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L
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elec
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t
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Co
m
pu
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E
lect
ro
nics
a
nd
Co
ntr
o
l
Vo
l.
1
8
,
No
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6
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Dec
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erforma
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phas
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bas
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a
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recog
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M
utha
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H
a
m
d
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ba
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Ra
s
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p
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p
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Al
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u
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n
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rsit
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I
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Art
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I
nfo
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ticle
his
to
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y:
R
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Ma
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2
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P
h
a
se
c
o
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g
ru
e
n
c
y
is
a
n
e
d
g
e
d
e
tec
to
r
a
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d
m
e
a
su
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m
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t
o
f
t
h
e
sig
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a
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t
fe
a
tu
re
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th
e
ima
g
e
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It
is
a
ro
b
u
st
m
e
th
o
d
a
g
a
i
n
st
c
o
n
tras
t
a
n
d
il
l
u
m
in
a
ti
o
n
v
a
riatio
n
.
I
n
th
is
p
a
p
e
r,
two
n
o
v
e
l
tec
h
n
i
q
u
e
s
a
re
in
tr
o
d
u
c
e
d
f
o
r
d
e
v
e
lo
p
in
g
a
lo
w
-
c
o
st
h
u
m
a
n
id
e
n
ti
fica
ti
o
n
sy
ste
m
b
a
se
d
o
n
fa
c
e
re
c
o
g
n
it
io
n
.
F
irstl
y
,
th
e
v
a
lu
a
b
le
p
h
a
se
c
o
n
g
ru
e
n
c
y
fe
a
tu
re
s,
th
e
g
ra
d
ien
t
-
e
d
g
e
s
a
n
d
th
e
ir
a
ss
o
c
iate
d
a
n
g
les
a
re
u
ti
li
z
e
d
se
p
a
ra
tely
f
o
r
c
las
sify
in
g
1
3
0
su
b
jec
ts
tak
e
n
fro
m
th
re
e
fa
c
e
d
a
tab
a
se
s
with
th
e
m
o
ti
v
a
ti
o
n
o
f
e
li
m
in
a
ti
n
g
t
h
e
fe
a
tu
re
e
x
trac
ti
o
n
p
h
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se
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By
d
o
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n
g
th
is,
th
e
c
o
m
p
lex
i
ty
c
a
n
b
e
sig
n
ifi
c
a
n
t
ly
re
d
u
c
e
d
.
S
e
c
o
n
d
l
y
,
t
h
e
train
i
n
g
p
ro
c
e
ss
is
m
o
d
ifi
e
d
wh
e
n
a
n
e
w
tec
h
n
iq
u
e
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c
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ll
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d
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v
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ra
g
in
g
-
v
e
c
to
rs
is
d
e
v
e
lo
p
e
d
to
a
c
c
e
lera
te t
h
e
train
in
g
p
r
o
c
e
ss
a
n
d
m
in
imiz
e
s th
e
m
a
tch
in
g
t
ime
to
th
e
l
o
we
st
v
a
lu
e
.
Ho
we
v
e
r,
f
o
r
m
o
re
c
o
m
p
a
riso
n
a
n
d
a
c
c
u
ra
te
e
v
a
lu
a
ti
o
n
,
th
re
e
c
o
m
p
e
ti
ti
v
e
c
las
sifiers
:
E
u
c
li
d
e
a
n
d
istan
c
e
(ED),
c
o
si
n
e
d
ista
n
c
e
(CD),
a
n
d
M
a
n
h
a
tt
a
n
d
istan
c
e
(M
D)
a
re
c
o
n
sid
e
re
d
in
th
is
wo
r
k
.
T
h
e
sy
ste
m
p
e
rfo
rm
a
n
c
e
is
v
e
ry
c
o
m
p
e
ti
ti
v
e
a
n
d
a
c
c
e
p
tab
le,
wh
e
re
th
e
e
x
p
e
rime
n
tal
re
su
lt
s sh
o
w
p
ro
m
isi
n
g
re
c
o
g
n
i
ti
o
n
ra
tes
with
a
re
a
so
n
a
b
le m
a
tch
in
g
ti
m
e
.
K
ey
w
o
r
d
s
:
Face
r
ec
o
g
n
itio
n
Featu
r
e
d
etec
tio
n
Gr
ad
ien
t
Or
ien
tatio
n
Ph
ase
co
n
g
r
u
e
n
cy
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r
th
e
CC B
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-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Mu
th
an
a
H.
Ham
d
,
Dep
ar
tm
en
t o
f
C
o
m
p
u
ter
E
n
g
i
n
ee
r
in
g
,
Un
iv
er
s
ity
o
f
Al
Mu
s
tan
s
ir
iy
a
h
,
B
ag
h
d
ad
,
I
r
aq
.
E
m
ail:
d
r
.
m
u
th
a
n
a@
u
o
m
u
s
tan
s
ir
iy
ah
.
ed
u
.
iq
1.
I
NT
RO
D
UCT
I
O
N
Ph
ase
co
n
g
r
u
en
c
y
(
PC
)
is
an
ac
cu
r
ate
ap
p
r
o
ac
h
f
o
r
f
ea
tu
r
es
d
etec
tio
n
wh
ich
u
n
lik
e
tr
a
d
itio
n
al
ed
g
e
d
etec
to
r
s
,
th
at
s
ea
r
ch
f
o
r
p
o
i
n
ts
o
f
m
ax
im
u
m
g
r
ad
ien
ts
,
t
h
e
p
h
ase
co
n
g
r
u
e
n
cy
s
ea
r
ch
es
f
o
r
th
e
o
r
d
er
ed
s
p
ec
tr
u
m
s
in
a
f
r
eq
u
en
c
y
d
o
m
ain
.
I
t
p
r
o
v
i
d
es
a
co
n
tr
ast
an
d
a
n
illu
m
in
atio
n
in
v
ar
ia
n
t
m
eth
o
d
o
f
ed
g
e
d
etec
tio
n
.
T
h
ese
s
ig
n
if
ican
t
PC
f
ea
tu
r
es:
th
e
lo
ca
l
-
o
r
ien
tatio
n
s
an
d
th
ei
r
ass
o
ciate
d
p
h
ases
h
av
e
in
s
p
ir
ed
a
n
ew
v
is
io
n
f
o
r
d
esig
n
in
g
a
lo
w
-
c
o
s
t
b
io
m
etr
i
c
s
y
s
tem
lik
e
f
ac
e
r
ec
o
g
n
itio
n
b
ased
o
n
t
h
o
s
e
PC
f
ea
tu
r
es
o
n
ly
,
wh
ich
m
ea
n
s
th
er
e
is
n
o
m
o
r
e
d
em
an
d
f
o
r
e
m
p
lo
y
in
g
f
ea
tu
r
e
ex
tr
ac
tio
n
p
h
ase
in
th
e
d
esig
n
p
lan
.
I
n
th
e
m
ea
n
tim
e,
f
ea
tu
r
e
ex
tr
ac
tio
n
is
a
d
im
en
s
io
n
r
ed
u
ctio
n
p
r
o
ce
s
s
b
y
wh
ich
an
o
r
ig
in
al
d
ataset
is
r
ed
u
ce
d
to
b
e
m
o
r
e
co
n
v
e
n
ien
t
g
r
o
u
p
s
.
Als
o
,
it
is
a
v
ital
o
p
e
r
atio
n
in
th
e
m
ac
h
i
n
e
lear
n
in
g
p
r
o
ce
s
s
f
o
r
b
u
ild
in
g
f
ea
tu
r
e
s
th
at:
f
ac
ilit
ate
th
e
s
p
ee
d
o
f
lear
n
in
g
,
s
av
in
g
tim
e,
an
d
p
h
ase
g
en
er
aliza
tio
n
.
I
t
is
u
s
u
ally
th
e
s
tep
th
at
th
e
cl
ass
if
icatio
n
p
r
o
ce
s
s
co
m
es
af
ter
.
Her
eb
y
,
ca
n
ce
llin
g
th
is
s
tep
r
esu
lted
in
a
lar
g
e
-
s
ize
f
ea
tu
r
e
v
ec
to
r
ca
u
s
in
g
u
n
wan
ted
d
ela
y
tim
e
in
th
e
tr
ain
in
g
a
n
d
m
atch
in
g
p
r
o
ce
s
s
.
So
,
th
is
wo
r
k
,
in
t
r
o
d
u
c
es
a
n
ew
tech
n
iq
u
e
f
o
r
m
an
i
p
u
latin
g
th
is
u
r
g
en
t
s
tatu
s
,
it
d
ep
en
d
s
o
n
th
e
d
eter
m
in
in
g
th
e
m
ea
n
f
ea
tu
r
e
v
ec
to
r
f
o
r
tr
ain
i
n
g
d
atasets
,
s
o
th
e
m
atch
in
g
o
r
class
if
icatio
n
p
r
o
ce
s
s
will
b
e
im
p
lem
en
ted
in
o
n
e
-
to
-
o
n
e
r
elatio
n
in
s
tead
o
f
o
n
e
-
to
-
m
a
n
y
.
T
h
is
p
ap
er
is
o
r
g
an
ized
as
f
o
ll
o
ws,
a
liter
atu
r
e
r
ev
iew
f
o
r
t
h
e
m
o
s
t
r
elate
d
wo
r
k
s
ar
e
p
r
esen
ted
in
s
e
ctio
n
2
,
wh
ile,
th
e
th
eo
r
etica
l p
ar
t o
f
th
e
p
h
ase
co
n
g
r
u
en
cy
ap
p
r
o
ac
h
an
d
its
ty
p
es is
illu
s
tr
ated
in
s
ec
tio
n
3
.
T
h
e
m
eth
o
d
o
lo
g
y
o
f
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1
6
9
3
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6
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3
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T
E
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KOM
NI
KA
T
elec
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m
m
u
n
C
o
m
p
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t E
l Co
n
tr
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l
,
Vo
l.
1
8
,
No
.
6
,
Dec
em
b
e
r
2
0
2
0
:
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1
-
30
49
3042
th
is
wo
r
k
is
ex
p
lain
e
d
in
s
ec
tio
n
4
.
Sectio
n
5
d
em
o
n
s
tr
ates
th
e
ex
p
er
im
en
tal
s
y
s
tem
r
esu
lts
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d
f
in
ally
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s
ec
tio
n
6
s
u
m
m
ar
ize
s
th
e
m
o
s
t im
p
o
r
tan
t a
s
p
ec
ts
an
d
is
s
u
es in
th
is
wo
r
k
.
2.
L
I
T
E
R
AT
U
RE
R
E
VI
E
W
In
[
1
,
2
]
u
s
ed
wav
elets
an
d
u
n
i
v
er
s
al
th
r
esh
o
ld
v
alu
e
o
v
e
r
a
wid
e
class
o
f
im
ag
es.
T
h
e
ca
lcu
latio
n
f
o
r
th
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-
d
im
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s
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n
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(
1
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D
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ig
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al
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ex
ten
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ed
to
2
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D
im
ag
e
s
,
also
it
is
ar
g
u
ed
th
at
h
ig
h
-
p
a
s
s
f
ilter
ca
n
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e
u
s
ed
to
o
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tain
im
ag
e
in
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o
r
m
atio
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if
f
er
en
t scale
s
.
I
n
2
0
0
7
,
[
3
,
4
]
p
r
o
p
o
s
ed
a
f
ac
e
r
ec
o
g
n
itio
n
t
ec
h
n
iq
u
e
aim
ed
at
im
p
r
o
v
in
g
th
e
r
ec
o
g
n
itio
n
ac
cu
r
ac
ies
o
f
th
e
f
ac
es
th
at
ar
e
af
f
ec
ted
d
u
e
to
v
ar
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n
g
illu
m
in
atio
n
s
,
p
ar
tial
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cc
lu
s
io
n
s
an
d
v
ar
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in
g
ex
p
r
ess
io
n
s
.
H.
R
ag
b
a
n
d
V.
K.
Asar
i
[
5
]
,
p
r
e
s
en
ted
a
d
escr
ip
to
r
b
ased
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n
th
e
p
h
ase
co
n
g
r
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en
cy
co
n
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p
t,
ca
lled
h
i
s
to
g
r
am
o
f
o
r
ie
n
ted
p
h
ase
(
H
OP)
u
s
ed
to
d
e
p
ict
an
d
r
ep
r
esen
t
th
e
h
u
m
an
o
b
jects
m
o
r
e
ef
f
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tly
th
an
th
e
g
r
a
d
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t
-
b
ased
ap
p
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ac
h
esp
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th
o
s
e
im
ag
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ex
p
o
s
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to
th
e
illu
m
in
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n
d
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tr
ast
v
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s
.
N.
D.
R
ao
p
r
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a
n
o
v
el
f
ac
e
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o
g
n
itio
n
tech
n
iq
u
e.
T
h
e
m
o
d
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lar
k
er
n
el
E
ig
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s
p
ac
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ap
p
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n
th
e
p
h
ase
co
n
g
r
u
en
cy
im
a
g
es
to
lo
ca
lize
n
o
n
lin
ea
r
f
ea
t
u
r
e
s
elec
tio
n
p
r
o
ce
d
u
r
e
f
o
r
o
v
er
co
m
i
n
g
th
e
b
o
ttlen
ec
k
s
o
f
illu
m
in
atio
n
v
ar
iatio
n
s
,
p
ar
ti
al
o
cc
lu
s
io
n
s
,
ex
p
r
ess
io
n
v
ar
i
atio
n
s
as
in
[
6
]
.
S.
Alav
i
in
[
7
]
d
ev
elo
p
ed
a
two
-
d
im
en
s
io
n
al
m
u
lti
-
s
ca
le
p
h
ase
co
n
g
r
u
en
c
y
(
2
D
-
MSPC
)
s
o
f
twar
e
f
o
r
d
etec
tin
g
an
d
e
v
alu
atio
n
o
f
im
ag
e
f
ea
tu
r
es.
Ma
n
y
p
ar
am
eter
s
ar
e
ap
p
r
o
p
r
iately
tu
n
ed
f
o
r
o
p
tim
al
im
ag
e
f
ea
tu
r
es
d
etec
tio
n
,
th
ese
p
ar
am
ete
r
s
ar
e
o
p
tim
ized
f
o
r
m
a
x
im
u
m
an
d
m
in
im
u
m
m
o
m
en
ts
.
T
h
e
d
esig
n
in
[
8
]
p
r
o
p
o
s
ed
a
m
o
d
if
ied
alg
o
r
ith
m
o
f
p
h
ase
c
o
n
g
r
u
en
cy
to
lo
ca
te
im
a
g
e
f
ea
t
u
r
es
u
s
in
g
th
e
Hilb
e
r
t
tr
an
s
f
o
r
m
.
T
h
e
l
o
ca
l
en
er
g
y
is
o
b
tain
ed
b
y
co
n
v
o
lu
tin
g
o
r
i
g
in
al
im
ag
e
with
two
o
p
er
ato
r
s
o
f
r
em
o
v
in
g
d
ir
ec
t
c
u
r
r
e
n
t
(
DC
)
co
m
p
o
n
en
t
o
v
e
r
th
e
cu
r
r
e
n
t
win
d
o
w
a
n
d
th
e
2
-
D
Hilb
er
t
tr
an
s
f
o
r
m
r
esp
ec
ti
v
ely
.
T
h
e
lo
ca
l
en
er
g
y
is
d
iv
i
d
ed
with
th
e
s
u
m
o
f
Fo
u
r
ier
am
p
litu
d
e
o
f
th
e
cu
r
r
en
t
win
d
o
w
to
r
etr
iev
e
th
e
v
a
lu
e
o
f
PC
[9
-
1
1
]
.
A
n
o
v
el
d
e
cisi
o
n
-
lev
el
f
u
s
io
n
m
eth
o
d
is
d
e
v
elo
p
ed
b
y
[
1
2
]
o
n
s
ev
er
al
AR
s
ets
to
im
p
r
o
v
e
f
ac
e
r
ec
o
g
n
itio
n
.
PC
f
ea
tu
r
e
m
ap
s
ar
e
u
tili
ze
d
in
s
tead
o
f
in
ten
s
ities
to
m
ak
e
th
e
r
ec
o
g
n
itio
n
p
r
o
ce
s
s
in
v
ar
ian
t
to
co
n
tr
ast
an
d
illu
m
i
n
atio
n
in
an
im
ag
e.
A
co
m
b
in
atio
n
o
f
Gab
o
r
wav
elets
(
GW
)
an
d
P
C
was
d
ev
elo
p
ed
b
y
[
1
3
]
f
o
r
f
ac
e
r
ec
o
g
n
itio
n
s
y
s
tem
,
f
ir
s
t,
th
e
PC
was
ap
p
lied
to
th
e
OR
L
f
ac
e
im
a
g
e,
th
e
n
th
e
s
p
atial
f
r
eq
u
e
n
cy
in
f
o
r
m
ati
o
n
was
o
b
tain
ed
u
s
in
g
th
e
s
et
o
f
Gab
o
r
-
f
ilter
s
.
T
h
e
in
itial r
es
u
lts
with
o
u
t
u
s
in
g
o
f
p
r
in
cip
al
co
m
p
o
n
en
t a
n
aly
s
is
(
PC
A
)
m
e
th
o
d
s
h
o
wed
9
8
%
r
ec
o
g
n
itio
n
r
ate.
Up
o
n
u
s
in
g
t
h
e
PC
A,
th
e
r
ec
o
g
n
itio
n
r
ate
w
as
s
till
r
e
tain
ed
b
y
9
8
%.
Als
o
,
th
e
r
ec
o
g
n
itio
n
r
ate
was
r
ed
u
ce
d
to
9
6
%
u
s
in
g
GW
an
d
PC
A
m
eth
o
d
s
o
n
ly
.
C
o
m
b
in
atio
n
s
o
f
PC
A,
m
o
d
u
lar
PC
A
(
MP
C
A)
,
m
o
d
u
lar
s
u
b
s
p
ac
e
PC
A
(
MPPC
A)
,
an
d
n
ei
g
h
b
o
u
r
h
o
o
d
m
o
d
u
le
PC
A
(
NM
PC
A)
wer
e
ap
p
lied
o
n
th
e
s
ig
n
if
ica
n
t
PC
f
ea
tu
r
es
o
f
A
R
d
atab
a
s
e.
T
h
e
PC
ap
p
r
o
ac
h
co
u
ld
im
p
r
o
v
e
th
e
r
ec
o
g
n
itio
n
ac
cu
r
ac
y
b
y
1
0
%
f
o
r
s
o
m
e
co
m
b
in
atio
n
lik
e
NM
PC
A
[
1
4
]
.
A
d
is
tin
ct
wav
elen
g
th
PC
(
DW
P
C
)
an
d
lo
g
-
Gab
o
r
f
ilter
s
wer
e
p
r
o
p
o
s
ed
f
o
r
m
atch
in
g
a
v
is
ib
le
an
d
in
f
r
ar
e
d
im
ag
e
,
th
e
PC
th
eo
r
y
was
u
tili
ze
d
to
d
eter
m
in
e
P
C
im
ag
es
with
af
f
lu
en
t
an
d
in
tr
in
s
ic
im
ag
e
f
ea
tu
r
es f
o
r
n
o
is
y
o
r
co
m
p
le
x
in
ten
s
ity
-
ch
a
n
g
e
im
ag
es
[
1
5
]
.
3.
P
H
ASE
CO
NG
RU
E
NCY
M
E
ASUR
M
E
N
T
S
So
m
e
p
r
o
b
lem
s
o
f
i
n
co
m
p
lete
ed
g
es
an
d
co
n
to
u
r
s
b
ec
a
u
s
e
o
f
th
e
ch
an
g
es
in
th
e
l
o
ca
l
illu
m
i
n
atio
n
an
d
h
en
ce
an
in
ad
eq
u
ate
s
e
lectiv
e
th
r
esh
o
ld
is
h
a
n
d
led
b
y
[
2
]
wh
en
a
h
ig
h
-
lev
el
tech
n
iq
u
e
is
co
n
s
id
er
ed
to
ac
co
m
m
o
d
ate
u
s
ef
u
l
d
ata
an
d
r
ejec
t
r
e
d
u
n
d
an
t
in
f
o
r
m
ati
o
n
.
T
h
r
ee
ty
p
e
s
o
f
PC
b
ased
f
r
e
q
u
en
c
y
d
o
m
ain
o
p
er
atio
n
s
th
at
c
o
n
s
id
er
ed
a
p
h
ase
in
th
eir
o
p
er
atin
g
a
r
e
p
r
e
s
en
ted
as f
o
llo
ws [
16
-
18
]:
3
.
1
.
F
o
urier
c
o
m
po
nents
b
a
s
ed
m
ea
s
ure
I
n
th
is
ty
p
e,
a
o
n
e
-
d
im
e
n
s
io
n
p
h
ase
co
n
g
r
u
e
n
cy
at
s
o
m
e
lo
ca
tio
n
p
o
in
t
x
is
d
ef
i
n
ed
as
c
o
n
g
r
u
en
cy
f
u
n
ctio
n
.
Featu
r
es
ar
e
d
etec
te
d
b
y
f
o
u
n
d
in
g
th
e
Fo
u
r
ier
co
m
p
o
n
e
n
ts
th
at
h
av
e
a
m
ax
im
u
m
p
h
ase
as
ex
p
lain
e
d
in
(
1
)
[
1
,
2
]
.
(
1
)
wh
er
e
:
an
d
ar
e
t
h
e
lo
ca
l
an
d
m
ea
n
p
h
ase
a
n
g
les o
f
th
e
f
r
eq
u
e
n
cy
co
m
p
o
n
en
t
at
x
T
h
e
aim
i
s
to
m
ax
im
ize
(
1
)
b
y
m
ax
im
izin
g
th
e
weig
h
ted
m
ea
n
a
m
p
litu
d
e
f
o
r
lo
ca
l
p
h
ase
an
g
le
f
o
r
all
co
n
s
id
er
ed
Fo
u
r
ier
p
o
in
ts
o
f
.
Her
eb
y
,
p
h
ase
co
n
g
r
u
en
c
y
is
a
r
ath
er
d
if
f
icu
lt
q
u
an
tity
to
b
e
c
o
m
p
u
te
d
,
as
fin
d
in
g
,
w
h
er
e
p
h
ase
co
n
g
r
u
en
cy
is
a
m
a
x
im
u
m
,
is
ap
p
r
o
x
im
ately
eq
u
i
v
alen
t
fin
d
in
g
wh
er
e
t
h
e
weig
h
te
d
v
ar
ian
ce
o
f
lo
ca
l
p
h
ase
an
g
les r
elativ
e
to
th
e
weig
h
ted
av
er
a
g
e
lo
ca
l
p
h
ase
is
a
m
in
im
u
m
[
1
9
-
21]
.
3
.
2
.
O
ne
-
dim
ens
io
n wa
v
elet
-
ba
s
ed
m
ea
s
ure
T
h
e
p
h
ase
co
n
g
r
u
e
n
cy
in
(
1
)
i
s
s
en
s
itiv
e
to
th
e
n
o
is
e
a
n
d
it
is
n
o
t
well
lo
ca
lize
d
b
ec
a
u
s
e
th
e
m
ea
s
u
r
e
ch
an
g
es
with
th
e
d
if
f
er
en
ce
i
n
p
h
ase
,
n
o
t
in
th
e
s
m
all
r
esp
o
n
s
es
o
r
m
ag
n
itu
d
e
i
ts
elf
,
s
o
f
o
r
θ
≈
ze
r
o
,
=
∅
∈
0
,
2π
co
s
(
∅
(
)
−
∅
(
)
|
|
∅
(
)
∅
(
)
∅
(
)
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
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KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
To
w
a
r
d
s
b
etter p
erfo
r
ma
n
ce
:
p
h
a
s
e
co
n
g
r
u
en
cy
b
a
s
ed
fa
ce
r
ec
o
g
n
itio
n
(
Mu
th
a
n
a
H.
Ha
m
d
)
3043
th
e
ex
p
lain
s
h
o
w
p
h
ase
d
if
f
e
r
e
n
ce
a
f
f
ec
ts
th
e
weig
h
te
d
m
a
g
n
itu
d
es
.
So
,
an
alter
n
ativ
e
ap
p
r
o
ac
h
is
n
ee
d
ed
to
f
in
d
m
ax
im
u
m
lo
ca
l
en
er
g
y
as
p
h
ase
co
n
g
r
u
e
n
cy
is
d
ir
ec
tly
p
r
o
p
o
r
tio
n
al
to
it.
[
1
9
]
im
p
r
o
v
e
d
th
e
p
h
ase
co
n
g
r
u
e
n
cy
p
er
f
o
r
m
an
ce
wh
e
n
1
-
D
W
av
elet
is
ap
p
lied
to
d
ef
in
e
a
m
ea
s
u
r
e
f
o
r
PC
with
th
e
p
r
esen
ce
o
f
n
o
is
e.
T
h
e
co
m
p
o
n
e
n
ts
,
F
(
x)
an
d
H(
x)
a
r
e
o
b
tain
ed
b
y
co
n
v
o
lv
in
g
th
e
q
u
ad
r
atu
r
e
f
ilter
s
with
th
e
s
ig
n
al.
I
n
o
r
d
e
r
to
d
eter
m
i
n
e
th
e
p
h
ase
in
f
o
r
m
atio
n
an
d
lo
ca
l
f
r
eq
u
en
c
y
i
n
th
e
s
ig
n
al,
lo
g
ar
ith
m
ic
Gab
o
r
f
u
n
ctio
n
s
ar
e
u
s
ed
t
o
o
b
tain
a
n
o
n
-
ze
r
o
DC
co
m
p
o
n
en
t
in
t
h
e
f
ilter
ed
s
ig
n
al.
If
I
(
x)
is
a
s
ig
n
al
an
d
an
d
d
en
o
te
th
e
ev
e
n
s
y
m
m
etr
ic
an
d
o
d
d
s
y
m
m
etr
ic
co
m
p
o
n
e
n
ts
o
f
th
e
lo
g
Gab
o
r
f
u
n
ctio
n
a
t
a
s
ca
le
n
,
th
e
am
p
litu
d
e
a
n
d
p
h
ase
in
th
e
tr
an
s
f
o
r
m
e
d
d
o
m
ain
ca
n
b
e
o
b
tain
ed
as :
(
2
)
(
3
)
wh
er
e
an
d
ar
e
th
e
ev
en
an
d
o
d
d
r
esp
o
n
s
es
o
f
q
u
ad
r
atu
r
e
p
air
o
f
f
ilter
s
.
T
h
e
r
esp
o
n
s
e
v
ec
to
r
is
illu
s
tr
ated
in
(
4
)
.
(
4
)
So
,
F
(
x)
an
d
H(
x)
ca
n
b
e
o
b
tai
n
ed
f
r
o
m
(
5
)
an
d
(
6
)
.
(
5
)
(
6
)
A
ll Fo
u
r
ier
a
m
p
litu
d
es
t
h
ey
ar
e
co
m
p
u
ted
at
p
o
in
t
x
,
a
r
e
v
er
y
s
m
all
,
th
e
n
a
s
m
all
p
o
s
itiv
e
co
n
s
tan
t
,
ɛ
(
b
etwe
en
0
an
d
1
)
is
ad
d
e
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ato
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7
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3
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.
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wo
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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T
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5.
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[
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r
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Li
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P
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1
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P
.
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v
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si,
"
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.
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].
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p
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.
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2
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u
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t
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,
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l.
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p
.
2
0
8
1
1
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4
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3
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la
z
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t
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l.
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in
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5
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M
.
H.
Ha
m
d
a
n
d
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Ra
so
o
l,
”
Op
ti
m
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d
m
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tr
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6
,
2
0
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0
.
[2
6
]
A.
Essa
a
n
d
V.
K
As
a
ri,
“
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irec
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p
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n
g
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g
,
2
0
1
4
.
[2
7
]
H.
M
o
k
h
tari,
e
t
a
l.
,
"
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rfo
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m
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tri
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1
2
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p
p
.
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3
.
[2
8
]
Y.
C.
S
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n
d
N
.
M
.
No
o
r,
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ra
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a
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9
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9
]
Th
e
Da
tab
a
se
o
f
F
a
c
e
s,
“
AT&
T
Lab
o
ra
to
ries
Ca
m
b
rid
g
e
,
”.
[On
l
in
e
].
Av
a
il
a
b
le:
h
tt
p
:/
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m
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rl.
c
o
.
u
k
/fac
e
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a
tab
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se
.
h
tml
[3
0
]
Z.
F
u
,
e
t
a
l.
,
"
HO
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P
C:
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Lo
c
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l
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a
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sin
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,
v
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l.
1
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8
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0
1
8
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1
]
Y.
Ye
,
e
t
a
l.
,
"
A
lo
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se
b
a
se
d
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tu
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try
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sin
g
,
v
o
l.
1
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2
,
p
p
.
2
0
5
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2
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1
,
2
0
1
8
.
[3
2
]
J.
M
e
i,
e
t
a
l.
,
"
M
u
lt
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-
f
o
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u
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Im
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u
sio
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