Int
ern
at
i
onal
Journ
al of Ele
ctrical
an
d
Co
mput
er
En
gin
eeri
ng
(IJ
E
C
E)
Vo
l.
10
,
No.
4
,
A
ugus
t
2020
,
pp.
4101
~
41
08
IS
S
N: 20
88
-
8708
,
DOI: 10
.11
591/
ijece
.
v10
i
4
.
pp
4101
-
41
08
4101
Journ
al h
om
e
page
:
http:
//
ij
ece.i
aesc
or
e.c
om/i
nd
ex
.ph
p/IJ
ECE
Lum
bar di
sk 3D modelin
g from li
mited nu
mb
er
of
MRI
ax
i
al slic
es
Asm
a’a Al
-
M
nayy
is
1
,
S
ana
a Abu
A
l
as
al
2
,
M
ohamm
ad
Alsmir
at
3
,
Q
ani
ta Bani
B
aker
4
,
Sh
ad
i
AlZu’bi
5
1
Depa
rtment of
Cli
nical
Scie
n
ces
-
Radi
olog
y
Div
ision
-
MSK
R
adi
ologi
st,
Facult
y
of
Medicine
,
Yarm
ouk
Univer
sit
y
,
Jordan
2,3,4
Depa
rtment
o
f
Com
pute
r
Sci
e
nce
,
Jordan
Univ
ersity
of
Sci
enc
e
and Technolog
y,
Jordan
5
Com
pute
r
Scie
n
ce
Dep
art
m
ent
Al
Zay
t
oonah
Univer
si
t
y
of
Jord
an
,
Jord
an
Art
ic
le
In
f
o
ABSTR
A
CT
Art
ic
le
history:
Re
cei
ved
Dec
6
, 2
019
Re
vised
Feb
1
0
,
2020
Accepte
d
Fe
b
24
, 202
0
Thi
s
pape
r
stud
i
es
the
probl
em
of
cl
in
ic
a
l
MRI
a
naly
s
is
in
th
e
field
of
lumbar
int
erv
ert
ebr
al
d
isk
her
nia
t
ion
dia
gnosis.
It
di
scuss
es
the
poss
ibi
li
t
y
of
assisting
rad
iol
o
gists
in
rea
ding
the
patient'
s
M
RI
images
b
y
c
onstruct
in
g
a
3D
m
odel
for
t
he
reg
ion
o
f
inte
rest
using
sim
ple
computer
v
isio
n
m
et
hods.
W
e
use
axi
al
MRI
slic
es
of
the
l
um
bar
are
a.
The
proposed
fra
m
ework
works
with
a
ver
y
sm
all
num
ber
of
MR
I
slic
es
and
goes
through
thre
e
m
ai
n
stage
s.
Nam
ely
,
th
e
r
e
gion
of
in
te
r
est
ext
r
action
an
d
enha
n
ce
m
ent,
int
er
-
slice
int
erp
ol
ation,
a
nd
3D
m
odel
construc
t
ion.
W
e
use
the
Mar
c
hing
Cubes
al
gorit
hm
to
con
struct
the
3D
m
odel
of
the
reg
io
n
of
int
ere
st.
Th
e
val
id
at
ion
of
our
3D
m
o
del
s
is
b
ase
d
on
a
r
adi
o
logi
st'
s
anal
y
s
is
of
the
m
odel
s
.
W
e
te
sted
the
p
roposed
3D
m
o
del
construction
on
83
ca
ses
and
W
e
have
a
95%
ac
cur
acy
accordi
ng
to
th
e
rad
iol
ogist
ev
al
ua
ti
on.
Thi
s
st
ud
y
show
s
tha
t
3D
m
odel
c
onstruct
ion
ca
n
gre
atl
y
e
ase
the
ta
sk
of
the
rad
io
logi
st
which
enha
nc
es
the
working
expe
ri
en
ce
.
Th
is
le
ads
e
vent
ua
lly
to
a
m
or
e
ac
cur
a
te
and
e
as
y
di
agno
sis proc
ess.
Ke
yw
or
d
s
:
3D m
od
el
ing
Disk
he
rn
ia
ti
on
Iso
s
urface
Ma
rch
in
g
c
ube
s
MRI
Copyright
©
202
0
Instit
ut
e
o
f Ad
vanc
ed
Engi
n
ee
r
ing
and
S
cienc
e
.
Al
l
rights re
serv
ed
.
Corres
pond
in
g
Aut
h
or
:
Moh
am
m
ad
Alsm
irat
,
Dep
a
rtm
ent o
f
Com
pu
te
r
S
c
i
e
n
c
e
,
Jo
r
da
n Un
i
ver
s
it
y of
Scie
nce
and tec
hnol
ogy,
A
r
R
a
m
t
h
a
3
0
3
0
،
A
r
-
Ra
m
tha, Jor
dan
.
Em
a
il
:
m
as
m
ir
at
@just.ed
u.j
o
1.
INTROD
U
CTION
Disk
herniat
io
n
is
on
e
of
t
he
m
ai
n
causes
of
low
bac
k
pain
.
It
is
a
cl
ass
of
disk
relat
ed
de
gen
e
rati
on
def
i
ned
as
a
lo
cal
disp
la
cem
e
nt
of
disk
i
ngr
edients
t
ow
a
rd
the
poste
rior
norm
al
m
arg
ins
of
t
he
inte
r
-
vert
ebr
a
l
disk
[
1].
In
m
os
t
cases,
hernia
ti
on
occ
ur
s
in
t
he
lo
we
r
lum
bar
area
,
a
nd
it
is
detect
ed
by
t
he
pr
e
sence
of
pai
n
in
the
lo
we
r
bac
k
area
e
xten
ding
towa
rd
s
the
le
gs
[2,
3].
Hernia
ti
on
is
usual
ly
cat
egorized
in
sever
al
ways [
4].
Ba
sed on t
he
t
ype s
uch as
protr
us
io
n,
e
xtr
usi
on, a
nd
seq
ue
strat
ion
.
Ba
sed on t
he
l
ocati
on s
uch as
central,
poster
olate
ral (
rig
ht
or left),
an
d for
a
m
inal (r
ig
ht,
l
eft or
both
).
Dep
e
ndin
g
on
wh
et
her
it
has
com
pr
ess
on
or
disp
la
ce
the
ne
rv
e
root,
wh
ic
h
is
a
cause
of
sever
e
pain
.
Ma
gn
et
ic
re
sonance
im
aging
(MRI)
is
one
of
the
r
ou
ti
nes
c
onduct
ed
in
the
m
anag
em
ent
and
t
h
e
diag
nosis
of
diseases
s
uc
h
as
sp
inal
ste
nosis,
disk
herni
at
ion
,
or
tum
ors
[4,
5].
MR
I
us
es
m
agn
et
ic
fiel
ds
to o
btain
a
s
et
of
m
ulti
planar
i
m
ages
of
the
body
organs.
T
hose
an
at
om
ic
detai
ls
of
the
3D
organ
a
re
pr
es
ented
as
a
set
of
2D
par
al
le
l
cr
os
s
-
s
ect
ion
al
(
axial
)
,
sa
gitt
al
or
co
ronal
im
ages
[
6].
MR
I
scan
s
are
the
m
os
t
w
idely
us
e
d
im
aging
m
od
al
ity
for
exam
ining
the
anatom
y
and
the
physi
ology
of
the
bo
dy
de
sp
it
e
bein
g
the
m
os
t
exp
e
ns
i
ve
one
[7
]
.
Mostl
y,
the
aut
om
atic
diagnostic
resea
rch
that
is
bas
ed
on
cl
inica
l
MR
I
data
us
es
on
ly
the
s
a
g
i
t
t
a
l
vie
ws
[8
-
10
]
,
e
ve
n
th
ou
gh
ra
diol
og
ist
s
scan
both
sa
gitt
al
and
axial
planes
to
m
ake
their
final
diag
nosis [
4].
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8708
In
t J
Elec
&
C
om
p
En
g,
V
ol.
10
, No
.
4
,
A
ugus
t
2020
:
4101
-
4108
4102
In
ge
ne
ral,
r
ea
ding
t
he
MR
I
i
m
ages
is
a
c
ha
ll
eng
in
g
proc
ess
an
d
nee
d
t
i
m
e
and
e
ffo
rt
from
bo
t
h
rad
i
ologist
s
be
fore
the
case
c
an
be
dia
gnos
e
d.
T
he
a
forem
entione
d
c
halle
ng
e
s
m
otivate
d
researc
he
rs
to
study
conve
rting
m
edical
i
m
ages
into
qu
a
ntit
at
ive
m
easur
em
e
nts
[4
,
11
-
13]
.
In
a
nothe
r
di
recti
on,
resea
r
c
her
s
stud
ie
d
the
po
ssibil
it
y
of
bu
i
lding
3D
m
od
el
s
fr
om
tho
se
m
edical
i
m
age
[2
,
13
-
16,
9,
10
]
to
m
ake
read
in
g
the im
ages easier fo
r
the
sp
eci
al
ist
s.
In
t
his
pa
per,
we
are
plan
ning
to
bu
il
d
a
3D
m
od
el
for
the
dis
ks
in
the
l
um
bar
area
from
a
set
of
s
t
a
c
k
e
d
2D
a
xial
MR
I
sli
ces.
The
a
rea
that
we
ar
e
stud
yi
ng
is
the
area
betw
een
the
l
um
bar
ve
rteb
rae
4
and
5
(
L
4
/
L
5
disk
le
vel).
O
ur
m
et
ho
d
can
be
us
e
d
to
buil
d
a
3D
m
od
el
from
a
ve
ry
lim
i
te
d
nu
m
ber
of
axi
al
MR
I
sli
ces
as
i
t
is
us
ua
ll
y
ver
y
diff
ic
ult
to
get
m
or
e
s
li
ces
in
this
area.
The
3D
m
od
el
that
we
bu
il
t
is
u
sed
in
visu
al
iz
in
g
the
dis
k
to
assist
the
s
pecial
ist
in
the
m
anu
al
diag
-
no
se
s
of
the
st
ud
ie
d
c
ases.
By
perform
in
g
the
analy
sis
and
the
evaluati
on
of
the
3D
m
od
el
s
,
the
rad
i
ologist
find
s
th
at
it
is
easi
er
t
o
reach
the
diagnosi
s
base
d
only
on
the
3D
m
od
el
in
95%
of
the
cases.
The
re
st
of
the
pa
per
i
s
organ
iz
e
d
as
fo
ll
ows.
I
n
th
e
nex
t
sect
ion
,
we
re
vi
ew
the
previ
ous
w
orks
i
n
t
he
fiel
d
of
t
his
s
t
u
d
y
,
and
s
ect
ion
3
disc
us
es
the
dataset
we
us
e
in
our
e
xperim
ent
s.
The
propo
sed
3D
m
od
el
co
ns
tr
uctio
n
is
detai
le
d
i
n
sect
ion
4.
Fin
al
ly
,
the
res
ul
ts
are
pr
ese
nted
in
s
e
ct
ion
5.
2.
LIT
ERATUR
E
REVIEW
Ma
ny
stu
dies
c
an
be
f
ound
in
the
li
te
ratur
e
t
hat
deal
with
m
edical
3D
m
od
el
c
onstr
uction
but
no
n
of
them
was
done
on
a
li
m
it
ed
num
ber
of
M
RI
axial
view
scans
of
the
di
sk
s
i
n
the
l
umbar
a
rea.
F
or
t
he
3D
m
od
el
ing
ap
proach
e
s
in
tum
or
fiel
d,
Ar
a
ke
ri
et
al
.
,
[2]
dev
el
op
e
d
a
3D
co
ns
tr
uctio
n
a
n
d
qu
a
ntific
at
ion
m
et
ho
d
for
assist
ing
the
physi
ci
ans
in
s
urgical
plan
nin
g
a
nd
volu
m
e
co
m
pu
ta
ti
on
of
br
ai
n
tum
or
s.
They
reconstr
uc
te
d
a
3D
br
ai
n
tum
or
from
a
giv
e
n
set
of
2D
MRI
sli
ces
of
the
br
ai
n
by
dev
el
opin
g
m
et
ho
ds
for
se
gm
entat
i
on,
inter
-
sli
ce
inter
po
la
ti
on,
m
esh
gen
e
rati
on an
d
sim
plific
ation
. S
li
ces
that
con
ta
i
n
tum
or
w
e
r
e
extracte
d
f
ro
m
a
giv
en
set
of
axial
sli
ces
of
the
br
ai
n.
They
us
ed
a
centro
i
d
al
ign
m
ent
te
chn
iqu
e
an
d
interp
ola
-
ti
on
in
enh
a
ncin
g
the
sh
ape
whic
h
helpe
d
in
est
i
m
ating
the
m
issi
ng
sli
ce
s
accuratel
y
betwee
n
the
c
ho
se
n
sli
ces.
Th
ei
r
ex
per
im
ental
resu
lt
s
sh
owe
d
that
the
pro
posed
3D
co
ns
tr
uction
a
ppr
oa
ch
can
gen
e
rate
an
ac
cur
at
e
3D
m
odel
in
le
ss
t
i
m
e,
and
it
can
assis
t
the
rad
iolo
gis
t
to
identify
the
sta
ge
of
the
t
um
or
and
t
he
treat
m
e
nt
plan
ning.
Ali
et
al
.
,
[
13
]
hav
e
de
velo
pe
d
a
f
ully
auto
,
e
a
s
y
,
and
ef
fec
ti
ve
segm
entat
i
on
te
c
hniq
ue
f
or
detect
ing
and
e
xtracti
ng
the
tum
or
reg
i
on
from
three
seq
uen
ti
al
T1
-
weig
hted
MR
I
sli
ces.
These
segm
entat
ion
r
esults
wer
e
us
e
d
in
orde
r
to
re
co
ns
t
ru
ct
a
3D
im
age
for
the
tum
or
reg
i
on.
The
n
t
he
res
ulted
3D
tum
or
was
ins
erted
in
3D
c
onto
ur
i
m
age
of
the
brai
n.
T
he
relat
ive
siz
e
of
the
tum
or
has
bee
n
m
easur
ed
wit
h
res
pect
to
the
br
ai
n
siz
e. Th
is
wor
k
sho
we
d
that t
he
pr
opos
e
d
m
et
hod
co
uld be
u
se
d
in
detect
ing
a
nd ex
t
racti
ng
t
he
brai
n
t
um
or
in
the
MRI
im
ages.
Also
,
they
showe
d
that
t
heir
m
et
ho
d
ca
n
be
inc
orporated
in
longit
udinal
stud
ie
s
f
or
anal
yz
in
g
the
evo
l
utio
n
of
the
tum
or
s
an
d
their
im
pact
on
the
s
urr
oundin
g
struct
ur
es
.
Fu
rt
her
m
or
e,
their
res
ults
showe
d
that t
heir
m
od
el
can
be used f
or
the
diag
nosi
s,
the treat
m
ent p
la
nn
i
ng, th
e
thera
peu
ti
c m
on
it
or
i
ng,
s
u
r
g
e
r
y
,
and
path
ologica
l b
r
ai
n
m
od
el
ing
.
Kızı
lgo
¨
z
et
a
l.
,
[17]
ha
ve
cond
ucted
a
c
om
par
ison
bet
ween
th
ree
-
di
m
ension
al
tu
r
bo
s
pin
-
ech
o
se
quences
versus
c
onve
ntio
nal
two
-
dim
ension
al
tu
rbo
s
pin
-
ech
o
se
quences
in
the
diag
nosis
of
l
um
bar
interve
r
-
te
br
al
discs.
They
c
oncl
uded
that
th
e
3D
feat
ur
e
s
a
re
ve
ry
us
ef
ull
and
it
us
e
is
co
m
par
able
to
th
e
use
of
the
co
nvent
ion
al
MR
I.
A
fr
am
ewo
r
k
f
or
3D
surface
-
m
esh
-
base
d
seg
m
entat
ion
of
he
al
thy
and
herniat
e
d
disk
s
of
the
lum
bar
sp
i
ne
over
sagitt
al
pl
anes
was
pro
pose
d
by
Ha
q
et
al
.
,
[
9].
In
add
it
io
n,
t
his
pap
e
r
pr
ese
nted
a
pr
oof
of
c
oncept
of
t
heir
se
gme
ntati
on
m
et
hod
as
par
t
of
a
processi
ng
pipe
li
ne
for
a
nato
m
ic
al
m
od
el
s
inp
ut
to
interact
ive
s
urger
y
sim
ulatio
n,
es
pecial
ly
of
a
discect
om
y
pr
ocedur
e
,
in
conjuncti
on
with
the
S
OFA
-
bas
ed
sim
ulati
on
that
captu
res
s
pin
e
path
olog
y
with
fi
delit
y.
G
rou
nd
trut
h
m
od
el
is
m
a
de
by
SO
F
A.
The
m
ean
a
bsolute
s
hap
e
dista
nce,
MAS
D,
(in
m
m
)
and
a
bso
lute
sta
ndar
d
dev
ia
ti
on
of
al
l
errors
(in
m
m
),
abso
lute
m
ean
sq
ua
re
distance
MS
D
(in
m
m
),
the
Hau
s
dor
ff
distance
(in
m
m
)
and
DI
CE
sim
i
la
rity
coeffic
ie
nt
c
om
par
ison
m
et
rics
ha
ve
be
en
cal
culat
ed
to
c
om
par
e
the
qu
al
it
y
of
their
s
egm
entat
ion
a
ppr
oac
h
with
gro
und
tr
uth
.
Where
th
e
Hau
s
dor
ff
di
sta
nce
is
the
m
axi
m
u
m
su
rfac
e
distance
be
tween
tw
o
s
urface
m
eshes
an
d q
ua
ntit
at
ively
r
ep
resen
ts
a m
eas
ur
e
of the
w
ors
t
segm
entat
ion
error.
3.
D
A
T
A
S
E
T
The
dataset
use
d
in
this
wor
k
is
ta
ken
f
ro
m
King
A
bdullah
Un
i
ver
sit
y
H
ospit
al
(KAUH)
-
Irbid
,
f
r
o
m
the
ra
dio
l
og
y
dep
a
rtm
ent
(h
t
tps:/
/bit
.ly
/2BEWkwM
)
.
T
he
sam
e
raw
data
set
is
us
e
d
to
e
xtract
the
im
ae
s
us
e
d
i
n
[7
,
18,
19]
.
Fr
om
the
raw
dataset
,
the
cases
that
hav
e
m
ulti
ple
sli
ces
per
disk
are
c
hosen
beca
us
e
th
ey
can
b
e
us
e
d
in
3D
const
ru
ct
io
n
of
t
he
disk
a
re
a.
A
ra
dio
l
og
i
st
helpe
d
us
in
the
an
nota
ti
on
a
nd
cl
arifica
ti
on
of
Evaluation Warning : The document was created with Spire.PDF for Python.
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t J
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disk
3D
modeli
ng fr
om li
mite
d n
umber
…
(
Asm
a’a
Al
-
Mn
ayyis
)
4103
the
c
a
s
e
s
.
Sh
e
al
so
bu
il
t
a
gro
und
tr
uth
f
or
t
he
stud
ei
d
im
a
ges.
And
fi
nally
,
sh
e
validat
e
the
resu
lt
s
of
the
3D
c
o
n
s
t
r
u
c
t
i
o
n
of the
cases.
Each
patie
nt
is
inv
ol
ve
d
in
only
on
e
im
aging
sessio
n.
Im
a
ging
res
ults
co
ntains
T
1
an
d
T2
wei
gh
te
d
seq
uen
ces
in
the
sagitt
al
plan
e
(ser
ie
s
from
rig
ht
to
le
ft)
in
ad
diti
on
to
ax
ia
l
T1
an
d
T2
sli
ces
that
are
cutti
ng
the
body
trans
ver
sel
y.
F
or
th
e
lu
m
bar
area,
the
nu
m
ber
of
sli
ces
in
the
s
agitt
al
view
is
betwee
n
11
an
d
13
.
In
the
a
xial
v
i
e
w
,
the
num
ber
of
sli
ces
is
bet
ween
10
a
nd
20
an
d
the
re
are
5
cuts
co
ver
t
he
inter
ver
te
bral
disk
betwee
n
eve
ry
two
ver
te
brae
(
sp
inal
se
gm
ent
).
T
hese
5
c
uts
are
posit
ion
e
d
at
the
lower
e
ndplate
of
t
he
uppe
r
ver
te
br
a,
up
pe
r
pa
rt
of
the
disk
,
m
id
of
the
disk,
bott
om
of
the
disk
a
nd
at
the
uppe
r
e
ndplate
of
the
lowe
r
ver
te
br
a.
T
h
e
s
e
locat
ion
s a
re t
he best t
o desc
ribe
t
he
inte
rv
e
rtebr
al
dis
k
s
ha
pe.
The
thic
kness
of
eac
h
sli
ce
is
4mm
in
aver
a
ge
,
but
this
do
e
s
not
m
ean
that
the
s
pace
bet
w
een
sli
ces
is
4mm
.
The
distances
bet
ween
sli
ces
are
diff
e
ren
t
an
d
are
de
te
rm
ined
by
th
e
sp
eci
al
ist
to
t
ake
sli
ces
in
certai
n
places
that
appear
necessa
ry
f
or
the
diag
no
st
ic
pr
oce
ss.
T
he
se
places
are
usual
ly
determ
ined
on
a
sagitt
al
s
c
o
u
t
i
m
ages
that
sta
rt
from
le
ft
to
rig
ht
so
th
at
th
e
sp
ine
is
c
ut
longit
udinall
y
to
s
how
the
s
pi
nal
co
rd,
the
ne
ur
al
canals,
an
d
sur
rou
nd
i
ng
ti
ss
ue
s.
W
e
can
no
t
ic
e
fr
om
Figu
r
e
1
that
there
is
a
big
distanc
e
between
e
very
two
sli
ces.
This
dis
ta
nce
il
lus
-
trat
es
the
s
hri
nki
ng
a
nd
the
disa
pp
ea
ra
nce
of
s
om
e
ti
ssu
es
lo
cat
ed
bet
wee
n
tho
se
sli
ces.
He
nce,
we
f
ound
t
h
a
t
i
t
is
bette
r
to
ge
ner
at
e
a
rtific
ia
l
sli
ces
betwee
n
each
tw
o.
The
arti
fici
al
sli
ce
s
are
gen
e
rated
u
si
ng inte
rpolat
ing
adj
ace
nt
or
i
gina
l
sli
ces.
Figure
1.
P
os
it
ion
s
of t
he
MR
I
cu
ts l
ow
e
r,
m
i
dd
le
a
nd
uppe
r
the
disk
In
this
w
a
y
,
we
can
buil
d
a
m
od
el
that
si
m
ulates
the
sh
a
pe
of
the
area
on
w
hi
ch
the
dia
gnos
i
s
is
a
p
p
l
i
e
d
.
Our
stu
dy
include
s
on
ly
the
axial
T2
weig
hted
i
m
age
that
s
hows
a
high
sign
al
inten
sit
y
fo
r
the
str
uctu
re
s
w
i
t
h
higher wat
er c
on
te
nt su
c
h
as
the cere
bros
pina
l fluid
CSF a
nd the
nu
cl
e
us
pulp
osus of th
e
disk
[4
]
. T
he
a
rea
to
be
dia
gnos
e
d
in
each
sli
ce
is
the
m
arg
in
that
li
es
between
the
poste
ri
or
of
the
lum
bar
disk
an
d
the
inter
ior
of
the thecal
sac
, t
his ar
ea is
il
lustrate
d
in
Fig
ur
e 2
.
In
the
a
xial
v
i
e
w
,
the
healt
hy
disk
looks
li
ke
a
ci
rcle
with
blac
k
m
arg
ins
an
d
gray
co
lore
d
m
idd
le
.
The
thecal
sac
area
looks
li
ke
a
tria
ng
le
;
with
hole
s
in
di
cat
e
the
passag
e
o
f
the
sp
i
na
l
ner
ve
s
thr
ough
it
.
Fo
r
la
te
ral
neural
foram
en
(NF),
they
a
pp
ea
r
cl
early
,
as
they
al
low
the
traver
si
ng
nerves
to
exit
from
th
e
sides
of
the
t
h
e
c
a
l
sa
c
to
sup
ply
the
orga
n
that
the
y
are
rel
at
ed
to
[20].
On
t
he
ot
her
hand,
in
di
sk
herniat
ion
c
ases,
the
disk
ap
pea
r
s
to
be
bulge
d
ou
t
of
t
he
NF
f
iber
go
i
ng
out
to
it
s
poste
rio
r
side
that
to
uc
hes
the
anteri
or
area
of
t
he
thecal
sa
c.
This
bulgin
g
ap
pear
s
i
n
the
form
of
a
blac
k
area
exte
nd
i
ng
poste
rior
ly
to
the
ante
rio
r
pa
rt
of
the thecal
sac
a
nd
N
F
.
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S
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:
2088
-
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In
t J
Elec
&
C
om
p
En
g,
V
ol.
10
, No
.
4
,
A
ugus
t
2020
:
4101
-
4108
4104
(a)
(b)
Figure
2. Re
d
l
ines that i
nd
ic
a
te
s the ar
e
a
of
i
nterest,
(a)
no
r
m
al
case, (
b) a
bnorm
al
case
We
obta
in
83
cases
div
ide
d
i
nto
45
a
bnorm
al
cases
a
nd
38
norm
al
cases.
T
he
rad
i
ologi
st
exam
ined
these
cases
to
bu
il
d
a
gr
ound
truth
f
or
them
.
In
the
a
bror
m
al
cases,
30
case
s
are
diffus,
1
5
cases
are
fo
ra
m
inal
(one Le
ft
-
fora
m
inal, on
e
Ri
ght
-
f
oram
inal a
nd 13 Bi
-
f
or
a
m
inal). Th
is
gr
ound tr
uth i
s det
ai
le
d
in Ta
ble 1
.
Table
1.
T
raini
n
g ca
ses
dis
tri
bu
ti
on
of cla
ss
es
Clas
s ty
p
e
No
.
o
f
cases
No
r
m
al
38
Dif
f
u
se
30
Bi
-
f
o
ra
m
in
al
13
Left
f
o
ra
m
in
al
1
Rig
h
t f
o
ra
m
in
al
1
4.
PROP
OSE
D L
UM
B
AR D
I
SK
3D MOD
EL
CONSTR
UC
TI
ON
The
pro
posed
lum
bar
dis
k
m
od
el
c
on
st
ru
ct
io
n
m
et
ho
d
is
s
um
m
arized
by
t
he
fo
ll
owin
g
ste
ps
.
G
i
v
e
n
three
sli
ces
that
cut
the
lu
m
bar
inter
-
ver
te
br
al
dis
k
that
exists
betwee
n
L4
-
L5
ve
rteb
rae
in
three
lo
cat
ion
s
(up
per
,
m
idd
le
and
,
lo
we
r),
(
A)
e
xtract
the
reg
i
on
of
inter
est
(ROI
)
fro
m
each
sli
ce
a
nd
e
nh
a
nce
th
e
m
by
app
ly
in
g
s
o
m
e
i
m
age
proce
s
sing
te
ch
nique
s,
(B)
inter
pola
te
the
three
avail
able
sli
ces
to
gen
e
rate
arti
fici
al
inter
-
sli
ces
bet
ween
them
,
(C)
sta
ck
the
s
li
ces
anf
the
a
rtific
ia
l
sli
ces
tog
et
he
r
in
one
3D
im
age,
(
D)
a
nd
visu
al
iz
e
the
3D
i
s
o
s
u
r
f
a
c
e
data u
sin
g
t
he
m
a
rch
i
ng cube al
gorithm
[
21
]
i
n o
rd
e
r
to
create
a 3D
m
esh.
4.1.
ROI
ex
tra
c
tio
n and
prepr
oc
essing
The
R
O
I
extra
ct
ion
all
ow
s t
he
CAD
syst
em
to w
or
k
easi
er
because
the anal
ysi
s includ
es
on
ly
a
sm
all
r
egi
on
in
t
he
i
m
age
rathe
r
t
ha
n
processi
ng
a
la
rg
e
detai
le
d
im
age
[18].
The
a
reas
t
o
be
sel
ect
ed
is
de
te
rm
ined
by
the
rad
i
olog
ist
’s
guida
nce
and
is
the
n
m
od
el
ed
to
be
detect
ed
a
uto
m
at
i
cal
ly
.
In
our
ca
se,
we
a
re
inter
est
ed
i
n
the
area
ar
ound
th
e
m
idd
le
of
the
a
xial
MR
I
sli
ce.
T
o
pe
rfo
r
m
R
O
I
extracti
on,
we
us
e
d
t
he
sam
e
m
et
ho
d
us
e
d
in
pr
e
vious
w
orks
[
7,
18]
.
Thi
s
m
et
ho
d
is
cal
le
d
the
He
uri
sti
c
R
O
I
extracti
on,
w
here
it
is
done
ov
e
r
t
wo
pa
sses;
ver
ti
cal
and
ho
rizo
ntal extract
ion
s
.
A
sam
ple of
R
O
I
extract
ion
ste
ps
a
nd
r
esults are
il
lustrate
d
i
n
Fi
gure
3.
(a)
(b)
(c)
Figure
3. RO
I e
xtracti
on
resul
ts, (a)
ori
gina
l sl
ic
e, (b) ve
rtic
al
ex
tract
io
n
,
(c)
final st
rip
of RO
I
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
Elec
&
C
om
p
En
g
IS
S
N: 20
88
-
8708
Lumbar
disk
3D
modeli
ng fr
om li
mite
d n
umber
…
(
Asm
a’a
Al
-
Mn
ayyis
)
4105
Af
te
r
e
xtracti
ng
the
RO
I,
we
perform
so
m
e
enh
a
ncem
ents
ov
e
r
the
e
xtrac
te
d
R
O
I
in
ord
er
to
inc
rease
the
detai
ls
in
the
i
m
age
wh
ic
h
increases
t
he
a
ccur
acy
of
t
he
nex
t
ste
ps
.
T
he
enh
a
ncem
ents
that
we
are
i
nterested
in
aim
s
to
incr
ease
the
detai
ls
that
show
t
he
edg
e
s
that
se
pa
rate
the
ti
ssu
es
from
each
oth
e
r
in
the
stri
ppe
d
R
O
I
.
The
m
et
ho
d
th
at
we
us
e
in
e
dg
e
s
harpin
g
i
s
cal
le
d
t
he
unsh
ar
p
m
askin
g
[
22
]
i
n
wh
ic
h
the
im
age
(its
el
f)
is
su
bt
racted
f
r
om
a
blu
r
re
d
(
unsha
r
p)
ver
si
on
of
t
he
im
age.
U
nshar
p
m
asking
pr
oduces
a
n
e
dgy
im
age
(
,
)
from t
he
input
i
ma
ge
(
,
)
a
s i
n th
e
fol
lowi
ng e
quat
ion:
(
,
)
=
(
,
)
−
ℎ
(
,
)
(1)
wh
e
re
f
sm
oo
th
(
,
)
is
a
sm
oo
thed
ver
si
on
of
the o
ri
gin
al
im
age
(
,
)
.
Finall
y,
we
c
om
bin
e
al
l
of
t
his
into
the equat
io
n:
ℎ
(
,
)
=
(
,
)
+
∗
(
,
)
(2)
w
he
re
is
a
sca
li
ng
co
ns
ta
nt.
Logica
l
va
lues
o
f
k
m
igh
t
be
w
it
hin
the
r
an
ge
[
0
,
2],
the
la
r
v
ge
r
val
ues
pro
vid
e
s
increasin
g
am
ounts
of
sh
a
rpenin
g.
By
e
xperim
enting
with
diff
e
ren
t
val
ues
of
,
we
s
et
it
s
value
to
0
.
6.
W
e
us
ed
the Ga
us
sia
n
bl
urrin
g
filt
er
[23]
in o
r
der
to
sm
oo
t
h
the
im
age.
The
re
su
lt
o
f
t
his
proces
s
is
il
lustrate
d
in Figu
re
4.
(a)
(b)
Figure
4. RO
I
enh
a
ncem
ent re
su
lt
s, (a)
be
fore e
nh
a
ncem
ent, (b)
a
fter e
nh
ancem
ent
4
.
2.
Int
er
-
sli
ce
int
erpola
tio
n
W
e
only
ha
ve
three
2D
sli
c
es
for
eac
h
di
sk
,
wh
e
re
the
disk
i
nfor
m
at
i
on
betwee
n
th
ese
sli
ces
is
un
know
n.
Thi
s
prob
le
m
can
be
so
lve
d
by
interp
olati
ng
the
avail
able
2D
sli
ces
to
try
to
recover
so
m
e
inf
or
m
at
ion
ab
ou
t
th
e
dis
k
ar
ea
betwee
n
the
avail
able
sli
ces.
D
oing
that
m
ay
le
ad
to
producin
g
3D
vo
lum
e
with
m
or
e
deta
il
s.
In
te
rpolat
io
n
is
a
m
et
ho
d
of
co
ns
tr
uctin
g
ne
w
data
po
i
nt
s
within
the
ra
ng
e
of
a
disc
re
te
set
of
da
ta
points
t
hat
are
kn
own
[24].
This
ste
p
can
be
done
by
a
si
m
ple
l
inear
inter
po
la
ti
on
te
ch
nique
w
hich
is
fast,
but
if
th
e
distance
bet
ween
th
e
sli
ces
is
too
m
u
ch,
the
n
the
m
et
ho
d
produ
ces
discre
pan
c
ie
s
in
the
inter
pola
te
d
sli
ces.
T
ho
s
e
disc
rep
a
ncie
s
ha
ppen
bec
ause
ti
ss
ues
c
an
e
xpan
d,
s
hri
nk,
be
nd
or
eve
n
disap
pear
betw
een
two
s
ucces
sive
sli
ces.
Let
us
say
that
S
1
and
S
2
are
tw
o
sli
ces
that
we
need
to
inter
po
la
te
,
a sli
ce
that i
s e
xactl
y half
way b
et
wee
n
S
1
a
nd
S
2 i
s calc
ulat
ed
us
in
g
t
he
f
ol
lowing e
qu
at
i
on
:
(
=
0
.
5
)
=
(
1
+
2
)
/
2
(3)
wh
e
re
t
is
the
sp
ace
betwee
n
i
m
ages
and
it
i
s
betwee
n
0
an
d
1.
I
n
gen
e
ral,
we
can
inter
pola
te
betwee
n
at
any
sp
ace
t
us
ing
t
he follo
wing e
qu
at
io
n
:
(
)
=
(
1
−
)
∗
1
+
∗
2
(4)
4
.3
.
3D
m
od
el
con
struc
tion a
nd
visua
li
z
at
io
n
At
this
ste
p,
w
e
com
bin
e
the
interp
olate
d
sli
ces
in
one
sin
gl
e
i
m
age
of
f
our
dim
ension
s
as
a
sta
ck.
Th
os
e
f
our
dim
ensio
ns
are
x*
x*1*n,
w
her
e
t
he
first
two
x
a
re
the
dim
ensio
ns
of
the
sli
ces,
the
third
dim
e
ns
io
n
is
for
t
he
im
age
col
or
data
a
nd
n
is
f
or
the
num
ber
of
i
nter
po
la
te
d
sli
ces.
H
o
w
e
v
e
r
,
si
nce
we
are
deali
ng
w
i
t
h
gr
ay
scal
e im
ages th
e t
hird d
i
m
ension is no l
onge
r neede
d;
so
, we
can
eli
m
inate
it
to
ha
ve
a
3D
a
r
r
a
y
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8708
In
t J
Elec
&
C
om
p
En
g,
V
ol.
10
, No
.
4
,
A
ugus
t
2020
:
4101
-
4108
4106
W
e
only
care
about
the
poste
r
ior
pa
rt
of
t
he
disk
in
the
a
rea
that
tou
che
s
th
e
upper
e
dge
of
the
sp
i
nal
canal
an
d
t
he
lowe
r
e
dg
e
of
t
he
disk.
This
re
gi
on
f
or
m
s
on
ly
a
bout
25%
of
the
fi
rst
of
t
he
y
-
axis.
Th
us
,
sub
-
volum
e
is
do
ne
by
cutti
ng
the
or
i
gin
al
3D
ar
r
ay
and
hav
i
ng
on
ly
the
firs
t
25
%
of
the
voxels.
The
data
we
ar
e
ha
ving
now
i
s
sti
ll
voxels,
wh
e
re
t
hey
are
pix
el
s
in
a
vol
um
e
sp
ace
[
25]
.
In
orde
r
t
o
c
onve
rt
vo
l
um
et
ric
dat
a
into
a
geo
m
e
tric
al
su
rf
ace,
we
ha
ve
to
conver
t
those
voxe
ls
to
tria
ng
le
s;
this
pr
o
cess
is
cal
le
d
Trian
gu
la
ti
on.
On
e
of
the
tri
angulat
ion
te
c
hn
i
qu
e
s
us
e
d
m
ai
nly
in
the
fiel
d
of
3D
re
const
ru
ct
in
g
f
r
om
CT
scans
or
MRI
is
the
Is
os
urf
ace.
Iso
s
urfac
e
is
a
co
m
m
o
n
m
e
tho
d
in
both
m
edical
i
m
age
processi
ng
a
nd
com
pu
te
r
gra
phic
s.
It
is
u
s
e
d
f
or
vis
ualiz
in
g
volum
es
bas
ed
on
th
e
3D
gr
i
ds
that
c
on
t
ai
n
discr
et
e
va
lues
of
a
den
sit
y
f
un
ct
ion
[
26]
.
S
o,
the
isos
urface
of
a
gr
i
d
for
a
s
pecific
iso
valu
e
is
the
set
of
whole
po
i
nts
t
hat
thei
r
densi
ty
equ
al
s
to
that
isov
al
ue
.
It
is
bei
ng
use
d
to
re
pr
e
sent
reg
i
ons
of
a
pa
rtic
ular
de
ns
it
y
in
a
3D
CT
or
MR
I
scans, al
lowi
ng the
v
is
ualiz
at
ion
of inter
nal
orga
ns
, b
on
e
s, or
o
t
her
st
ru
ct
ures.
Diff
e
re
nt
isova
lues
outp
ut
di
f
fer
e
nt
isos
urfa
ces,
with
le
ss
or
m
or
e
data
(
de
ta
il
s).
As
a
ru
l
e,
the
lo
wer
isov
al
ue
woul
d
invo
lve
m
or
e
data
in
the
is
os
urf
ace.
The
higher
iso
valu
e
would
dri
ve
ou
t
noise
,
but
we
will
ob
ta
in
fe
we
r
da
ta
.
The
com
mo
n
sit
uatio
n
is
to
try
diff
ere
nt
isov
al
ues
in
orde
r
to
fin
d
w
hich
one
w
ork
s
best.
The
iso
values
that
we
are
interest
ed
in
are
the
values
that
rep
rese
nt
the
bounda
ries
su
c
h
as
the
bounda
ries
separ
at
in
g
bet
ween
the
bone
an
d
th
e
s
of
t
ti
ssu
es
[
27]
.
I
so
s
urface
e
xtr
act
ion
im
ple
m
entat
ion
s
usua
ll
y
us
e
the
Ma
rc
hing
Cub
es
al
gorith
m
[2
5],
wh
ic
h
retu
r
n
a
t
rian
gu
la
r
s
urface
t
hat
lo
oks
li
ke
te
ssell
at
ed
s
urf
ace
.
Also
,
the
isoc
aps
(e
nds
of
is
os
urf
ace)
m
us
t
be
ext
racted.
Iso
ca
ps
a
re
ex
tract
ed
f
or
t
he
pur
po
se
o
f
cr
eat
in
g
end
-
ca
ps
f
or
isosurface
s
of
the
3D
data,
wh
e
re
it
pla
ces
caps
at
the
ope
n
en
ds
of
the
is
osu
rf
aces
.
These
t
rian
gu
l
at
ed
s
urfaces
a
re
set
s
of
fac
es
an
d
ver
ti
ces,
wh
e
re
eac
h
t
riang
le
is
a
face
and
the
points
on
the
corner
s
of
eac
h face a
re t
he
ve
rtic
es.
In
order
to
buil
d
a
sin
gle
so
li
d
and
c
ohere
nt
m
od
el
,
we
nee
d
to
c
om
bin
e
tho
s
e
isos
urface
s
and
i
s
o
c
a
p
s
in
one
m
esh.
I
n
order
to
buil
d
a
si
ng
le
so
l
i
d
a
nd
co
he
ren
t
m
od
el
,
we
ne
ed
to
com
bin
e
tho
se
is
osur
fac
es
an
d
isocaps
in
one
po
ly
go
nal
3D
m
esh.
A
poly
gonal
3D
m
esh
consi
sts
of
th
re
e
kinds
of
m
es
h
el
em
ents:
v
e
r
t
i
c
e
s
,
edg
e
s,
a
nd
fac
es
[25].
A
ver
t
ex
is
a
po
sit
io
n
or
a
c
oor
dina
te
in
a
3D
s
pa
ce
with
oth
e
r
inf
or
m
at
ion
s
uch
as
colo
r,
no
rm
al
v
ect
or
,
a
nd
te
xt
ur
e
c
oor
din
at
es
.
An
ed
ge
is
a
c
onnecti
on
bet
w
een
two
ve
rtic
es.
A
f
ace
is
a
cl
os
e
d
gro
up
of
ed
ges
an
d
a
tria
ngle
face
ha
s
th
ree
edg
e
s.
T
o
bu
il
d
the
m
esh,
we
com
bin
e
the
f
aces
an
d
the
ve
rtic
es
resu
lt
ed
from
t
he
isos
urfaces
with
those
w
hich
are
ext
racted
from
the
isocaps.
Me
s
h
el
em
ents
are
con
s
tructe
d
in
a
sp
eci
al
ty
pe
of
tria
ngulate
d
m
esh
data
structu
re
cal
le
d
F
a
c
e
-
V
e
r
t
e
x
Mesh
[
28
]
.
It
is
de
f
ine
d
for
each
face
(of
de
gr
ee
d);
store
d
r
efe
rence
s
to
incident
ver
ti
ces
for
each
ve
rtex,
a
nd
one
ref
e
ren
c
e
to
its
coo
rd
i
nates
.
Figure
5
s
how
s
the
m
od
el
we
obta
in
a
fter
c
om
bin
ing
the
isosurf
ace
with
t
he
is
ocap
s
.
As
m
entioned,
we
nee
d
on
ly
the
first
25%
of the y
-
ax
is i
n our
diag
nosin
g
proce
ss.
(a)
(b)
(c)
(d)
Figure
5. 3D m
esh visuali
zat
ion,
(a)
is
osur
fa
ce, (b)
isoca
ps
,
(
c)
co
m
bin
at
io
n resu
lt
,
(d) on
ly
25% y
-
axis
of the
m
od
el
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
Elec
&
C
om
p
En
g
IS
S
N: 20
88
-
8708
Lumbar
disk
3D
modeli
ng fr
om li
mite
d n
umber
…
(
Asm
a’a
Al
-
Mn
ayyis
)
4107
5.
R
E
S
U
L
T
S
The
pro
po
se
d
3D
m
od
el
c
onstructio
n
m
et
ho
d
is
ap
plied
on
the
83
cases
that
we
have
in
the
datase
t
descr
i
bed
in
s
e
ct
ion
3.
U
nfo
rtun
at
el
y,
it
is
i
m
po
ssible
to
hav
e
a
groun
d
trut
h
3D
m
od
el
that
m
od
el
s
l
um
bar
disk
s
a
s
they
m
ay
diff
er
fro
m
per
son
t
o
pe
rson.
For
that
r
easo
n,
the
e
val
uation
of
the
c
ases
in
our
da
ta
set
is
p
e
r
f
o
r
m
e
d
b
y
a
r
a
d
i
o
l
o
g
i
s
t
by
v
i
s
u
a
l
i
z
i
n
g
o
n
l
y
t
h
e
3
D
m
o
d
e
l
s
r
a
t
h
e
r
t
h
a
n
a
na
l
y
z
i
n
g
t
h
e
s
e
t
o
f
2
D
s
l
i
c
e
s
.
O
u
r
3
D
m
od
el
ing
fr
am
ewor
k
is
valida
te
d
by
c
om
par
ing
t
he
2D
diag
no
si
ng
res
ults
ver
s
us
t
he
3D
di
agnosin
g
resu
l
ts.
Ther
e
wer
e
only
four
case
s
in
wh
ic
h
th
e
rad
iol
og
ist
need
e
d
to
get
back
to
the
2D
im
ages.
Af
te
r
in
vestiga
ti
ng
these
case
s,
we
fin
d
that
the
pro
blem
in
the
con
str
uction
of
the
m
od
el
is
caused
by
so
m
e
erron
e
ous
sli
ces
that
m
ay
resu
lt
from
par
ti
al
vo
lum
e
ov
erla
p
betwee
n
the
dis
k
regi
on
an
d
the
bone
of
the
uppe
r
or
l
ower
ver
te
br
ae
.
By
loo
ki
ng
at
th
e
num
ber
s,
t
he
eval
uatio
n
sh
ows
t
hat
the
pro
po
se
d
3D
m
od
e
l
const
ru
ct
io
n ha
s an acc
uracy
of m
or
e tha
n
95
%.
6.
CONCL
US
I
O
N
In
t
his
pa
pe
r,
we
pr
ese
nted
a
si
m
ple,
rob
us
t
,
an
d
fu
ll
y
aut
om
at
ed
3D
m
od
el
co
ns
tr
uctio
n
f
ram
ewo
r
k
for
m
edical
i
mages
wit
h
a
spe
ci
al
fo
cus
on
axial
MR
I
of
the
lum
bar
spi
ne.
O
ur
fr
am
ework
was
te
st
ed
on
a
dataset
that
c
on
ta
in
s
83
pati
ent
cases.
W
e
f
irst
extr
act
e
d
t
he
RO
I,
the
n
we
e
nh
a
nce
t
he
ROI
ed
ges,
the
RO
Is
from
diff
eren
t sl
ic
es
are
then
interp
olate
d
to f
il
l
the
gap
s
be
tween
the
sli
de
s,
finall
y,
we
sta
cked
th
e
i
m
ages
in
a
3D
m
at
rix
t
o
be
use
d
in
t
he
extracti
on
of
the
m
od
el
.
The
3D
m
od
el
was
evaluate
d
by
a
rad
iolo
gi
st
and
the
eval
uation
resu
lt
ed
an
d
ac
cur
acy
of
m
or
e
than
95%.
I
n
the
f
uture,
we
hope
to
be
a
ble
to
us
e
the
m
odel
in
the d
ia
gm
os
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d=8
zX
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2VRqBA
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