electrom
agn
eti
c
tracking for transen
doc
ardi
al thera
peutic
injecti
ons: In-v
itro valid
atio
n and i
n
-viv
o
feasib
ilit
y.
Co
mputeri
z
e
d
Med
i
cal Ima
g
i
ng a
n
d
Graphics
. 20
13; 37(2): 1
62-
173.
[2]
D Clev
e
rt, A H
e
lck, PM Papr
ottka, P Z
enge
l,
C T
r
umm, MF
Reiser. U
l
tra
s
oun
d-gu
id
ed i
m
age fus
i
o
n
w
i
th
co
mp
u
t
ed
to
mo
g
r
a
phy a
n
d
ma
gn
e
t
ic re
so
na
n
c
e
ima
g
i
n
g
.
C
l
i
n
i
c
a
l
u
t
il
i
t
y
fo
r ima
g
i
n
g
and
interve
n
tion
al d
i
ag
nostics of h
epatic l
e
sio
n
s.
Der Ra
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