T
E
L
KO
M
N
I
KA
T
e
lec
om
m
u
n
icat
ion
,
Com
p
u
t
i
n
g,
E
lec
t
r
on
ics
an
d
Co
n
t
r
ol
Vol.
18
,
No.
3
,
J
une
2020
,
pp.
1621
~
1632
I
S
S
N:
1693
-
6930,
a
c
c
r
e
dit
e
d
F
ir
s
t
G
r
a
de
by
Ke
me
nr
is
tekdikti
,
De
c
r
e
e
No:
21/E
/KP
T
/2018
DO
I
:
10.
12928/
T
E
L
KO
M
NI
KA
.
v18i3.
14746
1621
Jou
r
n
al
h
omepage
:
ht
tp:
//
jour
nal.
uad
.
ac
.
id/
index
.
php/T
E
L
K
OM
N
I
K
A
C
on
t
o
u
r
e
vol
u
t
io
n
m
e
t
h
o
d
f
o
r
p
r
e
c
is
e
b
o
u
n
d
ar
y
d
e
li
n
e
at
io
n
of
m
e
d
ic
al
i
m
age
s
F
r
is
k
a
Nat
ali
a
1
,
Hi
r
a
M
e
id
ia
2
,
Nun
i
k
Af
r
il
ian
a
3
,
Ju
li
o
Chris
t
ia
n
Youn
g
4
,
S
u
d
S
u
d
irm
an
5
1
,2
,
3,
4
U
n
i
v
ers
i
t
a
s
Mu
l
t
i
me
d
i
a
N
u
s
an
t
ara,
In
d
o
n
e
s
i
a
5
L
i
v
erp
o
o
l
J
o
h
n
M
o
o
re
s
U
n
i
v
er
s
i
t
y
,
U
n
i
t
ed
K
i
n
g
d
o
m
Ar
t
icle
I
n
f
o
AB
S
T
RA
CT
A
r
ti
c
le
h
is
tor
y
:
R
e
c
e
ived
Aug
22
,
2019
R
e
vis
e
d
J
a
n
16
,
2020
Ac
c
e
pted
F
e
b
25
,
2020
I
m
a
g
e
s
e
g
m
e
n
t
a
t
i
o
n
i
s
a
n
i
m
p
o
r
t
a
n
t
p
re
c
u
r
s
o
r
t
o
b
o
u
n
d
a
r
y
d
e
l
i
n
e
a
t
i
o
n
o
f
me
d
i
ca
l
i
m
a
g
e
s
.
O
n
e
o
f
t
h
e
ma
j
o
r
c
h
a
l
l
e
n
g
e
s
i
n
a
p
p
l
y
i
n
g
a
u
t
o
ma
t
i
c
i
ma
g
e
s
e
g
m
e
n
t
a
t
i
o
n
i
n
me
d
i
ca
l
i
m
a
g
e
s
i
s
t
h
e
i
m
p
e
rf
ec
t
i
o
n
i
n
t
h
e
i
m
a
g
i
n
g
p
r
o
c
e
s
s
w
h
i
c
h
ca
n
r
e
s
u
l
t
i
n
i
n
c
o
n
s
i
s
t
e
n
t
c
o
n
t
r
a
s
t
a
n
d
b
r
i
g
h
t
n
es
s
l
e
v
e
l
s
,
a
n
d
l
o
w
i
ma
g
e
s
h
a
r
p
n
e
s
s
a
n
d
v
a
n
i
s
h
i
n
g
b
o
u
n
d
ar
i
e
s
.
A
l
t
h
o
u
g
h
re
ce
n
t
a
d
v
a
n
c
e
s
i
n
d
e
e
p
l
ea
r
n
i
n
g
p
r
o
d
u
c
e
v
a
s
t
i
m
p
r
o
v
em
e
n
t
s
i
n
t
h
e
q
u
a
l
i
t
y
o
f
i
ma
g
e
s
e
g
me
n
t
a
t
i
o
n
,
t
h
e
ac
c
u
r
ac
y
o
f
s
e
g
m
e
n
t
a
t
i
o
n
a
r
o
u
n
d
o
b
j
e
c
t
b
o
u
n
d
ar
i
e
s
s
t
i
l
l
re
q
u
i
re
s
i
m
p
r
o
v
em
e
n
t
.
W
e
d
e
v
e
l
o
p
e
d
a
n
e
w
a
p
p
r
o
a
c
h
t
o
c
o
n
t
o
u
r
e
v
o
l
u
t
i
o
n
t
h
a
t
i
s
m
o
r
e
i
n
t
u
i
t
i
v
e
b
u
t
s
h
a
re
s
s
o
m
e
c
o
m
m
o
n
p
r
i
n
c
i
p
l
e
s
w
i
t
h
t
h
e
a
c
t
i
v
e
c
o
n
t
o
u
r
m
o
d
e
l
me
t
h
o
d
.
T
h
e
m
e
t
h
o
d
u
s
e
s
t
w
o
c
o
n
c
e
p
t
s
,
n
a
me
l
y
t
h
e
b
o
u
n
d
ar
y
g
r
i
d
an
d
s
p
a
r
s
e
b
o
u
n
d
ar
y
r
e
p
re
s
e
n
t
a
t
i
o
n
,
a
s
a
n
i
m
p
l
i
c
i
t
a
n
d
e
x
p
l
i
c
i
t
r
e
p
r
e
s
e
n
t
a
t
i
o
n
o
f
t
h
e
b
o
u
n
d
a
r
y
p
o
i
n
t
s
.
W
e
t
e
s
t
e
d
o
u
r
me
t
h
o
d
u
s
i
n
g
l
u
m
b
ar
s
p
i
n
e
MR
I
i
ma
g
e
s
o
f
5
1
5
p
a
t
i
e
n
t
s
.
T
h
e
e
x
p
e
r
i
m
e
n
t
re
s
u
l
t
s
s
h
o
w
t
h
a
t
o
u
r
m
e
t
h
o
d
p
e
rf
o
rm
s
u
p
t
o
1
0
.
2
t
i
m
e
s
f
a
s
t
e
r
a
n
d
m
o
r
e
f
l
e
x
i
b
l
e
t
h
a
n
t
h
e
g
e
o
d
e
s
i
c
a
c
t
i
v
e
c
o
n
t
o
u
r
s
m
e
t
h
o
d
.
U
s
i
n
g
BF
-
s
c
o
re
c
o
n
t
o
u
r
-
b
a
s
e
d
me
t
r
i
c
,
w
e
s
h
o
w
t
h
a
t
o
u
r
me
t
h
o
d
i
mp
r
o
v
e
s
t
h
e
b
o
u
n
d
ar
y
a
c
c
u
r
ac
y
fr
o
m
7
4
%
t
o
8
4
%
a
s
o
p
p
o
s
e
d
t
o
6
3
%
b
y
t
h
e
l
a
t
t
e
r
me
t
h
o
d
.
K
e
y
w
o
r
d
s
:
B
ounda
r
y
de
li
ne
a
ti
on
C
ontour
e
volut
ion
I
mage
s
e
gmenta
ti
on
M
R
I
im
a
ge
s
Th
i
s
i
s
a
n
o
p
en
a
c
ces
s
a
r
t
i
c
l
e
u
n
d
e
r
t
h
e
CC
B
Y
-
SA
l
i
ce
n
s
e
.
C
or
r
e
s
pon
din
g
A
u
th
or
:
S
ud
S
udir
man
,
L
iver
pool
J
ohn
M
oor
e
s
Unive
r
s
it
y
L
iver
pool
L
3
3AF,
United
Kingdom
.
E
mail:
s
.
s
udir
man@
lj
mu
.
a
c
.
uk
1.
I
NT
RODU
C
T
I
ON
A
ba
s
ic
pr
oblem
in
c
omput
e
r
vis
ion
is
to
unde
r
s
tand
the
high
leve
l
of
inf
o
r
mation
c
ontaine
d
in
a
n
im
a
ge
or
a
s
e
r
ies
of
im
a
ge
s
.
M
a
ny
o
f
the
tas
k
s
in
c
omput
e
r
vis
ion
may
look
t
r
ivi
a
l
whe
n
pe
r
f
o
r
med
by
a
human.
T
a
s
ks
s
uc
h
a
s
de
tec
ti
ng
a
nd
dis
ti
nguis
hing
f
a
c
e
s
a
nd
objec
ts
in
im
a
ge
s
,
o
r
c
las
s
if
ying
ha
nd
ge
s
tur
e
s
in
videos
a
r
e
s
ome
of
the
e
xa
mpl
e
s
of
a
p
r
obl
e
m
that
hu
mans
c
a
n
do
with
r
e
lativ
e
e
a
s
e
but
c
ould
be
a
c
ha
ll
e
nge
f
or
a
c
omput
e
r
to
pe
r
f
o
r
m.
M
or
e
c
omp
lex
tas
ks
s
uc
h
a
s
de
tec
ti
on
o
f
a
nomalies
in
medic
a
l
im
a
ge
s
pos
e
a
n
e
ve
n
gr
e
a
ter
c
ha
ll
e
nge
due
to
it
s
high
a
c
c
ur
a
c
y
r
e
quir
e
ment
a
nd
high
-
r
is
k
f
a
il
ur
e
c
ons
e
que
nc
e
s
.
Unde
r
s
tanding
medic
a
l
i
mage
s
r
e
quir
e
s
a
s
pe
c
i
f
ic
s
e
t
of
s
kil
ls
a
nd
many
ye
a
r
s
of
e
xpe
r
ienc
e
wor
king
a
s
a
medic
a
l
pr
a
c
ti
t
ioner
s
uc
h
a
s
a
r
a
diol
ogis
t.
T
hus
,
in
buil
ding
a
c
omput
e
r
-
a
ided
diagnos
is
(
C
AD
)
s
ys
tem,
it
is
ne
c
e
s
s
a
r
y
to
a
dopt
the
wor
k
ing
pr
oc
e
dur
e
of
the
r
e
leva
nt
r
a
diol
og
is
t
a
nd
mod
e
l
it
a
s
a
n
a
lgor
it
hm
that
c
omput
e
r
s
c
a
n
e
xe
c
ute.
T
his
p
r
oc
e
s
s
is
a
c
ompl
e
x
tas
k
a
nd
may
r
e
qui
r
e
a
n
a
p
pli
c
a
ti
on
of
s
e
ve
r
a
l
im
a
ge
p
r
oc
e
s
s
ing
a
nd
c
omput
e
r
vis
i
on
tec
hniques
that
a
s
a
whole
c
ompl
e
ment
e
a
c
h
ot
he
r
.
I
mage
s
e
gmenta
ti
on
a
nd
bounda
r
y
de
li
ne
a
ti
on
a
r
e
two
im
po
r
tant
tas
ks
in
many
moder
n
i
mage
a
na
lys
is
pr
oc
e
s
s
e
s
including
c
omput
e
r
-
a
s
s
is
ted
diagno
s
is
thr
ough
medic
a
l
im
a
ge
a
na
lys
is
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
1693
-
6930
T
E
L
KO
M
NI
KA
T
e
lec
omm
un
C
omput
E
l
C
ontr
o
l
,
Vol.
18
,
No
.
3
,
J
une
2020:
1621
-
1632
1622
I
mage
s
e
gmenta
ti
on
ha
s
be
e
n
s
uc
c
e
s
s
f
ull
y
a
ppli
e
d
in
many
C
AD
s
ys
tems
wor
king
on
many
dif
f
e
r
e
nt
types
o
f
medic
a
l
im
a
ge
s
.
T
r
a
dit
ionally
,
i
mage
s
e
gmenta
ti
on
is
a
c
hieve
d
us
ing
c
lus
ter
ing
methods
,
s
uc
h
a
s
ge
n
e
ti
c
a
lgor
it
hm
[
1]
a
nd
f
uz
z
y
-
mea
ns
[
2]
,
of
a
number
of
manua
ll
y
de
s
igned
low
-
leve
l
f
e
a
tu
r
e
s
s
uc
h
a
s
pixel
va
lues
di
s
tr
ibut
ion
a
nd
his
togr
a
ms
of
gr
a
dients
.
S
tocha
s
ti
c
methods
a
r
e
a
ls
o
a
popul
a
r
a
ppr
oa
c
h
in
im
a
ge
s
e
gmenta
ti
on.
A
r
e
g
r
e
s
s
ion
s
e
gmenta
t
ion
f
r
a
mew
or
k
to
de
tec
t
va
s
c
ular
a
nomalies
in
c
a
r
d
iac
magne
ti
c
r
e
s
ona
nc
e
im
a
ging
(
M
R
I
)
i
mage
s
by
de
li
ne
a
ti
ng
bounda
r
ies
of
bi
-
ve
ntr
icle
f
r
om
wa
s
pr
opos
e
d
[
3
]
.
I
n
thi
s
f
r
a
mew
or
k,
a
r
e
g
r
e
s
s
ion
m
ode
l
ha
s
be
e
n
tr
a
ined
a
utom
a
ti
c
a
ll
y
on
a
de
e
p
be
li
e
f
ne
twor
k
by
us
ing
e
xtr
a
c
ted
DA
I
S
Y
f
e
a
tur
e
[
4]
a
s
input
a
nd
us
ing
a
utom
a
ti
c
a
ll
y
ge
ne
r
a
ted
bounda
r
y
point
s
a
s
labe
ls
.
T
he
method
wa
s
r
e
por
ted
to
yield
high
pe
r
f
o
r
manc
e
whe
n
tes
ted
o
n
2,
900
im
a
ge
s
take
n
f
r
om
145
c
li
nica
l
s
ubjec
ts
.
One
of
the
majo
r
c
ha
ll
e
nge
s
in
a
pplyi
ng
a
utom
a
ti
c
im
a
ge
s
e
gmenta
ti
on
in
medic
a
l
im
a
ge
s
s
uc
h
a
s
C
T
a
nd
M
R
I
is
the
im
pe
r
f
e
c
ti
on
in
the
im
a
ging
p
r
oc
e
s
s
whic
h
c
a
n
o
f
ten
r
e
s
ult
in
incons
is
tent
c
ont
r
a
s
t
a
nd
br
ight
ne
s
s
leve
ls
,
a
nd
low
im
a
ge
s
ha
r
pne
s
s
a
nd
va
nis
hing
bounda
r
ies
.
R
e
c
e
nt
a
dva
nc
e
s
in
de
e
p
lea
r
ning
pr
oduc
e
va
s
t
im
pr
ove
ments
in
the
qua
li
ty
of
im
a
ge
s
e
gmenta
ti
on.
As
a
r
e
s
ult
,
r
e
s
e
a
r
c
h
in
thi
s
f
ield
ha
s
s
hif
ted
i
ts
f
oc
us
to
us
ing
mor
e
c
ontempor
a
r
y
tec
hniques
s
uc
h
a
s
c
onvolut
ion
ne
ur
a
l
ne
twor
ks
[5
,
6]
a
nd
r
a
ndom
f
or
e
s
t
[
7]
.
I
n
one
o
f
our
e
a
r
li
e
r
publi
c
a
ti
ons
[
5]
,
we
pr
opos
e
d
a
nove
l
method
f
or
im
a
ge
s
e
gmenta
ti
on
a
nd
bounda
r
y
de
l
inea
ti
on
to
a
s
s
is
t
diagnos
is
of
lum
ba
r
s
pinal
s
tenos
is
in
M
R
I
im
a
ge
s
us
ing
S
e
gNe
t
[
8]
.
I
t
is
noted
the
a
c
c
ur
a
c
y
of
de
e
p
lea
r
ning
c
las
s
if
ier
s
may
a
ls
o
de
pe
nd
on
the
a
c
c
ur
a
c
y
of
t
he
gr
ound
tr
uth
labe
ls
that
a
r
e
us
e
d
to
tr
a
in
the
models
.
P
r
oduc
ing
labe
l
im
a
ge
s
manua
ll
y
is
a
labor
ious
a
nd
lengthy
pr
oc
e
s
s
.
I
t
is
ve
r
y
unli
ke
ly
that
medic
a
l
e
xpe
r
ts
’
ti
me
is
us
e
d
to
c
a
r
r
y
out
thi
s
a
c
ti
vi
ty
f
or
hun
dr
e
ds
or
e
ve
n
thous
a
nds
of
im
a
ge
s
.
E
ve
n
i
f
thei
r
ti
me
is
u
s
e
d
to
labe
l
a
f
e
w,
they
may
not
ha
ve
the
ne
c
e
s
s
a
r
y
s
kil
ls
in
us
ing
digi
tal
a
ppli
c
a
ti
ons
to
pr
oduc
e
a
c
c
ur
a
te
s
e
gmenta
ti
on.
A
pr
a
c
ti
c
a
l
s
olut
ion
to
thi
s
is
to
ha
ve
the
medic
a
l
e
xpe
r
ts
to
tr
a
in
s
e
ve
r
a
l
s
kil
led
im
a
ge
labe
ll
e
r
s
on
the
im
por
tant
pr
inciples
a
nd
wha
t
f
e
a
tur
e
s
to
look
f
o
r
a
nd
a
s
s
ign
the
labe
ll
e
r
s
to
pr
oduc
e
the
g
r
o
und
tr
uth
labe
l
im
a
ge
s
f
or
the
c
las
s
if
ier
t
r
a
ini
ng.
H
owe
ve
r
,
e
ve
n
with
thi
s
a
ppr
oa
c
h,
the
r
e
is
s
ti
ll
a
h
igh
leve
l
of
p
r
o
ba
bil
it
ies
of
inac
c
ur
a
c
ies
,
e
s
pe
c
ially
a
long
r
e
gion
bounda
r
ies
[
9]
.
T
o
im
pr
ove
the
s
e
gme
ntation
a
c
c
ur
a
c
y
a
long
r
e
g
ion
bounda
r
ies
,
a
n
a
c
ti
ve
c
ontour
model
c
a
n
be
a
ppli
e
d
to
the
labe
l
im
a
ge
s
.
How
e
ve
r
,
in
our
s
tudy
of
the
im
po
r
tant
pr
inciples
on
im
a
ge
labe
li
ng
pr
o
vided
by
medic
a
l
e
xpe
r
ts
,
we
f
ound
t
ha
t
the
e
xis
ti
ng
a
c
ti
ve
c
ontour
models
ha
ve
a
n
umber
of
dr
a
wba
c
ks
whe
n
a
r
e
us
e
d
to
labe
l
medic
a
l
i
mage
s
[
10]
.
T
hus
,
we
de
ve
lop
a
ne
w
a
ppr
oa
c
h
to
c
ontour
e
volut
ion
that
is
mor
e
int
uit
ive
but
s
ha
r
e
s
s
ome
c
omm
on
pr
inciples
wit
h
the
a
c
ti
ve
c
ontour
model
method.
T
hr
ough
a
n
a
lys
is
of
our
e
xpe
r
im
e
ntal
r
e
s
ult
s
,
we
s
how
that
our
method
ha
s
s
e
ve
r
a
l
pr
ope
r
ti
e
s
that
he
lp
ove
r
c
ome
the
p
r
o
blems
in
the
e
xis
ti
ng
a
c
ti
ve
c
ontour
models
.
T
his
pa
pe
r
s
ta
r
ts
by
dis
c
us
s
ing
the
pr
inciple
o
f
a
c
ti
ve
c
onto
ur
models
whic
h
is
f
oll
owe
d
by
the
de
s
c
r
ipt
ion
of
the
pr
oblems
in
a
pplyi
ng
thes
e
to
medic
a
l
im
a
ge
s
.
T
he
de
s
ign
of
ou
r
s
olut
ion
is
pr
ovided
in
s
e
c
ti
on
3
f
oll
owe
d
by
the
a
na
lys
is
of
the
e
xpe
r
im
e
ntal
r
e
s
ult
s
in
s
e
c
ti
on
4.
W
e
us
e
the
lum
ba
r
s
pin
e
im
a
ge
s
that
we
ha
ve
c
oll
e
c
ted
[
11]
a
nd
their
a
s
s
oc
iate
d
labe
l
im
a
ge
s
[
12]
in
our
e
xpe
r
im
e
nt.
T
h
is
da
tas
e
t
c
ontains
a
xial
M
R
I
s
c
a
ns
of
the
las
t
thr
e
e
int
e
r
ve
r
tebr
a
l
dis
c
s
of
515
pa
ti
e
nts
.
2.
AC
T
I
VE
CONT
OU
R
M
ODE
L
Ac
ti
ve
c
ontour
model
ha
s
be
e
n
us
e
d
to
s
e
gm
e
nt
a
nd
de
li
ne
a
te
bounda
r
ies
in
dif
f
e
r
e
nt
types
of
medic
a
l
im
a
ge
s
s
uc
h
a
s
e
c
hoc
a
r
diogr
a
phs
[
13]
,
M
R
I
[
14]
,
a
nd
C
omput
e
d
T
omog
r
a
phy
(
C
T
)
[
15]
.
I
t
is
a
popular
c
las
s
of
im
a
ge
s
e
gmenta
ti
on
a
nd
bounda
r
y
de
li
ne
a
ti
on
method
due
to
it
s
a
bil
it
y
to
f
it
a
c
ur
ve
to
a
n
objec
t
bounda
r
y
by
it
e
r
a
ti
ve
ly
e
xpa
nding
or
c
ontr
a
c
ti
ng
it
s
bounda
r
y
e
s
ti
mate
.
T
he
it
e
r
a
ti
ve
p
r
oc
e
s
s
s
tar
ts
by
de
f
ini
ng
a
n
ini
ti
a
l
c
ontour
0
a
nd
a
t
e
a
c
h
it
e
r
a
ti
on
,
the
c
ontour
e
volves
f
r
om
the
pr
e
vious
it
e
r
a
ti
on
−
1
s
uc
h
that
=
−
1
+
×
∆
,
whe
r
e
is
the
c
ontour
e
volut
ion
s
pe
e
d.
T
he
c
ontour
e
volut
ion
s
pe
e
d
is
not
a
s
ingul
a
r
e
nti
ty
but
r
a
the
r
a
mul
ti
-
va
lue
one
a
s
it
is
de
f
ined
a
da
pti
ve
ly
f
or
e
a
c
h
point
a
long
the
c
ontour
pos
it
ion
a
t
e
a
c
h
it
e
r
a
ti
on
.
T
his
is
il
lus
tr
a
ted
in
F
igu
r
e
1.
T
he
c
ontour
e
volut
ion
s
pe
e
d,
i.
e
.
,
the
r
e
d
a
r
r
ow
i
ll
us
tr
a
ted
in
F
igur
e
1
,
(
whic
h
is
o
f
ten
a
ls
o
r
e
f
e
r
r
e
d
to
a
s
F
or
c
e
de
noted
a
s
)
,
is
the
moveme
nt
of
e
a
c
h
point
a
long
the
c
ontour
.
T
he
f
or
c
e
ha
s
dir
e
c
ti
on
pe
r
pe
ndicula
r
to
the
tange
nt
o
f
the
c
ur
ve
.
T
he
v
a
lu
e
of
de
pe
nds
on
loca
l
pr
ope
r
ti
e
s
s
uc
h
a
s
c
ur
va
tur
e
,
global
pr
ope
r
ti
e
s
s
uc
h
a
s
s
ha
pe
,
a
nd
o
ther
indepe
nde
nt
p
r
ope
r
ti
e
s
[
16]
.
One
of
the
e
a
r
l
i
e
s
t
a
nd
mos
t
popular
a
c
ti
ve
c
ontour
models
is
S
na
ke
[
17]
.
I
t
c
a
n
a
r
gu
a
bly
be
c
ons
ider
e
d
a
s
the
ba
s
is
o
f
a
lm
os
t
a
ll
s
u
bs
e
que
nt
a
c
ti
ve
c
ontour
models
to
da
te.
I
n
thi
s
model,
the
f
or
c
e
is
c
a
lcula
ted
to
mi
nim
ize
a
n
e
ne
r
gy
f
unc
ti
o
n
that
is
a
f
unc
ti
on
of
the
c
ur
ve
’
s
in
ter
na
l
f
a
c
tor
s
e
.
g
.
,
th
e
f
ir
s
t
a
nd
s
e
c
ond
-
or
de
r
de
r
ivatives
of
the
c
ur
ve
a
s
we
ll
a
s
e
xter
na
l
f
a
c
tor
s
(
e
.
g
.
,
im
a
ge
de
pe
nde
nt
f
e
a
tur
e
s
s
uc
h
a
s
im
a
ge
gr
a
dient
or
e
dge
s
)
.
T
he
va
lu
e
of
is
the
int
e
gr
a
l
o
f
th
r
e
e
c
omponents
e
xpr
e
s
s
e
d
in
th
e
(
1)
:
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KO
M
NI
KA
T
e
lec
omm
un
C
omput
E
l
C
ontr
o
l
C
ontour
e
v
olut
ion
me
thod
for
pr
e
c
is
e
boundar
y
de
li
ne
ati
on
of
me
dical
image
s
(
F
r
is
k
a
N
atal
ia)
1623
=
∫
|
′
|
2
1
0
+
∫
|
′
′
|
2
1
0
+
∫
|
fe
a
tu
r
e
(
)
|
2
1
0
(
1)
whe
r
e
′
=
,
′′
=
2
2
,
a
nd
fe
a
tu
r
e
(
)
is
the
im
a
ge
f
e
a
tur
e
va
lue
c
a
lcula
ted
a
t
the
c
ontour
loca
ti
on.
T
he
model
us
e
s
thr
e
e
pa
r
a
mete
r
s
to
c
ontr
ol
th
e
e
f
f
e
c
t
of
e
a
c
h
c
omponent
on
the
c
ontour
e
volut
ion.
P
a
r
a
mete
r
s
a
nd
c
ontr
ol
the
c
ontr
ibut
ion
of
th
e
int
e
r
na
l
f
a
c
tor
s
whe
r
e
a
s
c
ontr
ols
the
c
ontr
ibu
ti
on
of
the
e
xter
na
l
f
a
c
tor
s
.
Almos
t
a
ll
of
the
s
ubs
e
qu
e
ntl
y
pr
opos
e
d
a
c
ti
ve
c
ontour
models
in
the
li
ter
a
tur
e
a
r
e
ba
s
e
d
on
thi
s
pr
inciple
.
Dif
f
e
r
e
nc
e
s
a
mongs
t
them
a
r
e
mainly
on
the
di
f
f
e
r
e
nt
wa
ys
of
c
a
l
c
ulating
a
nd
de
ter
mi
ning
e
a
c
h
of
the
thr
e
e
c
omponents
a
nd
their
pa
r
a
mete
r
s
.
F
igur
e
1.
T
he
e
volut
ion
o
f
the
c
ontour
(
b
r
own
li
ne
)
a
t
ti
me
f
r
om
the
pr
e
vious
c
ontou
r
−
1
(
blue
li
ne
)
with
the
r
e
d
a
r
r
ows
mar
king
the
c
ontou
r
e
volut
ion
s
pe
e
d
a
t
e
a
c
h
pos
it
ion
o
n
the
c
ontou
r
T
he
im
pleme
ntation
of
the
S
na
ke
a
c
ti
ve
c
ont
our
a
lgor
it
hm
us
e
s
the
z
e
r
o
leve
l
s
e
t
(
Z
L
S
)
f
r
a
mew
or
k
[
18]
.
T
his
f
r
a
mew
or
k
pr
opa
ga
tes
a
s
ha
pe
bou
nda
r
y
pe
r
pe
ndicu
lar
ly
to
the
c
ontou
r
b
y
mea
ns
of
a
n
E
uler
ian
f
or
mu
lation.
I
ns
tea
d
of
r
e
pr
e
s
e
nti
ng
the
bounda
r
y
a
nd
s
olve
the
e
volut
ion
pa
r
a
m
e
tr
ica
ll
y,
Z
L
S
r
e
pr
e
s
e
nts
2D
c
ontour
s
im
pl
icitl
y
a
s
a
s
e
t
of
point
s
of
whe
r
e
the
va
lue
of
a
f
unc
ti
on
c
r
os
s
e
s
z
e
r
o
(
e
it
he
r
f
r
om
po
s
it
ive
to
ne
ga
ti
ve
,
or
vice
ve
r
s
a
)
.
T
his
f
unc
ti
on
is
a
n
e
ve
r
ywhe
r
e
-
dif
f
e
r
e
nti
a
ble
im
a
ge
f
unc
ti
on
:
→
with
domain
2
.
T
he
f
unc
ti
on
is
a
s
pe
c
ial
i
mage
f
unc
ti
on
that
is
de
r
ived
f
r
om
a
labe
l
im
a
ge
.
Give
n
a
binar
y
im
a
ge
de
noti
ng
a
c
los
e
d
s
e
t
of
labe
ll
e
d
pixels
with
two
c
las
s
e
s
na
mely
a
nd
¬
,
whe
r
e
is
the
c
las
s
of
the
objec
t
of
int
e
r
e
s
t
in
the
i
mage
a
nd
¬
is
it
s
c
ompl
e
ment
c
la
s
s
,
the
f
unc
ti
on
ha
s
a
ne
ga
ti
ve
va
lue
a
t
pixels
that
be
long
to
a
nd
a
pos
it
ive
va
lue
a
t
pixels
whic
h
do
not.
S
inc
e
is
dif
f
e
r
e
nti
a
ble
e
ve
r
ywhe
r
e
,
it
s
va
lue
s
hould
be
z
e
r
o,
or
c
los
e
to
z
e
r
o,
a
t
bounda
r
y
loca
ti
ons
be
twe
e
n
a
nd
¬
r
e
gions
.
T
he
f
unc
ti
on
is
of
ten
il
lus
tr
a
ted
in
3D
wit
h
the
a
nd
a
xe
s
making
up
the
im
a
ge
plane
a
nd
the
f
or
the
va
lue
of
the
f
unc
ti
on
.
T
he
int
e
r
s
e
c
ti
on
of
th
e
f
unc
ti
on
with
the
=
0
plane
wi
ll
c
r
e
a
te
a
n
out
li
ne
of
the
bounda
r
y
o
f
the
two
r
e
gions
in
a
s
e
gmente
d
im
a
ge
.
T
h
is
s
e
t
o
f
po
int
s
is
c
a
ll
e
d
z
e
r
o
leve
l
s
e
t
a
nd
is
de
noted
a
s
.
C
ontour
e
volut
ion
us
ing
the
Z
L
S
me
thod
is
a
c
hieve
d
by
e
volvi
ng
the
f
unc
ti
on,
he
nc
e
the
s
tate
of
the
f
unc
ti
on
a
t
it
e
r
a
ti
on
is
de
noted
s
pe
c
if
ica
ll
y
a
s
.
T
he
r
e
f
o
r
e
,
a
t
a
ny
it
e
r
a
ti
on
,
the
z
e
r
o
-
leve
l
s
e
t
=
{
(
,
)
|
=
0
}
c
ontains
the
int
e
r
media
te
s
olut
ion
to
the
bound
a
r
y
de
li
ne
a
ti
on
pr
oblem.
T
he
pr
oc
e
s
s
to
c
ons
tr
uc
t
f
r
om
a
binar
y
labe
l
im
a
ge
is
il
lus
tr
a
te
d
in
F
igu
r
e
2
.
T
he
ini
ti
a
l
va
lue
of
,
i.
e
.
,
t
he
s
tate
of
the
f
unc
ti
on
a
t
the
s
tar
t
of
the
it
e
r
a
ti
on
,
de
noted
a
s
0
c
a
n
be
c
a
lcula
ted
f
r
om
the
ini
t
ial
s
e
gmente
d
im
a
ge
.
T
he
i
nit
ial
s
e
gmente
d
im
a
ge
is
a
binar
y
im
a
ge
with
pix
e
l
va
lues
of
1
f
or
e
ve
r
y
pixel
that
is
ins
ide
the
s
ha
pe
a
nd
0
other
wis
e
a
s
s
ho
w
n
in
F
igur
e
2
(
a
)
.
One
popular
method
to
c
ons
tr
uc
t
f
r
om
a
s
e
gmente
d
im
a
ge
is
by
c
a
lcula
ti
ng
the
s
igned
dis
tanc
e
f
unc
ti
on
(
s
d
f
)
[
19
]
.
F
or
e
a
c
h
p
ixel,
is
c
a
lcula
ted
a
s
the
dis
tanc
e
be
twe
e
n
that
pi
xe
l
to
the
c
los
e
s
t
point
on
.
T
his
may
s
ound
li
ke
a
n
e
gg
-
a
nd
-
c
hicke
n
pr
oblem
with
r
e
ga
r
ds
to
a
nd
,
but
in
pr
a
c
ti
c
e
,
the
c
a
n
be
c
a
lcula
ted
us
i
ng
the
E
uc
li
dian
dis
tanc
e
tr
a
ns
f
or
m
(
Edt
)
of
the
bina
r
y
s
e
gmente
d
im
a
ge
.
M
or
e
pr
e
c
is
e
ly,
the
is
c
a
lcula
te
d
a
s
the
dif
f
e
r
e
nc
e
of
the
E
uc
li
d
ian
dis
tanc
e
t
r
a
ns
f
or
m
of
the
binar
y
s
e
gmente
d
im
a
ge
a
nd
the
E
uc
li
dian
dis
tanc
e
tr
a
ns
f
or
m
of
the
inver
s
e
o
f
the
b
inar
y
s
e
g
mente
d
im
a
ge
,
i
.
e
.
,
=
(
)
−
(
¬
)
(
2)
whe
r
e
is
the
binar
y
s
e
gmente
d
im
a
ge
a
nd
¬
is
i
ts
inver
s
e
.
A
d
is
tanc
e
tr
a
ns
f
or
m
is
a
n
ope
r
a
to
r
t
ha
t
is
a
ppli
e
d
to
e
ve
r
y
pixel
in
it
s
input
binar
y
im
a
ge
to
c
a
lcula
te
the
dis
tanc
e
be
twe
e
n
the
pixel
to
the
ne
a
r
e
s
t
non
-
z
e
r
o
pixel
[
20]
.
F
igur
e
2
(
b
)
a
nd
F
igur
e
2
(
c
)
s
how
the
c
or
r
e
s
ponding
of
the
binar
y
im
a
ge
in
2
D
a
nd
3D,
r
e
s
pe
c
ti
ve
ly.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
1693
-
6930
T
E
L
KO
M
NI
KA
T
e
lec
omm
un
C
omput
E
l
C
ontr
o
l
,
Vol.
18
,
No
.
3
,
J
une
2020:
1621
-
1632
1624
Us
ing
Z
L
S
,
the
e
volut
ion
of
the
c
ontour
is
a
c
hie
ve
d
thr
ough
a
n
e
volut
ion
of
thi
s
s
igned
dis
tanc
e
f
unc
ti
on
.
T
he
f
i
r
s
t
,
0
is
r
e
quir
e
d
a
s
the
ini
t
ial
va
lue
to
s
tar
t
with.
T
he
r
e
lations
hip
be
tw
e
e
n
the
ne
w
a
nd
the
c
ontour
e
volu
ti
on
s
pe
e
d
is
given
a
s
the
lev
e
l
s
e
t
e
qua
ti
on
[
16]
:
=
−
×
|
−
1
|
(
3)
s
ince
it
s
int
r
oduc
ti
on,
ther
e
a
r
e
a
number
of
v
a
r
iations
of
the
Z
L
S
f
r
a
mew
or
k.
S
ome
methods
a
p
ply
dif
f
e
r
e
nt
e
ne
r
gy
m
ini
mi
z
a
ti
on
pr
oc
e
dur
e
s
whe
r
e
a
s
other
s
us
e
dif
f
e
r
e
nt
im
a
ge
f
e
a
tur
e
s
whe
n
c
a
lcula
ti
ng
.
One
of
the
mos
t
popula
r
is
the
e
dge
-
ba
s
e
d
Ge
ode
s
ic
Ac
ti
ve
C
ontour
s
(
GA
C
)
[
21
]
.
I
n
thi
s
a
ppr
oa
c
h,
t
he
f
or
c
e
a
c
ti
ng
on
the
s
igned
dis
tanc
e
f
unc
ti
on
is
c
a
lcula
te
d
a
s
:
=
+
+
(
⃑
⃑
)
(
4)
whe
r
e
is
the
s
pe
e
d
f
unc
ti
on
c
omponent
de
r
ived
f
r
om
the
f
e
a
tur
e
of
the
input
i
mage
.
W
he
n
a
po
s
it
ive
va
lue
of
is
us
e
d,
thi
s
c
ompone
nt
a
lwa
ys
a
c
ts
o
utwa
r
d
to
d
r
ive
the
c
ontou
r
to
e
xpa
nd.
T
he
s
e
c
on
d
c
omponent
of
the
s
pe
e
d
f
unc
ti
on,
,
is
the
mea
n
c
ur
va
tur
e
o
f
the
c
ontour
.
T
he
pa
r
a
mete
r
he
nc
e
c
ontr
ols
the
s
moot
hne
s
s
of
the
e
volvi
ng
c
ontour
.
T
he
th
ir
d
c
omponent,
∇
⃑
⃑
is
the
a
d
ve
c
ti
on
f
or
c
e
that
dr
a
ws
the
c
ontour
towa
r
ds
the
ne
a
r
e
s
t
e
dge
s
a
long
the
no
r
mal
ve
c
tor
o
f
the
c
ontour
.
(
a
)
(
b)
(
c
)
F
igur
e
2.
An
i
ll
us
tr
a
ti
on
o
f
the
c
ons
tr
uc
ti
on
of
the
s
igned
dis
tanc
e
f
un
c
ti
on
f
r
om
a
binar
y
labe
l
im
a
ge
;
(
a
)
i
nput
la
be
l
im
a
ge
is
us
e
d
to
de
ve
lop
it
,
(
b)
c
or
r
e
s
ponding
,
(
c
)
s
hows
the
s
a
me
a
s
view
e
d
in
3D
with
it
s
z
e
r
o
l
e
ve
l
s
e
t
mar
ke
d
in
r
e
d
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KO
M
NI
KA
T
e
lec
omm
un
C
omput
E
l
C
ontr
o
l
C
ontour
e
v
olut
ion
me
thod
for
pr
e
c
is
e
boundar
y
de
li
ne
ati
on
of
me
dical
image
s
(
F
r
is
k
a
N
atal
ia)
1625
As
the
na
me
s
ugge
s
ts
,
the
GA
C
method
c
a
lcula
tes
the
f
e
a
tur
e
us
ing
the
gr
a
dient
magnitude
inf
or
mation
o
f
the
input
im
a
ge
.
I
n
pa
r
ti
c
ula
r
,
it
is
c
a
lcula
ted
pe
r
p
ixel
a
s
:
=
1
1
+
|
|
2
(
5)
whe
r
e
the
f
e
a
tur
e
us
e
d
is
=
‖
(
∗
)
‖
‖
(
∗
)
‖
(
6)
t
his
f
e
a
tur
e
is
mor
e
popular
ly
known
a
s
the
nor
malize
d
gr
a
dient
magnitude
o
f
the
input
i
mage
.
T
he
ope
r
a
ti
on
(
∗
)
is
a
c
onvolut
i
on
of
the
i
mage
with
a
Ga
us
s
ian
ke
r
ne
l
with
width
.
2.
1.
Dr
awbacks
in
u
s
in
g
ac
t
ive
c
on
t
ou
r
m
od
e
ls
t
o
s
e
gm
e
n
t
m
e
d
ical
i
m
age
s
Ac
c
ur
a
te
s
e
gmenta
ti
on
of
im
a
ge
s
,
including
medic
a
l
im
a
ge
s
,
with
s
igni
f
ica
nt
int
e
ns
it
y
inhom
oge
ne
it
y
withi
n
the
s
a
me
r
e
gion
,
is
of
ten
dif
f
icult
to
a
c
hieve
[
22
]
.
I
n
our
s
tudy
of
s
e
ve
r
a
l
medic
a
l
im
a
ge
types
,
topol
ogy
,
a
nd
ge
ometr
y,
a
nd
while
guided
by
the
r
e
lev
a
nt
medic
a
l
e
xpe
r
ts
,
we
f
o
und
that
the
e
xis
ti
ng
a
c
ti
ve
c
ontour
models
ha
ve
a
numb
e
r
of
dr
a
wba
c
ks
whe
n
they
a
r
e
us
e
d
to
s
e
gment
medic
a
l
im
a
ge
s
.
Although
in
thi
s
pa
pe
r
we
only
f
oc
us
on
the
s
e
gmenta
ti
on
of
lum
ba
r
s
pine
M
R
I
im
a
ge
s
a
s
a
c
a
s
e
s
tudy,
our
r
a
ti
ona
le
a
nd
f
indi
ngs
s
hould
a
pply
ge
ne
r
a
ll
y.
B
or
r
owing
f
r
om
the
a
ppr
oa
c
h
we
took
in
o
ur
pr
e
vious
s
tudy
whe
n
de
li
ne
a
ti
ng
thi
s
type
of
im
a
g
e
s
[
5]
to
de
tec
t
lu
mbar
s
pinal
s
tenos
is
[
23]
,
ther
e
a
r
e
f
ive
r
e
gions
of
int
e
r
e
s
ts
in
e
a
c
h
im
a
ge
.
T
he
y
a
r
e
the
int
e
r
ve
r
teb
r
a
l
dis
c
s
(
I
VD
)
,
pos
ter
ior
e
leme
n
t
(
P
E
)
,
thec
a
l
s
a
c
(
T
S
)
,
a
r
e
a
be
twe
e
n
a
nter
ior
a
nd
p
os
ter
ior
(
AA
P
)
ve
r
teb
r
a
e
e
leme
nts
,
a
nd
Othe
r
(
O
T
)
.
T
he
dr
a
wba
c
ks
that
we
f
ound
a
r
e
s
umm
a
r
ize
d
a
s
f
oll
ow:
−
T
he
tr
ue
bounda
r
y
of
a
n
objec
t
r
e
gion
may
not
b
e
f
ound
by
jus
t
us
in
g
a
s
ingl
e
type
of
im
a
ge
f
e
a
t
ur
e
s
be
c
a
us
e
it
c
ould
de
pe
nd
on
s
e
ve
r
a
l
di
f
f
e
r
e
nt
one
s
.
F
or
e
xa
mpl
e
,
the
bounda
r
y
be
twe
e
n
the
I
VD
with
A
AP
r
e
gions
is
c
ha
r
a
c
ter
ize
d
by
s
tr
ong
pixel
int
e
ns
it
y
d
if
f
e
r
e
nc
e
s
howe
ve
r
the
bounda
r
y
be
twe
e
n
I
VD
a
n
d
T
S
is
not.
T
he
r
e
f
or
e
,
if
the
i
mage
gr
a
dient
f
e
a
tur
e
a
lo
ne
is
us
e
d
to
im
pr
ove
the
bounda
r
y
of
I
VD
it
may
r
e
s
ult
in
it
s
de
ter
ior
a
ti
on
ins
tea
d.
W
hil
e
many
d
if
f
e
r
e
nt
models
of
a
c
ti
ve
c
ontour
a
lgor
it
hms
ha
ve
be
e
n
pr
opos
e
d
in
the
li
ter
a
tu
r
e
whic
h
us
e
dif
f
e
r
e
nt
types
of
im
a
g
e
f
e
a
tur
e
s
,
ther
e
is
none
,
to
the
be
s
t
of
our
knowl
e
dge
,
whic
h
a
ll
ows
mul
ti
ple
di
f
f
e
r
e
nt
one
s
to
be
a
da
pti
v
e
ly
a
ppli
e
d
a
long
the
c
ur
va
tur
e
.
−
T
he
inclus
ion
o
f
a
ll
thr
e
e
c
omponents
of
s
pe
e
d
f
unc
ti
ons
in
one
c
a
lcula
ti
on
make
s
it
ha
r
de
r
to
f
ind
the
r
ight
c
ombi
na
ti
on
t
o
yield
the
be
s
t
r
e
s
ult
s
.
T
he
e
f
f
e
c
t
o
f
a
djus
ti
ng
one
c
ontr
ol
pa
r
a
mete
r
may
c
o
unter
the
e
f
f
e
c
t
of
a
djus
ti
ng
the
other
s
.
I
n
GA
C
,
f
or
e
xa
mpl
e
,
ge
ne
r
a
ll
y
us
ing
a
lar
ge
γ
va
lue
pus
he
s
the
c
o
ntour
ha
r
de
r
towa
r
ds
a
n
e
dge
r
e
s
ult
ing
in
a
c
ontour
e
volut
ion
that
mov
e
s
s
tr
ongly
towa
r
ds
ha
r
d
e
dge
s
whic
h
will
make
it
f
it
s
thes
e
e
dge
s
r
igi
dly.
How
e
ve
r
,
incr
e
a
s
ing
the
va
lue
of
β
c
ould
c
a
n
c
e
l
that
e
f
f
e
c
t
out
be
c
a
us
e
it
pe
na
li
z
e
s
high
c
ur
va
tur
e
.
As
a
r
e
s
ult
,
f
i
nding
the
r
ight
c
ombi
na
ti
on
o
f
pa
r
a
mete
r
va
lues
is
ve
r
y
tr
icky
a
nd
c
a
n
be
a
ppli
c
a
ti
on
de
pe
nde
nt.
T
h
is
phe
nomenon
is
il
lus
tr
a
ted
in
F
igu
r
e
3
,
that
s
hows
the
de
li
ne
a
ti
on
of
a
n
unmodi
f
ied
labe
l
im
a
ge
(
F
igu
r
e
3
(
a
)
)
a
nd
the
e
f
f
e
c
ts
of
a
pplyi
ng
the
GA
C
a
lgor
it
hm
us
ing
dif
f
e
r
e
nt
c
ombi
na
ti
ons
of
γ
a
nd
β
va
lues
to
the
labe
l
i
mage
(
F
igur
e
3
(
b
)
)
.
T
he
bounda
r
y
o
f
e
a
c
h
r
e
gion
pa
ir
is
c
olor
-
c
ode
d
to
a
ll
ow
e
a
s
ier
ins
pe
c
ti
on
.
T
he
f
igur
e
s
hows
that
ha
ving
lo
w
va
lues
of
γ
a
nd
β
pr
oduc
e
s
the
wor
s
t
r
e
s
ult
s
(
top
r
ow
a
nd
f
ir
s
t
f
ou
r
c
olum
ns
)
.
T
he
r
e
s
ult
s
a
r
e
be
tt
e
r
whe
n
a
lar
ge
va
lue
of
β
is
us
e
d
(
top
r
ow
–
f
i
f
th
c
olum
n
)
.
W
hil
e
f
ixi
ng
thi
s
β
va
lue,
the
e
f
f
e
c
t
of
c
ha
nging
γ
va
lues
doe
s
not
p
r
o
duc
e
s
igni
f
ica
ntl
y
dif
f
e
r
e
nt
r
e
s
ult
s
(
las
t
c
olum
n
)
.
How
e
ve
r
,
whe
n
the
lar
ge
s
t
γ
va
lue
is
us
e
d
the
e
f
f
e
c
t
of
c
ha
nging
β
a
ppe
a
r
s
to
r
e
ve
r
s
e
.
T
his
ti
me
lowe
r
i
ng
β
va
lue
s
hows
a
n
im
pr
ove
ment
in
the
qua
li
t
y
of
the
de
li
ne
a
ti
on.
On
a
f
ur
ther
note,
we
noti
c
e
that
mos
t
a
c
ti
ve
c
o
ntour
mode
ls
a
r
e
a
ppli
e
d
mainly
to
a
n
im
a
ge
in
it
s
or
igi
na
l
s
ize
.
T
his
li
mi
ts
the
p
r
e
c
is
ion
of
bounda
r
y
point
s
to
ha
lf
a
p
ixel.
I
nc
r
e
a
s
ing
the
s
ize
by
up
s
a
mpl
ing
the
im
a
ge
a
nd
it
s
labe
l
number
of
ti
mes
,
whe
r
e
∈
ℕ
,
c
a
n
incr
e
a
s
e
the
pr
e
c
is
ion
to
the
ne
a
r
e
s
t
2
−
(
+
1
)
.
How
e
ve
r
,
thi
s
a
ppr
oa
c
h
s
igni
f
ica
ntl
y
incr
e
a
s
e
s
the
number
of
pixels
to
c
ons
ider
a
n
d
our
e
xpe
r
ienc
e
s
hows
that
a
c
ti
ve
c
ontour
models
c
a
n
s
c
a
le
poor
ly
with
the
number
of
pixels
.
B
a
s
e
d
on
thes
e
f
a
c
tor
s
,
we
s
pe
c
if
y
th
r
e
e
r
e
quir
e
ments
tha
t
mus
t
be
met
f
o
r
a
s
uit
a
ble
c
ontou
r
e
volut
ion
method.
T
he
y
a
r
e
1)
it
mus
t
a
ll
ow
a
n
a
ppli
c
a
ti
on
of
e
v
olut
ion
on
a
s
ubs
e
t
of
c
ontour
a
s
opp
os
e
d
to
t
he
e
nti
r
e
c
ontour
.
T
his
will
make
it
pos
s
ibl
e
to
tailor
the
e
volut
ion
pr
oc
e
s
s
us
ing
dif
f
e
r
e
nt
im
a
ge
f
e
a
tur
e
type
f
or
dif
f
e
r
e
nt
pa
r
ts
o
f
the
c
ontour
a
nd
2
)
it
s
hould
de
c
o
uple
the
di
f
f
e
r
e
nt
c
omponents
of
e
volut
ion
f
unc
ti
o
n
s
o
that
the
bounda
r
y
f
it
t
ing
c
a
n
be
opt
im
ize
d
indepe
nde
ntl
y
in
e
a
c
h
c
omponent
s
pa
c
e
.
L
a
s
tl
y,
a
s
the
thi
r
d
r
e
quir
e
ment
3)
the
method
mus
t
s
c
a
le
we
ll
with
th
e
incr
e
a
s
e
in
pixel
number
s
due
to
up
s
a
mpl
ing
to
incr
e
a
s
e
the
de
li
ne
a
ti
on
pr
e
c
is
ion.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
1693
-
6930
T
E
L
KO
M
NI
KA
T
e
lec
omm
un
C
omput
E
l
C
ontr
o
l
,
Vol.
18
,
No
.
3
,
J
une
2020:
1621
-
1632
1626
(
a
)
(
b)
F
igur
e
3.
(
a
)
De
li
ne
a
ti
on
o
f
the
o
r
igi
na
l
labe
l
im
a
g
e
of
a
lum
ba
r
s
pine
M
R
I
i
mage
,
(
b)
T
he
r
e
s
ult
o
f
a
pplyi
ng
the
GA
C
a
lgor
i
thm
us
in
g
dif
f
e
r
e
nt
c
ombi
na
ti
ons
of
a
nd
va
lues
;
F
r
om
lef
t
to
r
ight
,
the
va
lues
us
e
d
a
r
e
0.
1,
0.
5
,
1
.
0
,
1.
2
,
a
nd
5.
0
.
F
r
om
top
to
b
ot
tom
the
va
lues
us
e
d
a
r
e
0.
1,
0.
5
,
1
.
0,
a
nd
1
.
2.
T
he
va
lue
of
is
f
ixed
a
t
1
thr
oughou
t
3.
T
HE
P
ROP
OS
E
D
CONT
OUR
E
VOL
UT
I
ON
M
E
T
HO
D
I
mage
s
e
gmenta
ti
o
n
is
a
pr
oc
e
s
s
that
c
lus
ter
s
pixe
ls
int
o
mu
lt
ipl
e
r
e
gions
.
T
he
mos
t
s
tr
a
ight
f
o
r
wa
r
d
wa
y
to
r
e
pr
e
s
e
nt
the
r
e
gions
in
a
n
i
mage
is
by
u
s
ing
a
matr
ix
of
labe
ls
with
the
s
a
me
s
ize
a
s
the
or
igi
na
l
im
a
ge
.
As
a
n
e
xa
mpl
e
,
a
n
ins
tanc
e
whe
r
e
a
4x4
im
a
ge
that
is
s
e
gme
nted
int
o
th
r
e
e
r
e
gions
is
il
lus
tr
a
ted
in
F
igur
e
4.
T
he
f
igur
e
de
picts
the
r
e
gion
bounda
r
i
e
s
a
s
r
e
d
li
ne
s
be
twe
e
n
pixels
that
ha
ve
di
f
f
e
r
e
nt
labe
ls
.
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KO
M
NI
KA
T
e
lec
omm
un
C
omput
E
l
C
ontr
o
l
C
ontour
e
v
olut
ion
me
thod
for
pr
e
c
is
e
boundar
y
de
li
ne
ati
on
of
me
dical
image
s
(
F
r
is
k
a
N
atal
ia)
1627
F
igur
e
4.
(
a
)
An
e
xa
mpl
e
o
f
a
4x4
im
a
ge
,
(
b)
T
he
i
mage
s
e
gmente
d
int
o
thr
e
e
r
e
gions
3.
1.
B
ou
n
d
ar
y
in
f
or
m
a
t
ion
r
e
p
r
e
s
e
n
t
at
ion
s
B
ou
nda
r
y
lo
c
a
ti
ons
a
r
e
n
a
t
u
r
a
ll
y
s
ub
-
pi
xe
ls
be
c
a
us
e
i
t
e
x
is
ts
be
twe
e
n
a
d
ja
c
e
nt
p
ix
e
ls
.
T
h
e
y
c
a
n
be
s
to
r
e
d
a
s
a
b
ou
nd
ar
y
g
r
i
d
,
w
h
ic
h
is
a
m
a
t
r
ix
w
ho
s
e
s
i
z
e
is
tw
ic
e
th
a
t
of
th
e
la
be
l
i
ma
ge
m
in
us
o
ne
.
A
ve
r
s
ion
o
f
th
e
B
o
un
da
r
y
G
r
i
d
tha
t
is
us
e
d
in
[
2
4
]
us
in
g
the
la
be
l
i
ma
ge
s
how
n
in
F
i
gu
r
e
4
(
b
)
is
s
h
ow
n
i
n
F
i
gu
r
e
5
.
F
igur
e
5.
B
ounda
r
y
G
r
id
of
the
labe
l
im
a
ge
s
hown
in
F
igur
e
4
(
b
)
I
n
t
he
a
b
ove
e
x
a
m
pl
e
,
c
e
l
ls
wi
th
b
ou
nda
r
y
in
f
o
r
ma
ti
o
n
a
r
e
s
ha
de
d
in
r
e
d
.
No
t
a
l
l
c
e
l
ls
in
a
b
ou
nd
a
r
y
g
r
id
c
a
n
be
bo
un
da
r
y
c
e
l
ls
a
n
d
i
n
ge
ne
r
a
l
on
l
y
c
e
l
ls
t
ha
t
ha
ve
e
i
t
he
r
1
)
a
n
e
ve
n
r
ow
n
u
mbe
r
a
nd
a
n
o
dd
c
ol
um
n
nu
m
be
r
o
r
2
)
a
n
e
v
e
n
c
o
lu
mn
n
um
be
r
a
nd
a
n
o
dd
r
ow
nu
mb
e
r
c
a
n
be
bo
un
da
r
y
c
e
ll
s
.
F
u
r
t
he
r
mo
r
e
,
bo
un
da
r
y
c
e
l
ls
in
c
a
t
e
g
or
y
(
1
)
ma
r
k
on
ly
h
o
r
iz
on
ta
l
b
ou
nda
r
ies
w
he
r
e
a
s
th
os
e
i
n
c
a
teg
o
r
y
(
2
)
ma
r
k
on
ly
ve
r
t
ic
a
l
b
ou
nd
a
r
i
e
s
.
Any
o
f
th
e
c
e
l
ls
t
ha
t
m
e
e
t
t
he
c
r
it
e
r
ia
bu
t
a
r
e
no
t
bo
un
da
r
y
c
e
ll
s
a
r
e
i
l
lus
t
r
a
ted
a
s
b
la
nk
s
qu
a
r
e
s
.
W
e
ma
de
a
s
ma
l
l
m
o
di
f
ica
t
io
n
to
th
is
id
e
a
b
y
in
c
l
ud
i
ng
i
ma
ge
f
e
a
tu
r
e
v
a
l
ue
s
i
nt
o
t
he
s
e
c
e
l
ls
.
T
he
t
ype
o
f
i
ma
ge
f
e
a
tu
r
e
c
hos
e
n
is
a
de
s
i
gn
de
c
is
io
n
a
n
d
i
t
i
s
im
po
r
ta
nt
t
o
t
he
a
c
c
u
r
a
c
y
a
n
d
s
ui
ta
bi
li
t
y
of
the
a
l
g
or
i
th
m
t
o
a
gi
ve
n
p
r
ob
le
m
.
How
e
v
e
r
,
i
n
th
is
pa
pe
r
,
we
us
e
a
s
im
i
la
r
ty
pe
o
f
im
a
ge
f
e
a
tu
r
e
a
s
GA
C
t
o
e
ns
ur
e
it
s
di
r
e
c
t
r
e
le
va
n
c
e
wh
e
n
c
om
pa
r
in
g
t
o
t
he
la
tt
e
r
.
W
e
r
e
f
e
r
t
o
t
h
is
mo
di
f
ica
ti
on
a
s
the
mo
d
if
ie
d
b
ou
nd
a
r
y
g
r
i
d
,
d
e
n
o
ted
a
s
′
.
T
h
e
i
ma
ge
f
u
nc
ti
on
o
f
′
is
g
ive
n
a
s
:
′
:
{
→
ℒ
|
(
1
2
)
≠
0
∧
(
2
2
)
≠
0
→
|
(
1
2
)
=
0
⊕
(
2
2
)
=
0
→
Ø
|
ℎ
(
7)
w
he
r
e
i
s
the
ℎ
e
l
e
m
e
n
t
o
f
a
nd
ℒ
=
{
1
,
…
,
}
w
h
e
r
e
is
th
e
m
a
x
im
um
n
um
be
r
o
f
r
e
gi
on
s
i
n
t
he
im
a
ge
.
T
h
e
a
l
go
r
it
h
m
to
c
ons
t
r
u
c
t
o
u
r
′
i
s
a
s
f
ol
lo
ws
:
L
e
t
:
→
be
t
he
i
np
ut
im
a
ge
f
u
nc
ti
on
a
nd
:
→
ℒ
b
e
i
ts
a
s
s
o
c
i
a
te
d
la
be
l
im
a
ge
f
u
nc
ti
on
,
b
ot
h
wi
th
d
o
ma
in
2
.
A
t
l
o
c
a
ti
ons
w
he
r
e
(
1
m
od
2
)
≠
0
∧
(
2
m
od
2
)
≠
0
,
′
c
on
ta
ins
th
e
la
be
l
in
f
or
ma
t
io
n
a
s
p
r
e
s
c
r
ib
e
d
i
n
.
A
t
l
oc
a
t
io
ns
w
h
e
r
e
(
1
m
od
2
)
=
0
∧
(
2
m
od
2
)
≠
0
,
′
c
o
n
tai
ns
ve
r
ti
c
a
l
g
r
a
d
ie
nts
a
nd
a
t
lo
c
a
ti
ons
w
he
r
e
(
1
m
od
2
)
≠
0
∧
(
2
m
od
2
)
=
0
,
′
c
on
ta
ins
ho
r
iz
on
ta
l
g
r
a
di
e
n
ts
.
I
n
pr
a
c
ti
c
e
,
the
gr
a
dient
va
lues
a
r
e
c
a
l
c
ulate
d
us
ing
the
c
onvolut
ion
of
the
input
im
a
ge
with
a
Ga
us
s
ian
ke
r
ne
l
of
width
to
mi
n
im
ize
high
-
f
r
e
que
nc
y
e
leme
nts
in
the
de
r
ivative
ope
r
a
t
ion.
He
nc
e
the
hor
izonta
l
a
nd
ve
r
ti
c
a
l
g
r
a
dient
im
a
g
e
f
unc
ti
ons
ℎ
:
→
a
nd
:
→
a
r
e
de
f
ined
a
s
ℎ
=
∇
ℎ
(
∗
)
a
nd
=
∇
(
∗
)
,
r
e
s
pe
c
ti
ve
ly.
T
he
s
ize
of
the
hor
izo
ntal
a
nd
ve
r
ti
c
a
l
gr
a
dient
im
a
ge
s
a
r
e
×
(
−
1
)
a
nd
(
−
1
)
×
,
r
e
s
pe
c
ti
ve
ly.
T
o
il
lus
tr
a
te
the
pr
oc
e
s
s
to
c
ons
tr
uc
t
our
′
let’
s
a
s
s
ume
that
the
hor
izonta
l
a
nd
ve
r
ti
c
a
l
gr
a
dient
i
mage
s
of
the
inpu
t
im
a
ge
s
we
us
e
d
p
r
e
vious
ly
a
r
e
s
hown
in
F
igur
e
6
(
a
)
a
nd
F
igur
e
6
(
b)
,
r
e
s
pe
c
ti
ve
ly.
T
he
r
e
s
ult
ing
′
is
s
hown
in
F
igu
r
e
6
(
c
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
1693
-
6930
T
E
L
KO
M
NI
KA
T
e
lec
omm
un
C
omput
E
l
C
ontr
o
l
,
Vol.
18
,
No
.
3
,
J
une
2020:
1621
-
1632
1628
F
igur
e
6.
Gr
a
dient
im
a
ge
s
o
f
the
input
i
mage
s
hown
in
F
igu
r
e
5
(
a
)
,
(
a
)
hor
izonta
l
,
(
b)
ve
r
ti
c
a
l,
(
c
)
the
r
e
s
ult
o
f
modi
f
ie
d
bounda
r
y
g
r
id
T
his
r
e
pr
e
s
e
ntation
is
,
howe
ve
r
,
ne
it
he
r
e
f
f
icie
nt
nor
c
ompac
t
if
we
wa
nt
to
us
e
it
in
a
n
it
e
r
a
ti
on
to
s
e
a
r
c
h
f
or
the
c
oor
dinate
s
of
a
s
pe
c
if
ic
r
e
gion's
bounda
r
y.
T
o
c
ompens
a
te
thi
s
s
hor
tcoming,
we
a
ls
o
us
e
a
s
par
s
e
boundar
y
r
e
p
r
e
s
e
ntat
ion
,
de
noted
a
s
,
a
s
a
look
-
up
table
to
index
pa
ir
s
of
ne
ighbour
ing
r
e
gions
.
T
his
is
a
much
mor
e
c
ompac
t
a
nd
e
f
f
icie
nt
r
e
pr
e
s
e
ntation
of
the
bounda
r
y
inf
or
mation
be
c
a
us
e
a
ny
s
e
a
r
c
h
or
inf
or
mation
r
e
tr
ieva
l
ope
r
a
ti
ons
that
a
r
e
c
a
r
r
ied
o
ut
in
thi
s
r
e
pr
e
s
e
ntation
a
r
e
c
a
r
r
i
e
d
out
f
a
s
ter
due
to
them
be
ing
de
pe
nde
nt
only
on
the
numbe
r
of
bounda
r
y
pixels
r
a
ther
than
the
number
o
f
pixels
.
W
e
c
a
n
c
ons
tr
uc
t
f
r
om
′
by
pa
r
s
ing
the
latter
onc
e
,
to
ga
ther
a
ll
e
dge
c
oor
dinate
s
f
or
e
a
c
h
ne
ighbor
ing
r
e
gion
pa
ir
s
.
T
a
ble
1
s
hows
th
e
s
pa
r
s
e
bounda
r
y
r
e
pr
e
s
e
ntation
of
the
B
ounda
r
y
Gr
id
e
xa
mpl
e
we
us
e
d
e
a
r
li
e
r
.
Note
that
matr
ix
s
ubs
c
r
ipt
s
a
r
e
e
xpr
e
s
s
e
d
a
s
r
ow
a
nd
c
olum
n
or
de
r
.
T
a
ble
1
.
S
pa
r
s
e
bounda
r
y
r
e
pr
e
s
e
ntation
N
e
ig
hbor
s
E
dge
ma
tr
ix
s
ubs
c
r
ip
ts
(
)
a
,
b
(
1,6)
(
2,5)
(
3,4)
a
,
c
(
4,1)
(
4,3)
b
,
c
(
4,5)
(
5,6)
(
6,7)
3.
2.
T
h
e
c
on
t
o
u
r
e
volu
t
ion
algori
t
h
m
I
n
thi
s
s
e
c
ti
on,
we
will
dis
c
us
s
the
a
lgor
it
hm
to
e
volve
the
r
e
gion
bounda
r
ies
us
ing
the
two
bounda
r
y
r
e
pr
e
s
e
ntations
de
s
c
r
ibed
pr
e
vious
ly.
L
e
t
be
a
s
e
t
c
ontaining
the
matr
ix
s
ubs
c
r
ipt
pa
ir
s
of
a
ll
the
bounda
r
y
point
s
that
we
wa
nt
to
e
volve
us
i
ng
our
c
hos
e
n
im
a
ge
f
e
a
tur
e
.
W
e
c
ons
tr
uc
t
dir
e
c
tl
y
by
que
r
ying
.
F
or
e
a
c
h
e
leme
nt
in
,
we
f
ind
it
s
loca
ti
on
in
′
,
a
nd
ba
s
e
d
on
the
va
lues
o
f
the
c
oo
r
dinate
we
c
a
n
a
s
c
e
r
t
a
in
the
type
of
e
dge
it
is
.
A
hor
izont
a
l
e
dge
is
e
volved
hor
izonta
ll
y
by
e
va
luating
th
e
f
e
a
tur
e
ve
c
tor
s
in
the
hor
izonta
l
dir
e
c
ti
on
.
L
ikew
is
e
,
ve
r
ti
c
a
l
e
dge
s
a
r
e
e
volved
ve
r
ti
c
a
ll
y.
W
e
ne
e
d
t
o
de
c
ide
the
va
lue
o
f
a
pa
r
a
mete
r
,
whe
r
e
∈
ℕ
a
nd
≠
0
,
whic
h
is
t
he
s
e
a
r
c
h
width
(
in
pixel)
o
f
the
e
volut
ion
.
T
he
va
lue
of
a
f
f
e
c
ts
the
s
pe
e
d
a
nd
a
c
c
ur
a
c
y
of
the
e
volut
ion
a
nd
typi
c
a
ll
y
we
wa
nt
to
us
e
a
s
mall
number
.
L
a
r
ge
va
lue
may
r
e
s
ult
in
a
labe
l
that
is
ve
r
y
dif
f
e
r
e
nt
f
r
om
the
or
igi
na
l
e
s
ti
mate
.
T
he
e
v
olu
ti
on
of
the
bounda
r
y
c
ontour
will
be
ba
s
e
d
dir
e
c
tl
y
on
a
nd
is
done
by
a
lt
e
r
ing
t
he
labe
l
c
ontent
s
of
′
a
s
de
s
c
r
ibed
in
Algor
it
hm
1
s
hown
in
F
igu
r
e
7
.
Our
ne
w
c
ontour
is
then
obtaine
d
dir
e
c
tl
y
by
pa
r
s
ing
the
e
volved
′
while
ge
ne
r
a
ti
ng
the
ne
w
.
T
he
a
lgor
i
thm
is
e
xe
c
uted
it
e
r
a
ti
ve
ly
unti
l
the
number
of
pix
e
ls
in
the
B
ounda
r
y
G
r
id
that
c
ha
nge
f
r
om
one
it
e
r
a
t
ion
to
the
ne
xt,
a
ve
r
a
ge
d
out
ove
r
number
of
it
e
r
a
ti
ons
,
c
onve
r
ge
s
be
low
a
s
pe
c
if
ied
thr
e
s
hold
.
3.
3.
S
u
b
p
ixel
b
o
u
n
d
ar
y
loca
t
ion
T
o
f
u
r
ther
im
pr
ove
the
pr
e
c
is
ion
of
our
method,
we
ups
a
mpl
e
our
input
a
nd
labe
l
im
a
ge
s
a
t
the
e
n
d
of
e
a
c
h
c
ompl
e
te
e
volut
ion.
W
e
c
a
n
r
e
pe
a
t
thi
s
f
or
number
of
ti
mes
,
whe
r
e
∈
ℕ
,
to
incr
e
a
s
e
the
bounda
r
y
pr
e
c
is
ion
to
the
ne
a
r
e
s
t
2
−
(
+
1
)
of
a
pixel
a
s
de
s
c
r
ibed
in
a
lgor
it
hm
2
s
hown
in
F
igur
e
7
.
3.
4.
Adap
t
ive
c
u
r
ve
s
m
oot
h
in
g
W
e
de
s
ign
our
method
to
a
ll
ow
the
de
c
oupli
ng
of
the
dif
f
e
r
e
nt
c
omponents
of
the
c
ontour
e
volut
ion
s
pe
e
d.
T
o
th
is
e
f
f
e
c
t,
we
a
pply
a
n
a
da
pti
ve
c
ur
ve
s
moot
hing
f
unc
ti
on
a
t
the
e
nd
o
f
the
a
bove
c
ontour
e
volut
ion
pr
oc
e
s
s
.
T
he
r
a
ti
ona
le
f
or
thi
s
is
to
a
ll
o
w
us
to
a
djus
t
the
ti
ghtnes
s
of
the
c
u
r
ve
to
the
f
e
a
tur
e
a
nd
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KO
M
NI
KA
T
e
lec
omm
un
C
omput
E
l
C
ontr
o
l
C
ontour
e
v
olut
ion
me
thod
for
pr
e
c
is
e
boundar
y
de
li
ne
ati
on
of
me
dical
image
s
(
F
r
is
k
a
N
atal
ia)
1629
only
c
onc
e
r
n
a
bout
s
moot
hing
the
r
e
s
ult
s
a
f
ter
wa
r
d.
T
he
c
u
r
ve
s
moot
hing
is
a
da
pti
ve
,
in
s
uc
h
a
wa
y
that
in
a
r
e
a
s
whe
r
e
s
t
r
ong
im
a
ge
f
e
a
tur
e
s
a
r
e
pr
e
s
e
nt
it
a
ppli
e
s
a
we
a
ke
r
s
moot
hing
f
unc
ti
on
to
pr
e
s
e
r
ve
the
e
dge
than
in
a
r
e
a
s
whe
r
e
the
im
a
ge
f
e
a
tur
e
s
a
r
e
we
a
k.
W
e
a
c
hieve
thi
s
by
mea
ns
of
va
r
iable
width
movi
ng
a
ve
r
a
ge
method.
L
e
t
=
⟨
|
∈
ℕ
a
nd
<
ca
r
d
(
)
⟩
whe
r
e
∈
2
be
a
s
o
r
ted
s
e
que
nc
e
of
s
e
t
.
W
e
de
f
ine
the
s
or
t
ope
r
a
ti
on
s
uc
h
that
‖
−
−
1
‖
f
or
1
≤
<
ca
r
d
(
)
is
mi
nim
ize
d.
W
e
then
a
pply
a
movi
ng
a
ve
r
a
ge
on
a
t
e
ve
r
y
point
a
long
it
s
c
ur
va
tur
e
with
va
r
iable
ha
lf
-
width
∈
ℕ
s
uc
h
th
a
t:
=
∑
+
=
−
2
×
+
1
(
8)
f
o
r
∀
t
h
a
t
me
e
ts
th
e
<
<
ca
r
d
(
)
−
r
e
qu
i
r
e
m
e
n
t
.
T
h
e
v
a
l
ue
of
i
s
s
e
t
be
t
we
e
n
m
i
n
a
nd
m
a
x
a
nd
t
ied
t
o
t
he
i
mag
e
f
e
a
tu
r
e
a
t
t
he
lo
c
a
ti
on
o
f
th
e
b
ou
nd
a
r
y
po
i
n
ts
.
I
n
o
ur
e
x
pe
r
im
e
n
t
,
w
e
us
e
t
he
s
e
c
ond
d
e
r
i
va
ti
ve
o
f
th
e
im
a
g
e
f
u
nc
ti
on
′′
a
s
th
e
im
a
ge
f
e
a
tur
e
a
n
d
s
e
t
t
o
m
i
n
w
he
n
t
he
′′
i
s
a
t
it
s
l
ow
e
s
t
v
a
l
ue
,
t
o
m
a
x
w
he
n
t
he
′′
i
s
a
t
i
ts
h
i
ghe
s
t
va
l
ue
a
n
d
l
in
e
a
r
l
y
i
n
te
r
p
ol
a
ted
a
n
d
r
ou
nd
e
d
t
o
t
he
n
e
a
r
e
s
t
i
nt
e
g
e
r
i
n
be
tw
e
e
n
.
F
igur
e
7
.
(
a
)
Algor
i
thm
1
to
e
volve
the
bounda
r
ies
s
tor
e
d
in
a
B
ounda
r
y
Gr
id
a
nd
a
S
pa
r
s
e
B
ounda
r
y
R
e
pr
e
s
e
ntation
a
nd
(
b)
Algor
it
hm
2
that
i
ter
a
ti
ve
ly
up
-
s
a
mpl
e
s
the
input
a
nd
labe
l
im
a
ge
s
a
nd
make
s
c
a
ll
s
to
Algor
it
hm
1
to
a
c
hieve
s
ub
-
pixel
bounda
r
y
e
volut
i
on.
4.
E
XP
E
RI
M
E
NT
AL
RE
S
U
L
T
S
AN
D
AN
AL
YSI
S
W
e
tes
ted
our
method
on
a
da
tas
e
t
of
lum
ba
r
s
pine
M
R
I
im
a
ge
s
that
we
ha
ve
c
oll
e
c
ted
[
11
]
a
nd
thei
r
a
s
s
oc
iate
d
labe
l
im
a
ge
s
[
12]
.
T
he
da
tas
e
t
c
ontain
s
a
xial
M
R
I
s
c
a
ns
of
the
las
t
th
r
e
e
int
e
r
ve
r
tebr
a
l
dis
c
s
of
515
pa
ti
e
nts
.
W
e
pr
e
s
e
nt
in
thi
s
s
e
c
ti
on,
on
e
–
in
our
view
the
be
s
t
–
e
xa
mpl
e
c
a
s
e
be
c
a
us
e
it
c
ontai
ns
a
ll
o
f
the
pr
oblems
to
s
o
lve
a
s
de
s
c
r
ibed
in
the
las
t
pa
r
t
of
s
e
c
ti
on
2.
T
his
e
xa
mpl
e
c
a
s
e
is
de
s
c
r
ibed
a
nd
il
lus
tr
a
ted
in
F
igur
e
8
.
T
he
f
igu
r
e
s
hows
the
c
olo
r
-
c
ode
d
bounda
r
ies
of
a
manua
ll
y
c
r
e
a
ted
labe
l
im
a
ge
.
T
h
e
f
igur
e
s
hows
a
number
of
pr
oblems
with
the
bounda
r
i
e
s
.
Ar
e
a
s
labe
ll
e
d
(
a
)
-
(
d)
a
r
e
e
xa
mpl
e
s
of
ga
ps
be
twe
e
n
r
e
gions
that
we
r
e
mea
nt
to
be
ne
ighbour
s
.
Ar
e
a
labe
ll
e
d
(
e
)
il
lus
tr
a
tes
inac
c
ur
a
te
bounda
r
ies
that
a
r
e
a
f
e
w
pixels
a
wa
y
f
r
om
the
tr
ue
e
dge
.
And
las
tl
y,
we
note
that
thes
e
bounda
r
ies
in
ge
ne
r
a
l
ha
ve
high
c
ur
va
tur
e
whic
h
c
a
n
be
s
e
e
n
f
r
om
it
s
jagge
dne
s
s
s
uc
h
a
s
thos
e
labe
ll
e
d
(
f
)
.
T
he
pa
r
a
mete
r
s
that
we
us
e
a
r
e
a
s
f
oll
ows
:
im
a
ge
f
e
a
tur
e
s
=
∇
(
∗
)
,
the
s
e
a
r
c
h
width
=
2
,
the
number
of
ups
a
mpl
ing
leve
ls
=
2
,
the
it
e
r
a
ti
on
a
ve
r
a
g
ing
window
=
10
,
the
s
tanda
r
d
de
via
ti
on
thr
e
s
hold
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
1693
-
6930
T
E
L
KO
M
NI
KA
T
e
lec
omm
un
C
omput
E
l
C
ontr
o
l
,
Vol.
18
,
No
.
3
,
J
une
2020:
1621
-
1632
1630
=
2
,
the
m
in
a
nd
max
s
moot
hing
window
ha
l
f
-
widths
m
i
n
=
5
a
nd
m
a
x
=
20
,
r
e
s
pe
c
ti
ve
ly.
W
e
a
ppli
e
d
ou
r
method
to
only
e
volve
bounda
r
ies
that
we
ha
v
e
pr
io
r
knowle
dge
to
be
gr
a
dient
de
pe
nde
nt
w
hil
e
a
ls
o
im
pr
oving
the
s
moot
hne
s
s
of
the
other
s
.
F
or
c
ompar
is
on,
we
a
ls
o
a
pply
the
GA
C
a
lgor
it
hm
[
21]
to
the
labe
l
im
a
ge
,
s
e
que
nti
a
ll
y
f
or
a
ll
r
e
gions
e
xc
e
pt
OT
.
W
e
e
xpe
r
im
e
nted
wi
th
s
e
ve
r
a
l
c
om
binati
ons
of
,
a
nd
va
lues
to
pr
oduc
e
a
n
a
c
c
e
pt
a
ble
c
ompr
omi
s
e
be
twe
e
n
a
c
c
ur
a
c
y
a
nd
s
moot
hne
s
s
,
a
nd
we
de
c
ided
to
us
e
=
1
,
=
160
a
nd
=
500
to
be
the
be
s
t.
W
e
a
ls
o
a
pply
a
mo
r
phologi
c
a
l
c
los
ing
on
the
input
labe
l
im
a
ge
pr
ior
to
a
pplyi
ng
e
a
c
h
tec
hnique
to
r
e
mo
ve
a
ny
s
mall
holes
a
nd
ga
ps
in
the
im
a
ge
.
F
igur
e
8
.
C
olor
-
c
ode
d
bounda
r
ies
of
a
manua
ll
y
c
r
e
a
ted
labe
l
im
a
ge
il
lus
tr
a
ti
ng
(
a
-
d)
ga
ps
be
twe
e
n
s
uppos
e
dly
ne
ighbour
ing
r
e
gions
,
(
e
)
inac
c
ur
a
te
b
ounda
r
y
a
nd
(
f
)
high
c
ur
va
tu
r
e
On
a
ve
r
a
ge
,
the
e
xe
c
uti
on
s
pe
e
d
of
our
method
c
ompar
e
d
to
GA
C
a
t
up
s
a
mpl
ing
leve
ls
=
0
,
1
a
nd
2
a
r
e
10.
2
,
8.
6
,
a
nd
5.
2
ti
mes
f
a
s
ter
,
r
e
s
pe
c
ti
ve
ly.
W
e
obs
e
r
ve
d
that
the
main
r
e
a
s
on
why
our
method
is
s
igni
f
ica
ntl
y
f
a
s
ter
is
that
it
c
a
r
r
ies
out
a
s
hor
ter
number
of
it
e
r
a
ti
on
be
f
or
e
it
c
onve
r
ge
s
.
As
c
a
n
b
e
s
e
e
n
in
F
igur
e
9
,
ou
r
method
s
olv
e
s
the
bulk
of
the
pixel
c
ha
nge
s
in
the
f
ir
s
t
it
e
r
a
ti
on
r
e
s
ult
ing
in
a
much
quicke
r
c
onve
r
ge
nc
e
than
GA
C
.
F
igur
e
9
.
A
typ
ica
l
number
of
p
ixel
c
ha
nge
s
be
twe
e
n
s
uc
c
e
s
s
ive
it
e
r
a
ti
ons
,
(
a
)
pr
opos
e
d,
(
b)
ge
ode
s
ic
a
c
ti
ve
c
ontour
s
T
he
c
ontour
e
volut
ion
r
e
s
ult
s
of
the
two
methods
a
r
e
s
hown
in
F
igur
e
10
.
T
he
r
e
a
r
e
two
notable
im
pr
ove
ments
of
our
method
c
ompar
e
d
to
GA
C
.
Our
method
pr
im
a
r
il
y
p
r
oduc
e
s
bounda
r
ies
that
a
r
e
mor
e
tig
htl
y
a
li
gne
d
wi
th
the
tr
ue
e
dge
-
mar
ke
d
a
s
(
e
)
in
F
igur
e
8
while
a
t
the
s
a
me
t
im
e
pr
oduc
e
s
a
g
e
ne
r
a
ll
y
s
moot
he
r
c
ontour
than
the
latter
.
Note
a
ls
o
the
f
a
c
t
that
GA
C
wor
s
e
ns
the
bounda
r
y
be
twe
e
n
I
VD
a
nd
T
S
s
ince
thi
s
type
of
bounda
r
y
is
not
c
ha
r
a
c
ter
ize
d
by
s
tr
ong
int
e
ns
i
ty
dif
f
e
r
e
nc
e
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.