TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 12, No. 8, August 201
4, pp. 6190 ~ 6197
DOI: 10.115
9
1
/telkomni
ka.
v
12i8.470
6
6190
Re
cei
v
ed O
c
t
ober 1
1
, 201
3; Revi
se
d May 18, 20
14; Acce
pted Jun
e
3, 2014
Slice Interpolation for MRI Using Disassemble-
Reassemble Method
Qinghua Lin
*
1
，
Min Du
1,2
，
Yuemin Gao
2
1
Colle
ge of Ele
c
trical Eng
i
ne
e
r
ing a
nd Autom
a
tion, F
u
zho
u
Univers
i
t
y
2
F
u
jian Ke
y L
a
b
of Medica
l Instrument and P
ha
rmac
eutica
l
T
e
chnolog
y, F
u
zho
u
Univ
ersi
t
y
,
2 Xue Yu
an Ro
ad, Univ
ersit
y
T
o
w
n
, F
u
zhou,
F
u
jian 3
5
0
108
, P. R. CHINA,
+
86 591 9
3
7
5
9
450
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: fzulins2
11@
163.com
A
b
st
r
a
ct
Due to p
h
ysic
a
l li
mitati
ons i
n
here
n
t in Mag
n
e
tic reson
anc
e
ima
ge (MRI) s
c
ann
ers, the in
ter-slice
resol
u
tion of M
R
I is coarse. T
hus, interp
olati
on is o
ften use
d
to comp
ens
a
t
e it. MRI correspon
ds to a thin
slice thro
ugh t
he hu
man b
o
d
y
, and contai
ns
all the infor
m
a
t
ion in the sl
ice
.
Based on this
characteristic, a
nove
l
slic
e inte
rpol
ation
al
gori
t
hm us
in
g dis
a
ssembl
e
-reass
e
mbl
e
(D-R)
method
is pro
p
o
s
ed for d
o
in
g
MRI
slice i
n
terp
olat
ion. T
he a
l
g
o
r
i
thm first dis
a
ssembl
e
s all t
he inf
o
rmatio
n
contai
ned
in
MRI, and th
en
reasse
mbles t
h
e
m
un
der a heur
istic appr
oach of ne
ig
h
borh
ood co
nsi
s
tency to get high
er inter-s
lic
e
resol
u
tion. Ser
i
es virtua
l i
m
a
g
e
s that
i
m
itate
the char
acteris
t
ic of MRI w
e
re used to
expl
ai
n the pr
inci
pl
e of
prop
osed
a
l
g
o
rithm,
an
d th
e
process
of
pro
pose
d
al
go
ri
thm
wa
s d
e
r
i
v
ed fro
m
de
ta
il
ana
l
ysi
s. Fin
a
l
l
y
,
we
perfor
m
e
d
a
la
rge n
u
m
b
e
r of
interp
ol
ation
exper
iment
an
d co
mp
are
d
th
e pro
pos
ed
al
gorith
m
t
o
sev
e
ra
l
other inter
p
o
l
ation tec
hni
qu
es. Results s
how
t
hat the propos
ed a
l
gorith
m
o
u
tpe
r
forms the ot
her
interp
olati
on a
l
gorith
m
s, w
h
ic
h me
ans the D
-
R me
th
od is
more suita
b
le for
MRI interpol
ati
on.
Ke
y
w
ords
: dis
a
ssem
b
le-reas
semble meth
od, MRI, slice interpolation
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
Magneti
c
Re
son
a
n
c
e Ima
ge (MRI) is
a tomog
r
a
p
h
y
imaging
m
odality for
produ
cing
image
s of a slice thro
ugh t
he huma
n
bo
dy and can b
e
use
d
to visualize intern
a
l
structu
r
e
s
of
th
e
body in detail
.
MRI has the
follow advant
age
s: prov
ide
s
goo
d cont
ra
st betwe
en the different sof
t
tissu
es; can i
m
age in any
plane a
nd do
esn’t u
s
e
ioni
zing radiatio
n
.
These adva
n
tage
s let MRI
be u
s
ed
wid
e
ly in clini
c
a
l
purp
o
ses
a
nd medi
cal
sci
en
ce. But due to the
MRI tech
ni
cal
cha
r
a
c
teri
stic, image
time
acqui
sition
and
patient
dose con
s
id
e
r
ation
s
,
tra
d
itionally
M
R
I are
acq
u
ire
d
a
s
high resolutio
n
2D
sli
c
es
with rel
a
tively large
sli
c
e t
h
ickne
s
s in compa
r
ison to
the
inter-sli
c
e re
solution. As sh
own in Fig
u
re
1,
these ima
ges a
r
e thre
e
neighbo
rin
g
MRI of huma
n
head g
o
t from hospital. In the DICOM
information
of these ima
ges, the ‘Ma
nufactu
re
r’ is ‘GE
MEDICAL SYSTEMS’, the ‘Ins
titution
Name’ is
‘Fuj
ian Tumor Hos
p
it
al’,
t
he ‘Rows and Columns
’
are
both ‘5
1
2
’, the ‘Slice
Thickne
s
s’ i
s
‘5mm’,
an
d
the ‘Spa
ce B
e
twee
n Slice
s
’ is ‘6mm’.
For
these im
age
s, the inter-sli
c
e resolution
is ‘6mm’, a
n
d
intra
-
sli
c
e
one i
s
le
ss t
han ‘1m
m
’. The
inter-sli
c
e re
solution of these imag
es
were
coarse, thus ma
ny image-
processi
ng appli
c
atio
ns
(su
c
h a
s
im
age visu
alization and a
c
curate q
u
a
n
titative analysis) n
eed
some
kind
s of
interpol
ation betwe
en
the slices.
There are m
any slice int
e
rpol
ation al
gorithm
s pro
posed in literature
s
. Broa
dly, these
interpol
ation
algorith
m
s ca
n be
divided
i
n
to two
categ
o
rie
s
: sce
n
e
-
based
and
ob
ject-b
ased. T
he
scene
-ba
s
e
d
method
s use the
inten
s
ity values
of
the
given
scene
to dete
r
min
e
t
he inte
rpol
ate
d
scene
inten
s
it
y values.
The
obje
c
t-ba
sed
metho
d
s u
s
e
the o
b
je
ct inf
o
rmatio
n extracted
from
th
e
given scen
e
to guide the
interpol
ation
pro
c
e
ss. In
these lite
r
at
ure
s
, Thom
a
s
compa
r
e
d
the
traditional int
e
rpol
ation m
e
thod
s: 1) Truncated
and
windo
wed
sinc; 2) Nearest neig
hbo
r; 3)
Linea
r;
4) Qu
adrati
c
;
5) Cubic and app
roximati
on te
chni
que
s a
n
d
had the
co
n
c
lu
sion th
at ‘one
might have
troubl
e in fin
d
ing the
opti
m
al kern
el
f
o
r a
spe
c
ific interp
olation
appli
c
ation’
[1].
Pervez
utilized amal
gam
ation of bi-cubic int
e
rp
ol
ation and
2d
interpol
ation
filter to pro
duce
s
u
per
res
o
lution [2]. Fei used multis
urfac
e
fitting
to
a
c
hieve
imag
e
SR
re
con
s
truction
fram
e
w
ork
[3]. Konstantinos imp
o
se
d Hermite
kernel
s irre
sp
ectively of the maximum
order of si
gnal
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Slice Interp
ol
ation for MRI
Usi
ng Di
sa
ssem
b
le-Rea
ssem
ble Metho
d
(Qing
hua Li
n)
6191
derivative an
d achieved fa
ster
ex
ecutio
n and
sm
aller interp
olation
error [4, 5]. S
unil p
r
opo
se
d
a
low complex
conte
n
t adapt
ive interpolati
on for re
al time appli
c
ation
[6].
Figure 1. Three Nei
ghbo
ri
ng MRI of Hu
man He
ad
The alg
o
rith
ms p
r
op
ose
d
in literatures
a
r
e
alge
brai
cally de
mandin
g
int
e
rpol
ation
method
s that utilized info
rmation of the values
of the signal to
be interpol
a
t
ed at distinct
positio
ns. T
h
e funda
ment
al of the
s
e
al
gorithm
s i
s
th
e inform
ation
of the valu
e
s
of the
si
gn
al to
be interp
olate
d
sho
u
ld be p
r
eci
s
e at di
stinct poi
nt
s. These al
gorithm
s are fit for photos, which i
s
point imagi
ng
. But for MRI,
this a
s
sumpt
i
on is
ha
rd
to
achi
eve. MRI corre
s
po
nd
s to a thin
slice
throug
h th
e h
u
man
bo
dy, a
nd
contai
ns a
ll the i
n
form
ation in
the
sli
c
e. Thu
s
mea
n
s th
e i
n
ten
s
i
v
e
value of the given scen
e of MRI is for voxel,
other than point. For that, the
results of th
ese
method
s are coa
r
sene
ss. The interpolat
ion re
sults h
a
d
forge
s
, and
the edge
s we
re dimme
d.
To imp
r
ove t
he inte
rpol
ation of M
R
I, th
is pa
pe
r p
r
op
ose
s
a novel
app
roa
c
h
to
do the
MRI interpol
a
t
ion, which
we call it as D-R met
hod. M
R
I corre
s
po
n
d
s to a thin slice thro
ugh the
human
body,
and contain
s
all the information in the
slice. Base
d on this
cha
r
a
c
teri
stic, the
D-R
method first disa
ssembl
es the information c
ontai
ned
in MRI, and then re
assem
b
les them un
de
r
the heuri
s
tic appro
a
ch of approa
chi
n
g con
s
iste
ncy to get hig
her sli
c
e
-
resolution. The
o
ry
analysi
s
and
experiment
results all proved the
feasibility and e
ffective of th
e prop
osed
slice
interpol
ation algorith
m
.
2. Rese
arch
Metho
d
As sho
w
n in
Figure 1, the inter-slice
re
solution
o
f
MRI is
wo
rse. In th
e
DICO
M
informatio
n o
f
these
M
R
I, the ‘Sli
ce T
h
ickne
s
s’ i
s
‘
5
mm’, an
d th
e ‘Spa
ce B
e
twee
n Slices’
i
s
‘6mm’. We
want to imp
r
ov
e the inte
r-sli
c
e
re
solu
tio
n
of these
MRI,
and th
e ‘Slice Thi
c
kne
ss’
will
be ‘1mm’. E
s
sentially, one ‘5mm’ thick
slice is
comp
osed by five ‘1mm’ thin ones, likes
building
blocks. Thi
s
gives
us som
e
tips to d
o
t
he
slice inte
rpolation.
Co
n
s
ide
r
se
rie
s
i
m
age
s a
s
sh
own
in Fig
u
re
2
(
a). Th
ese
1
20 im
age
s
are
con
s
tru
c
ted a
r
tificial.
Three
con
c
entric ri
ng
s
with
differen
c
e
dia
m
eters a
nd g
r
ayscale
s
are
in the
ce
nt
er of these ima
ges. Fi
gu
re 2
(
b) is th
e
cent
e
r
coronal pl
ane
of Figure 2
(
a
)
. Every six image
s in
Fig
u
re 2
(
a)
we
re
con
s
ide
r
ed a
s
a group. Th
e
first five ima
g
e
s i
n
o
ne
gro
up
comp
ose
corre
s
p
ondin
g
on
e ima
ge
in Figu
re
2(c), with the
sixt
h
image in the grou
p missin
g. So Figure 2(c) ha
s
20 image
s. Figure 2(d) i
s
the cente
r
co
ron
a
l
plane of Fig
u
re 2(c). In Fig
u
re 2
(
c), the inter-sl
i
c
e resolution of the
image
s is
worse. The im
ag
es
have forg
es,
and the e
d
ges
are
dim
m
ed. Image
-pro
ce
ssi
ng a
pplication
s
(su
c
h a
s
ima
ge
visuali
z
ation
and a
c
cu
rate
quantitative
analysi
s
) n
e
e
d
some
kin
d
s of interpolati
on bet
wee
n
t
he
slices. F
r
om
the a
s
sumpti
on, the im
ag
es i
n
Fig
u
re
2(c)
co
ntain t
he info
rmatio
n of Fig
u
re 2
(
a).
Thus, we ca
n disa
ssembl
e the image
s in Figure 2
(
c), and
rea
s
semble them
as the imag
e
s
in
Figure 2(a
)
, a
nd it will improve the in
ter-slice re
solutio
n
of the images.
Base
on
the
analysi
s
abov
e, we
defin
e t
he n
imag
es i
n
Figu
re
2
(
c)
as i
nput i
m
ag
es, the
p*n imag
es i
n
Figu
re 2
(
a) as outp
u
t im
age
s. The g
r
ay value at p
o
int (
i
,
j
) in th
e
k
level of i
nput
image is
f
k
(
i
,
j
), 1
≤
k
≤
n,
k
is integer. Th
e gray value at point (
i
,
j
) in the
m
level of output imag
e is
g
m
(
i
,
j
). 1
≤
m
≤
p*n,
m
is inte
ger. O
ne ima
ge in in
put i
m
age
s is
co
mposed by p
image
s in o
u
tput
image
s. Sin
c
e MRI
co
rrespond
s
a
slice
throu
gh th
e
human
bo
dy, the
same
hu
man tissu
e
h
a
s
identical type of g(i,j), and
identical typ
e
of
g
(
i
,
j
) we
re nea
rby. Di
fferent huma
n
tissu
es h
a
v
e
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02-4
046
TELKOM
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KA
Vol. 12, No. 8, August 2014: 619
0 –
6197
6192
different type
s of
g
(
i
,
j
) in
MRI. With
out
loss
of g
e
n
e
rality, we a
s
sume
that t
he pixel
in i
n
put
image
f
(
i
,
j
) i
s
combi
ned
by
two type
s of
pixels i
n
o
u
tp
ut image
g
(
i
,
j
) at mos
t. If
f
(
i
,
j
) is compo
s
ed
by more type
s of
g
(
i
,
j
), the analysi
s
p
r
o
c
essing i
s
the
same,
b
u
t co
mplex. Thu
s
, we ju
st co
nsi
d
e
r
the situation
of two at most in this paper.
(a)
(b
)
(c
)
(d
)
Figure 2. Imitation the Pro
c
e
ssi
ng of MRI; (a) 12
0 ori
g
inal virtual i
m
age
s, (b)
ce
nter co
ro
nal
plane of ori
g
i
nal image
s, (c) 20
com
p
o
s
e image
s.
(d)
cente
r
co
ro
na
l plane of co
mpose imag
e
s
2.1. Disass
e
m
ble the Inp
u
t Image
The pixel
s
in
input imag
e
can
be cate
gori
z
ed i
n
to two type
s: smooth type a
nd ed
ge
type. As sho
w
n in
form
ula
(1
), the
smo
o
th type pixel
s
a
r
e th
ose p
i
xels who
s
e
gradi
ent a
r
e
not
large
than
th
e threshold,
and th
at me
a
n
the
s
e
pixel
s
a
r
e
in
obje
c
t. The
ed
ge
type pixel
s
are
those
pixel
s
who
s
e
gradie
n
t are la
rge
than th
e th
re
shold, a
nd th
a
t
mean
the
s
e
pixels were
on
the edge
s of obje
c
ts.
T
j
i
G
j
i
E
T
j
i
G
j
i
S
j
i
f
)
,
(
)
,
(
)
,
(
)
,
(
)
,
(
(1)
W
h
er
e
S
(
i
,
j
) i
s
the
smooth
type pixels,
E
(
i
,
j
) i
s
th
e e
d
g
e
type
pixels,
G
(
i
,
j
) is
th
e gr
a
d
i
en
t
of
f
(
i
,
j
), T is the threshold.
For the
smoo
th type pixels
S
(
i
,
j
) in the in
put image, th
e co
rre
sp
ondi
ng
g
(
i
,
j
) in th
e
output
image is the
same, an
d ca
n be derive
d
by formula (2
).
1)
-
(
/
)
,
(
)
,
(
p
j
i
S
j
i
g
(2)
After all the smooth type pi
xels are co
nfirmed.
We co
me to the edg
e type pixels. For the
edge
type pix
e
ls
E
(
i
,
j
)
in
the
in
pu
t ima
ge, it s
h
ou
ld
c
o
n
f
ir
m th
e e
dge
b
e
l
o
n
g
to
wh
ic
h tw
o o
b
j
ec
ts
firs
t. As
sume
E
(
i
,
j
) belo
ng t
o
two o
b
je
ct of
'
g
and
'
'
g
, then the co
rrespo
nding
g
(
i
,
j
) in
the output
image can be
derived by formula (3).
p
b
a
j
i
g
b
j
i
g
a
j
i
E
)
,
(
)
,
(
)
,
(
(3)
Whe
r
e a an
d
b are no ne
g
a
tive integer.
)
,
(
'
j
i
g
and
)
,
(
'
'
j
i
g
are the
gray values
of
'
g
and
'
'
g
.The form
ula (2
) is the
simple
situati
on of formula
(3)
whe
r
e a o
r
b is zero.
2.2. Reas
se
mble the Inp
u
t Image
For th
e smoo
th type pixels, the
g
k
(
i
,
j
),
g
k
+1
(
i
,
j
), …,
g
k
+p
(
i
,
j
) a
r
e id
enti
c
al, an
d the
r
e
are
no
probl
em
of reassem
b
le.
But for the
edge
type pi
xels, the
g
k
(
i
,
j
),
g
k
+1
(
i
,
j
), …,
g
k
+p
(
i
,
j
)
ar
e
differen
c
e
s
, a
nd the
r
e
nee
d a
heu
risti
c
approa
ch to
reassem
b
le th
em. Since M
R
I corre
s
po
n
d
s
a
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Slice Interp
ol
ation for MRI
Usi
ng Di
sa
ssem
b
le-Rea
ssem
ble Metho
d
(Qing
hua Li
n)
6193
slice thro
ugh
the huma
n
b
ody, the sa
m
e
huma
n
tissue ha
s id
enti
c
al type of
g
(
i
,
j
), and id
enti
c
al
type of
g
(
i
,
j
)
were n
e
a
r
by. Differe
nt hu
man tissu
e
s
have differen
t
types of
g
(
i
,
j
) in MRI. As
formula (4)
or formul
a (5), we a
s
su
me
g
k
(
i
,
j
),
g
k
+1
(
i
,
j
), …,
g
k
+p
(
i
,
j
) are several
)
,
(
'
j
i
g
and
)
,
(
'
'
j
i
g
.
]
),
,
(
,
),
,
(
),
,
(
[
)]
,
(
,
),
,
(
),
,
(
[
'
'
'
'
p
1
j
i
g
j
i
g
j
i
g
j
i
g
j
i
g
j
i
g
k
k
k
(4)
Or:
]
),
,
(
,
),
,
(
),
,
(
[
)]
,
(
,
),
,
(
),
,
(
[
'
'
'
'
p
1
j
i
g
j
i
g
j
i
g
j
i
g
j
i
g
j
i
g
k
k
k
(5)
The pixel
E
(
i
,
j
) is ed
ge type pixel, and
belon
g to two
object
s
. Accordin
g to the
g
(
i
,
j
) in
one obj
ect i
s
identical,
we
can d
e
ci
de
)
,
(
'
j
i
g
is
at left, or
)
,
(
'
'
j
i
g
is
at left, or it is
s
a
ndwich
st
ru
ct
ur
e.
For the missing (p*
k
-1) la
yers, the pro
posed algo
rit
h
m can tre
a
t it as the method
s
prop
osed in li
terature. In this pap
er, we j
u
st use the linear inte
rp
ola
t
ion for simpl
e
.
2.3. Propose
d
Algorithm
From the the
o
ry analysi
s
, the pro
p
o
s
ed
algorith
m
wo
rks a
s
follo
ws:
1) It calculate
s
the gradient
of each pixel
in input imag
es.
2) If the g
r
a
d
i
ent is l
a
rg
e t
han a
predefi
ned
th
re
shol
d, the pixel i
s
kno
w
n
as
an ed
ge
type pixel, else the pixel is kno
w
n a
s
a smooth type pixel.
3) Fo
r ea
ch
smooth type
pixel, the gra
y
value and
positio
n is
used to de
cid
e
whi
c
h
obje
c
t the pixel belon
gs.
4) Fo
r ea
ch
edge type pi
xel, the gray
value and
po
sition i
s
used
to decid
e which t
w
o
obje
c
ts the pi
xel belong
s.
5) Use formul
a (2) a
nd formula (3
) to disa
ssemble th
e pixels.
6) Use formul
a (4) o
r
(5
) to rea
s
sembl
e
the edg
e type pixels.
7) Use line
a
r
interpol
ation to
recons
truc
t the miss
layers
.
8) Outp
ut the inter-sli
c
e im
age
s.
3. Results a
nd Analy
s
is
In orde
r to evaluate the pe
rforma
nce of the pr
op
osed
inter-slice interpol
ation alg
o
rithm
,
we have
con
ducte
d exten
s
ive experi
m
ents in comp
arison three
other inte
r-sli
c
e inte
rpolati
on
method
s: Lin
ear inte
rpolati
on, Spline interpol
ati
on an
d Cubi
c interpolation.
The
test environ
m
ent
is MATLAB 7
.
1. The Line
a
r
, Spline a
n
d
Cubi
c inte
rp
olation i
s
em
bedd
ed in M
A
TLAB 7.1, and
can
ea
sy to u
s
e th
em. To
obje
c
tively evaluate th
e int
e
rpol
ation
s
ef
fect, the me
a
n
ab
solute
e
r
ror
(MAE) is u
s
e
d
to give performa
n
ce. The crite
r
ion i
s
defined a
s
fol
l
ow:
)
,
(
)
,
(
1
'
j
i
f
j
i
g
N
M
MAE
(6)
M* N
wa
s th
e total pixel n
u
mbe
r
of the
grayscal
e im
age
s;
)
,
(
j
i
g
is the
output imag
e
;
)
,
(
'
j
i
f
is the origi
nal
desired ima
g
e
.
The first te
st 20 image
s a
r
e sho
w
n in Fi
gure
2(c), an
d the image
s were 200*
20
0*8 bits
grayscal
e im
age
s. The 2
0
image
s in Fi
gure
2(c)
will
be interpolate
d
out as
120 i
m
age
s, and t
he
origin
al outpu
t images are sho
w
n in Fig
u
re 2(a)
. Each image in Fi
gure 2
(
c) correspon
ds to
six
image
s in Fi
gure 2
(
a
)
. Some part of th
e interpol
at
io
n re
sults i
s
shown in Figu
re 3. The
ce
nter
coronal
pla
n
e
of the
re
sult
s i
s
sho
w
n
in
Figu
re
4, a
n
d
Ta
ble
1
sh
ows the
MA
E re
sult fo
r t
he
above-mentio
ned alg
o
rithm
s
.
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6194
In Table
1, th
e MAE calcul
ated by
pro
p
o
se
d alg
o
rith
m wa
s l
o
wer
than the
MA
E of any
of the state of the art interpolation meth
ods. Fo
r the prop
osed alg
o
rithm,
the 28th, 38th, 58th,
68th, 88th, 9
8
th level ima
ges
we
re
achieved
by
D-R meth
od. T
he MAE of t
hese ima
g
e
s
wa
s
zeros,
whi
c
h
mean
s the in
terpolatio
n re
sults
re
st
ored
the origi
nal i
m
age
s very
well. The
18t
h,
48th, 78th,
1
08th level
im
age
s
were th
e multiple
of
six; from th
e
assu
mption
in pa
rt two, the
informatio
n o
f
these ima
g
e
s was
not containe
d
in i
m
age
s of Fig
u
re 2
(
c), and
the D-R met
hod
coul
dn’t work.
For th
ese lev
e
ls, the
propo
sed
al
go
rithm
used lin
ear
method fo
r
si
mple. Since t
h
e
neigh
bori
ng l
e
vels
we
re
re
store
d
well, t
he inte
rp
olation
re
sults we
re
also a
c
cep
t
able. Th
e M
A
E
of othe
r inte
rpolation
was bigg
er,
whi
c
h mea
n
s tha
t
there
were
bigg
er
difference in
outp
u
t
images and
original imag
es. The reason for that was these
algorithm
s
utilized the intensity
values of the
given
scene
to inte
rpolate
at distin
c
t
positions
. But the intens
ity values
of the given
scene
we
re f
o
r voxels, n
o
t
points. To
some ext
ent, these inten
s
ity values of the given
sce
ne
were n
o
t correct
at the
d
i
stinct
point,
so th
e inte
rp
olation
re
sult
s
were
wo
rse. But for th
e
prop
osed alg
o
rithm, the method first di
sassembl
ed
th
e information
in the given scen
e, and the
n
rea
s
sembl
e
d
them to get interpolate
d
images. So
the prop
osed
algorithm
works bette
r than
other a
r
t interpolation alg
o
rithms.
(b
)
(c)
(d)
(e)
(
f)
(a
)
Figure 3. Some Part of the Experiment
Results;
(a
) test image, (b) original im
ag
es, (c) Lin
ear
method, (d
) Spline metho
d
, (e) Cubi
c me
thod, (f) prop
ose
d
method.
(b
)
(a
)
(c
) (
d
)
(e)
(f)
Figure 4. The
Center
Co
ro
nal Plane of the Exper
ime
n
t Results; (a
) test image, (b) ori
g
inal
image
s, (c) Li
near m
e
thod,
(d) Spline m
e
thod,
(e
) Cu
bic metho
d
, (f) pro
p
o
s
ed m
e
thod
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Slice Interp
ol
ation for MRI
Usi
ng Di
sa
ssem
b
le-Rea
ssem
ble Metho
d
(Qing
hua Li
n)
6195
Table 1. MAE Compa
r
i
s
on
of Interpolate
d
Images by
Different Met
hod
s
Image
Linear
Spline Cubic Propose
algorith
m
18 4.53
4.53
4.53
0
28 9.50
9.63
9.47
0
38 17.45
17.65
17.54
0
48 19.87
19.87
19.87
0.26
58 15.13
14.62
15.13
0
68 23.46
23.67
23.15
0
78 35.42
35.42
35.42
0.31
88 42.44
44.15
42.44
0
98 31.02
33.04
31.43
0
108 5.90
5.90
5.90
2.93
… …
…
…
…
Avera
g
e
17.27
17.83
17.33
0.06
As sh
own in
Figure 5, the
se
con
d
teste
d
th
ree
MRI
were the th
ro
at of human,
and
were
extr
ac
ted form Figure 1. These MR
I
w
e
re 33*
65*8 bits
grayscale images
.
The r
e
ason
w
e
cho
o
se hum
a
n
throat fo
r e
x
perime
n
t wa
s that the
r
e
were only two obje
c
ts i
n
i
m
age
s, mu
scle
and ba
ckgro
u
nd.
So
it wa
s easy
to
confirm
the state o
f
pixels,
m
u
scl
e, ba
ckgro
u
n
d
or ed
ge
s. I
n
DICO
M information of the
s
e ima
g
e
s
, the ‘Slice Thi
c
kne
ss’ i
s
‘5
mm’. The inter-sli
c
e resolution
wa
s lower, an
d we wanted
to improve th
e inter-sli
c
e resol
u
tion to ‘1mm’.
The interpola
t
ion re
sults o
f
using
D-R
met
hod
were
sho
w
n in Fi
gure
6. The
pixels of
image
s in the
first line
we
re disassem
bl
ed an
d then
reassem
b
led i
n
the next five line
s
imag
e
s
.
The variatio
n
s
of the interp
olation re
su
lt
s we
re
con
s
istent with hum
an physi
cal.
The inte
rp
ola
t
ion re
sult
s o
f
usin
g Lin
e
a
r
, Spline
and
cu
bic metho
d
s
we
re
sh
o
w
n i
n
Figure 7. The
s
e alg
o
rithm
s
utilized the i
n
tensity va
lu
es of the give
n scene to b
e
interpol
ated
a
t
distin
ct positi
ons. So the
edge
s in the
image
s
we
re
coa
r
se
ne
ss
and dimm
ed,
they also ha
ve
some fo
rge a
r
ea
s.
Figure 5. Three Nei
ghbo
ri
ng MRI of Hu
man Th
roat
Figure 6. Interpolatio
n
Re
s
u
lts by
D-
R M
e
thod
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ISSN: 23
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KA
Vol. 12, No. 8, August 2014: 619
0 –
6197
6196
(a)
(b)
(c
)
Figure 7. Interpol
ation Re
sults by othe
r Me
thods; (a) Linear m
e
tho
d
, (b) Spline
method, (c)
cubi
c metho
d
4. Conclusio
n
MRI
corre
s
p
ond
s to
a t
h
in
slice through
the
hu
man b
ody,
and
co
ntain
s
all the
informatio
n in
the sli
c
e. T
h
us, the i
n
ten
s
ive valu
e
of
MRI is for v
o
xels, othe
r t
han p
o
ints. T
h
is
bring
s
so
me
obsta
cle
to traditional
interpolation
alg
o
rithm, whi
c
h
n
eed
s the
valu
es
of the
si
gn
al
to be inte
rpo
l
ated shoul
d
be p
r
e
c
ise.
The inte
rpol
a
t
ion re
sult
s o
f
traditional
a
l
gorithm
s
we
re
coa
r
sene
ss. Based o
n
the cha
r
a
c
teri
stic of
MRI, this pap
er p
r
opo
se
s a no
vel interpolati
on
method,
whi
c
h is
calle
d a
s
D-R metho
d
. The al
gor
i
t
hm first di
sa
ssemble
s
all
the inform
ation
contai
ned in
MRI, and the
n
rea
s
sembl
e
s them un
d
e
r the heu
ri
stic approa
ch
of appro
a
chi
n
g
con
s
i
s
ten
c
y to get
high
er
slice-re
solutio
n
. The
pri
n
ci
p
l
e an
d p
r
og
re
ss of the
p
r
o
posed
algo
rithm
are formulate
d
in detail. The qua
ntitative exper
im
ent
results sho
w
n that the pro
posed alg
o
rit
h
m
outperfo
rm
s the other inte
rpolation meth
ods, whic
h mean
s the D-R method is m
o
re suitable f
o
r
MRI interp
ola
t
ion.
Ackn
o
w
l
e
dg
ements
The autho
rs woul
d like to
express he
a
r
tfelt
thanks t
o
the financi
a
l supp
ort from the
Nation
al Natural S
c
ien
c
e
Found
ation o
f
China
(6
12
0139
7), the
Program of I
n
ternatio
nal
S&T
Coo
peration
unde
r Grant (S2013G
R0
18
8).
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ISSN:
2302-4
046
Slice Interp
ol
ation for MRI
Usi
ng Di
sa
ssem
b
le-Rea
ssem
ble Metho
d
(Qing
hua Li
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