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1
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I
n
[
2
]
,
a
m
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ased
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.
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r
ec
is
e
f
o
u
n
d
.
Fi
n
all
y
,
t
h
e
f
ea
t
u
r
es
o
f
t
h
e
eleg
an
ce
-
u
n
iq
u
e
d
ictio
n
ar
y
ar
e
ex
tr
ac
ted
w
i
th
t
h
e
h
elp
o
f
E
i
g
en
f
ac
e
tec
h
n
iq
u
e.
A
d
ee
p
f
ac
e
r
ec
o
g
n
itio
n
s
y
s
t
e
m
t
h
at
ad
d
r
ess
e
s
t
h
e
p
r
o
b
lem
s
o
cc
u
r
s
in
a
n
o
p
en
s
et
p
r
o
to
co
l
is
d
is
cu
s
s
ed
in
[
5
]
.
T
h
e
m
et
h
o
d
u
s
e
s
th
e
an
g
u
lar
s
o
f
t
m
ax
lo
s
s
th
at
ac
tiv
es
t
h
e
co
n
v
o
l
u
tio
n
al
n
eu
r
al
n
et
w
o
r
k
i
n
o
r
d
er
to
lear
n
th
e
f
ea
t
u
r
es
o
f
th
e
a
n
g
u
lar
d
is
cr
i
m
i
n
atio
n
.
I
n
th
e
g
eo
m
e
tr
ical
p
er
ce
p
tio
n
,
t
h
e
a
n
g
u
lar
s
o
f
t
m
a
x
lo
s
s
is
i
m
p
o
s
ed
as
th
e
d
is
cr
i
m
in
ati
v
e
co
n
s
tr
ain
t
s
o
n
th
e
h
y
p
er
s
p
h
er
e.
A
ls
o
,
t
h
e
an
g
u
lar
m
ar
g
in
al
s
ize
ca
n
b
e
ad
j
u
s
ted
q
u
an
t
itati
v
el
y
b
y
a
p
ar
a
m
eter
.
An
ad
ap
tiv
e
li
n
ea
r
d
is
cr
i
m
i
n
an
t
r
eg
r
es
s
io
n
cla
s
s
i
f
icat
io
n
a
lg
o
r
ith
m
f
o
r
f
ac
e
r
ec
o
g
n
itio
n
s
y
s
te
m
is
d
is
cu
s
s
ed
in
[
6
]
.
T
h
e
alg
o
r
ith
m
is
u
s
ed
to
f
ir
s
t
ch
ar
ac
ter
ize
th
e
v
ar
io
u
s
co
n
tr
ib
u
tio
n
s
o
f
t
h
e
tr
ain
i
n
g
s
a
m
p
le
s
w
it
h
t
h
e
h
e
lp
o
f
t
h
e
d
i
f
f
er
en
t
w
ei
g
h
ts
.
T
h
en
t
h
e
w
ei
g
h
ti
n
g
i
n
f
o
r
m
atio
n
i
s
u
s
ed
to
ca
lcu
lat
e
th
e
r
ec
o
n
s
tr
u
ctio
n
er
r
o
r
s
o
f
w
it
h
in
-
cla
s
s
a
n
d
b
etw
ee
n
-
clas
s
er
r
o
r
s
.
Fin
all
y
,
t
h
e
alg
o
r
ith
m
m
a
x
i
m
ize
s
th
e
r
a
tio
o
f
th
e
b
et
w
ee
n
-
class
r
ec
o
n
s
tr
u
ct
io
n
er
r
o
r
o
v
er
th
e
w
i
th
i
n
-
clas
s
r
ec
o
n
s
t
r
u
ctio
n
er
r
o
r
b
y
m
ea
n
s
o
f
th
e
o
p
ti
m
al
p
r
o
j
ec
tio
n
m
atr
i
x
.
A
m
eth
o
d
u
s
ed
f
o
r
u
n
co
n
s
tr
ain
ed
f
ac
e
r
ec
o
g
n
it
io
n
in
t
h
e
w
ild
th
at
p
u
s
h
e
s
th
e
f
r
o
n
ti
er
s
o
f
th
e
ex
tr
e
m
e
p
o
s
e
v
ar
iat
io
n
s
is
d
is
cu
s
s
ed
in
[
8
]
.
A
s
i
n
g
le
m
o
d
el
o
f
p
o
s
e
i
n
v
ar
ia
n
t
i
s
lear
n
ed
b
y
th
e
g
r
ea
ter
a
m
o
u
n
t
o
f
tr
ain
i
n
g
d
ata
s
a
m
p
le
s
th
at
n
o
r
m
alize
t
h
e
s
in
g
le
f
r
o
n
tal
p
o
s
e.
T
h
e
m
eth
o
d
u
s
e
s
th
e
m
u
ltip
le
p
o
s
e
-
s
p
ec
if
ic
m
o
d
el
s
o
f
th
e
r
en
d
er
ed
f
ac
e
i
m
ag
e
s
in
o
r
d
er
to
tack
le
th
e
p
o
s
e
v
ar
iatio
n
s
ex
p
lic
it
l
y
.
T
h
en
th
e
d
ee
p
co
n
v
o
lu
tio
n
al
n
eu
r
al
n
et
w
o
r
k
is
u
s
ed
to
l
ea
r
n
th
e
d
is
cr
i
m
i
n
at
iv
e
r
ep
r
esen
tatio
n
s
o
f
t
h
e
i
m
a
g
es.
A
m
et
h
o
d
o
f
f
ac
e
r
ec
o
g
n
itio
n
s
y
s
te
m
b
ased
o
n
t
h
e
ar
b
itra
r
il
y
s
h
ap
ed
k
er
n
els
in
th
e
p
r
esen
ce
o
f
s
p
ac
e
v
ar
y
i
n
g
b
lu
r
m
o
tio
n
i
s
d
is
cu
s
s
ed
in
[
8
]
.
T
h
e
b
lu
r
r
ed
f
ac
e
i
m
ag
e
s
ar
e
u
s
ed
as
th
e
m
o
d
el
f
o
r
th
e
co
n
v
e
x
co
m
b
i
n
atio
n
o
f
th
e
g
eo
m
etr
ic
all
y
tr
an
s
f
o
r
m
ed
in
s
tan
ce
s
to
s
h
o
w
t
h
at
co
n
v
e
x
s
et
o
f
i
m
a
g
es
ar
e
o
b
tain
ed
b
y
th
e
n
o
n
-
u
n
if
o
r
m
l
y
b
l
u
r
r
in
g
o
f
th
e
i
m
a
g
es.
A
ls
o
,
a
m
et
h
o
d
b
ased
o
n
th
e
n
o
n
-
u
n
i
f
o
r
m
b
lu
r
r
o
b
u
s
t
alg
o
r
ith
m
is
u
s
ed
to
b
u
ild
an
en
er
g
y
f
u
n
c
tio
n
f
r
o
m
s
p
ar
s
e
ca
m
er
a
tr
aj
ec
to
r
y
w
it
h
t
h
e
l1
-
n
o
r
m
co
n
s
tr
ain
t
o
f
t
h
e
s
p
ac
e
m
o
tio
n
.
A
s
y
s
te
m
o
f
f
ac
e
r
ec
o
g
n
itio
n
m
eth
o
d
b
ased
o
n
th
e
L
o
ca
l
Z
er
n
i
k
e
Mo
m
e
n
t
s
(
L
Z
M)
is
d
is
cu
s
s
ed
in
[
9
]
.
T
h
e
m
et
h
o
d
is
o
f
t
w
o
s
ch
e
m
e
s
.
At
f
ir
s
t,
t
h
e
p
h
ase
m
a
g
n
it
u
d
e
h
is
to
g
r
a
m
is
u
s
e
d
o
v
er
th
e
co
m
p
lex
co
m
p
o
n
e
n
t
s
o
f
L
Z
M.
Seco
n
d
l
y
,
t
h
e
L
o
ca
l
Z
er
n
i
k
e
Xo
r
P
att
er
n
s
(
L
Z
XP
)
is
g
en
er
ated
a
n
d
u
s
ed
f
o
r
en
co
d
i
n
g
th
e
p
h
ase
co
m
p
o
n
en
t
s
.
Fo
r
b
o
th
th
e
s
c
h
e
m
e
s
t
h
e
i
m
a
g
e
s
ar
e
d
iv
id
ed
in
to
th
e
s
u
b
-
r
e
g
io
n
s
,
an
d
th
e
n
b
y
co
n
ca
ten
ati
n
g
th
e
h
i
s
to
g
r
a
m
s
,
th
e
f
ea
tu
r
e
v
ec
to
r
s
ar
e
co
n
s
tr
u
cted
f
o
r
all
s
u
b
-
b
a
n
d
s
.
An
al
y
s
i
s
o
f
r
eg
r
es
s
io
n
-
b
ased
class
i
f
icatio
n
m
et
h
o
d
f
o
r
f
ac
e
r
ec
o
g
n
it
io
n
s
y
s
te
m
i
s
d
is
c
u
s
s
ed
in
[
1
0
]
.
T
h
e
s
y
s
te
m
u
s
e
s
th
e
n
u
clea
r
n
o
r
m
r
eg
u
lar
ized
r
eg
r
ess
io
n
m
et
h
o
d
alo
n
g
w
it
h
th
e
o
cc
lu
s
io
n
f
o
r
r
ec
o
g
n
itio
n
.
T
h
e
m
et
h
o
d
in
te
g
r
ates t
h
e
er
r
o
r
s
u
p
p
o
r
t a
n
d
er
r
o
r
d
etec
tio
n
in
to
o
n
e
m
o
d
el
o
f
r
eg
r
es
s
io
n
.
A
f
ac
e
r
ec
o
g
n
i
tio
n
s
y
s
te
m
,
b
a
s
ed
o
n
th
e
m
e
th
o
d
ca
lled
co
m
p
leted
lo
ca
l
b
in
ar
y
p
att
er
n
al
g
o
r
ith
m
t
h
at
u
s
e
s
th
e
te
x
t
u
r
e
f
ea
t
u
r
es i
s
d
is
cu
s
s
ed
in
[
1
1
]
.
T
h
e
m
eth
o
d
is
u
s
ed
to
in
v
est
ig
ate
t
h
e
v
ar
ian
t
s
o
f
th
e
lo
ca
l b
i
n
ar
y
p
atter
n
in
t
h
e
f
ield
s
o
f
s
ce
n
e,
tex
t
u
r
e
an
d
ev
e
n
t
s
o
f
t
h
e
f
ac
e
i
m
a
g
e
clas
s
i
f
icatio
n
.
A
m
o
d
i
f
ied
v
er
s
io
n
o
f
th
e
L
ea
s
t
T
r
im
m
ed
Sq
u
ar
es
(
L
T
S)
alo
n
g
w
it
h
a
g
e
n
etic
al
g
o
r
ith
m
is
d
is
c
u
s
s
ed
in
[
1
2
]
.
T
h
e
m
et
h
o
d
is
u
s
ed
m
o
d
i
f
y
t
h
e
L
T
S
alo
n
g
w
i
th
g
e
n
etic
al
g
o
r
ith
m
m
et
h
o
d
.
T
h
e
u
s
e
o
f
t
h
e
g
e
n
etic
a
lg
o
r
it
h
m
s
i
s
to
co
n
s
tr
u
ct
io
n
o
f
th
e
s
u
b
s
ets r
at
h
er
th
a
n
t
h
e
r
an
d
o
m
s
e
lectio
n
o
f
t
h
e
b
asic s
u
b
s
ets.
A
m
et
h
o
d
b
ased
o
n
th
e
o
n
e
-
d
i
m
en
s
io
n
a
l
h
id
d
en
Ma
r
k
o
v
cla
s
s
i
f
icatio
n
m
o
d
el
f
o
r
p
er
f
o
r
m
i
n
g
t
h
e
lo
w
f
ac
e
r
ec
o
g
n
itio
n
i
s
d
is
cu
s
s
ed
i
n
[
1
3
]
.
T
h
e
m
e
th
o
d
u
s
es
t
h
r
ee
s
tep
s
f
o
r
th
e
e
x
tr
ac
tio
n
o
f
t
h
e
f
ac
ial
f
ea
tu
r
e
s
as
s
u
c
h
;
t
h
e
ca
lc
u
lat
io
n
o
f
t
h
e
h
i
s
to
g
r
a
m
o
f
o
r
ie
n
ted
g
r
ad
ie
n
ts
d
escr
ip
to
r
an
d
th
e
Gab
o
r
f
ilt
er
s
,
th
e
n
t
h
e
li
n
ea
r
d
is
cr
i
m
i
n
an
t
an
al
y
s
is
m
et
h
o
d
is
u
s
ed
to
r
e
m
o
v
e
t
h
e
r
ed
u
n
d
an
t
i
n
f
o
r
m
atio
n
a
n
d
to
r
ed
u
ce
t
h
e
f
ea
tu
r
e
s
izes
a
n
d
at
last
th
e
ca
n
o
n
ical
co
r
r
elatio
n
an
al
y
s
is
m
eth
o
d
is
u
s
ed
to
co
m
b
i
n
e
t
h
e
f
e
at
u
r
es b
ef
o
r
e
t
h
e
class
i
f
icatio
n
.
A
m
et
h
o
d
f
o
r
th
e
r
ec
o
g
n
itio
n
o
f
th
e
f
ac
e
a
f
ter
th
e
p
la
s
tic
s
u
r
g
er
y
b
ased
o
n
t
h
e
E
n
tr
o
p
y
b
ased
s
ca
le
in
v
ar
ia
n
t
f
ea
t
u
r
e
tr
an
s
f
o
r
m
(
E
V
-
SIFT
)
m
et
h
o
d
is
d
is
cu
s
s
ed
in
[
1
4
]
.
T
h
is
f
ea
t
u
r
e
w
ill
e
x
t
r
ac
t
th
e
k
e
y
p
o
in
ts
an
d
th
e
s
ca
le
-
s
p
ac
e
s
tr
u
ct
u
r
e
v
o
lu
m
e
i
n
f
o
r
m
atio
n
.
Si
n
ce
t
h
e
en
tr
o
p
y
i
s
a
t
y
p
e
o
f
th
e
h
ig
h
er
o
r
d
er
s
tatis
tica
l
f
ea
t
u
r
e,
th
e
u
n
ce
r
tai
n
t
y
v
ar
iati
o
n
s
i
n
th
e
w
il
l
h
av
e
t
h
e
lea
s
t
ef
f
ec
ts
in
it
an
d
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u
p
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t v
ec
to
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m
ac
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i
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ier
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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N
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1
.
2
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Sta
t
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m
e
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elo
p
in
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a
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au
to
m
ati
c
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ac
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r
ec
o
g
n
it
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y
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m
o
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e
m
a
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e
n
co
u
n
ter
f
e
w
p
r
o
b
le
m
s
s
u
ch
a
s
:
a)
I
t
is
k
n
o
w
n
t
h
at
f
o
r
th
e
r
ec
o
g
n
itio
n
o
f
f
ac
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th
e
s
ize
o
f
t
h
e
i
m
ag
e
w
ill
b
e
q
u
ite
s
m
all
th
at
ac
ts
as
th
e
d
is
ad
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an
ta
g
es a
s
th
e
f
ac
e
r
ec
o
g
n
i
tio
n
s
y
s
te
m
t
h
at
p
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el
y
d
ep
en
d
s
o
n
t
h
e
ac
cu
r
ate
f
ea
tu
r
e
lo
ca
lizatio
n
s
.
b)
T
h
e
p
r
o
b
lem
o
f
p
r
o
d
u
cin
g
t
h
e
ac
cu
r
ate
f
ea
t
u
r
e
lo
ca
tio
n
is
d
if
f
icu
l
t
in
o
r
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er
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o
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o
d
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o
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p
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o
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m
an
ce
.
1
.
3
.
T
he
P
ro
po
s
ed
So
lutio
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T
o
o
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co
m
e
t
h
e
s
e
p
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o
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lem
s
,
an
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to
m
ati
c
f
ac
e
r
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o
g
n
it
io
n
m
eth
o
d
b
ased
o
n
al
g
o
r
ith
m
ca
lled
th
e
DT
MBW
T
tr
an
s
f
o
r
m
f
r
o
m
wh
ich
t
h
e
f
ea
tu
r
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e
ex
tr
ac
te
d
b
y
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s
in
g
t
h
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d
if
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er
en
t
f
ea
t
u
r
es
p
r
esen
t
i
n
th
e
tr
an
s
f
o
r
m
atio
n
alg
o
r
it
h
m
.
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h
e
n
th
e
s
y
s
te
m
is
clas
s
i
f
ied
b
y
u
s
in
g
t
h
e
KNN
clas
s
i
f
ier
s
c
h
e
m
e.
T
h
e
p
ap
er
o
r
g
an
ized
in
a
wa
y
t
h
at
th
e
s
ec
tio
n
2
e
x
p
lain
es
ab
o
u
t
t
h
e
m
et
h
o
d
o
lo
g
y
,
t
h
e
f
ea
t
u
r
es
ex
tr
ac
tio
n
f
ilter
s
an
d
t
h
e
clas
s
if
icatio
n
m
eth
o
d
s
u
s
ed
.
T
h
en
th
e
s
ec
t
io
n
3
s
h
o
w
s
d
is
c
u
s
s
io
n
ab
o
u
t
t
h
e
r
es
u
lts
o
b
tain
ed
an
d
th
e
s
ec
tio
n
4
g
i
v
es a
co
n
clu
s
io
n
f
o
r
th
is
a
u
to
m
atic
f
ac
e
r
ec
o
g
n
itio
n
s
y
s
te
m
.
2.
M
E
T
H
O
DO
L
O
G
Y
T
h
e
p
r
o
p
o
s
ed
f
ac
e
r
ec
o
g
n
itio
n
s
y
s
te
m
is
m
ad
e
u
p
o
f
t
w
o
t
y
p
es
o
f
o
p
er
atio
n
s
s
u
c
h
as
tr
ain
i
n
g
a
n
d
th
e
test
i
n
g
p
h
ase
s
.
I
n
t
h
e
tr
ai
n
i
n
g
p
h
ase,
a
ll
t
h
e
tr
ain
i
n
g
f
ac
e
i
m
ag
e
s
ar
e
u
s
ed
f
o
r
th
e
ex
tr
ac
tio
n
o
f
t
h
e
f
ea
t
u
r
es
.
B
ef
o
r
e
th
e
ex
tr
ac
tio
n
o
f
f
ea
t
u
r
es,
th
e
in
p
u
ts
ar
e
d
ec
o
m
p
o
s
e
d
b
y
u
s
in
g
t
h
e
alg
o
r
ith
m
k
n
o
w
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as
D
u
al
T
r
ee
M
-
B
an
d
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r
an
s
f
o
r
m
(
DT
MB
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T
)
tr
an
s
f
o
r
m
.
T
h
en
t
h
e
f
ea
tu
r
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r
e
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tr
ac
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f
r
o
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t
h
e
tr
an
s
f
o
r
m
ed
i
m
ag
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b
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v
ar
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n
g
th
e
d
if
f
er
e
n
t
f
i
lter
av
ailab
le
in
DT
MB
W
T
an
d
ar
e
s
av
ed
as
th
e
tr
ai
n
ed
d
atab
ase.
T
h
en
th
e
te
s
ti
n
g
p
h
ase
i
s
d
o
n
e
b
y
u
s
in
g
t
h
e
te
s
t
i
m
ag
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an
d
to
cla
s
s
i
f
y
t
h
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f
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tu
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t
h
at
ar
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e
x
tr
ac
ted
f
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o
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t
h
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te
s
ti
n
g
s
et
o
f
i
m
a
g
es.
T
o
p
er
f
o
r
m
th
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ac
tio
n
o
f
class
i
f
icat
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n
th
e
clas
s
i
f
i
er
alg
o
r
ith
m
u
s
ed
in
th
e
p
r
o
p
o
s
ed
s
y
s
te
m
is
th
e
KNN
class
if
ier
.
T
h
e
b
l
o
ck
d
iag
r
a
m
o
f
t
h
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p
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p
o
s
ed
s
y
s
te
m
i
s
s
h
o
w
n
i
n
F
i
g
u
r
e
1
.
Fig
u
r
e
1
.
B
lo
ck
d
iag
r
a
m
f
o
r
th
e
p
r
o
p
o
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ed
f
ac
e
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ec
o
g
n
itio
n
s
y
s
te
m
2
.
1
.
F
ea
t
ure
E
x
t
ra
ct
io
n
I
n
an
y
cla
s
s
i
f
icatio
n
o
r
r
ec
o
g
n
i
tio
n
s
y
s
te
m
,
t
h
e
f
ea
tu
r
e
ex
tr
ac
tio
n
p
r
o
ce
s
s
is
ca
r
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ied
o
u
t
v
er
y
i
m
p
o
r
tan
tl
y
.
T
h
e
f
ea
tu
r
es
t
h
at
ar
e
ex
tr
ac
ted
f
r
o
m
t
h
e
in
p
u
t
i
m
ag
e
s
ar
e
u
s
e
f
u
l
f
o
r
th
e
clas
s
i
f
icatio
n
p
u
r
p
o
s
e
as
th
e
cla
s
s
i
f
ier
i
n
p
u
t
s
.
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n
o
u
r
p
r
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p
o
s
ed
s
y
s
te
m
al
s
o
t
h
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f
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t
u
r
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ex
tr
ac
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n
p
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ce
s
s
is
p
er
f
o
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m
ed
b
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u
s
i
n
g
th
e
alg
o
r
ith
m
k
n
o
w
n
as
t
h
e
DT
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W
T
tr
an
s
f
o
r
m
al
g
o
r
ith
m
.
As
th
is
al
g
o
r
ith
m
i
s
o
n
e
o
f
th
e
t
y
p
e
s
o
f
w
a
v
ele
t
tr
an
s
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o
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m
m
et
h
o
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tr
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ted
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ea
n
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o
f
th
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s
u
b
-
b
a
n
d
co
ef
f
icien
ts
.
Us
in
g
th
e
DT
MB
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tr
an
s
f
o
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m
,
th
e
h
i
g
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a
n
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en
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b
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b
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d
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ef
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icie
n
ts
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o
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tain
ed
f
r
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m
th
e
i
n
p
u
t
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m
ag
e
s
ar
e
o
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tain
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……….
T
rai
ning
Fa
ce
I
mage
s
A
p
prox
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mat
e Su
b
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band
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f
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Fe
atures
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mage
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Fe
atures
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l
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t
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ce
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mage
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M
B
WT
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rans
f
orm
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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827
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b
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Seles
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ick
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1
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an
d
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s
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h
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s
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y
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t
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s
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ated
as
1
2
J
M
J
h
er
e
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e
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as
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n
u
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o
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n
d
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is
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er
r
ed
as t
h
e
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m
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o
f
f
ilter
b
an
k
s
.
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h
e
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d
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tr
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s
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m
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2
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2
.
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h
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s
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s
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n
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is
u
s
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o
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m
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ce
s
s
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s
.
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m
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p
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lar
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te
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s
to
t
h
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s
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s
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s
f
o
r
m
(
DT
T
)
f
ilter
s
p
ec
if
ica
tio
n
s
.
F
r
o
m
t
h
e
a
v
ailab
le
f
i
lter
f
o
r
th
e
DT
T
,
th
e
f
ilter
s
li
k
e
Haa
r
b
an
d
,
Me
y
er
b
an
d
,
S
y
m
let
s
b
an
d
f
ilter
s
ar
e
ex
p
lai
n
ed
as f
o
llo
w
s
:
2
.
2
.
1.
H
AAR
Wa
v
elet
F
ilte
r
T
h
e
w
a
v
elet
h
aa
r
is
s
aid
to
b
e
a
s
eq
u
en
ce
o
f
s
q
u
ar
e
-
s
h
ap
e
d
r
escaled
f
u
n
ct
io
n
s
t
h
at
to
g
et
h
er
f
o
r
m
a
w
a
v
elet
b
asi
s
o
r
f
a
m
il
y
as
d
i
s
cu
s
s
ed
in
[
1
6
]
.
T
h
e
an
al
y
s
is
o
f
w
av
ele
t
is
a
s
s
i
m
ilar
to
t
h
a
t
o
f
t
h
e
Fo
u
r
ier
an
al
y
s
is
t
h
at
allo
w
s
th
e
tar
g
et
f
u
n
ctio
n
to
b
e
r
ep
r
esen
ted
as
o
r
th
o
n
o
r
m
al
b
asi
s
f
u
n
ctio
n
o
v
er
an
in
ter
v
al
o
f
ti
m
e.
T
h
e
h
aa
r
w
av
ele
ts
ar
e
r
ep
r
esen
ted
as (
)
an
d
th
e
s
ca
li
n
g
w
a
v
elet
is
r
ep
r
esen
ted
as (
).
2
.
2
.
2
.
M
E
YE
R
Wa
v
elet
F
ilte
r
T
h
e
Me
y
er
w
av
ele
t
f
u
n
ctio
n
ca
n
b
e
r
ep
r
esen
ted
as
th
e
d
is
c
r
ete
f
o
r
m
at
o
f
D
m
e
y
w
a
v
elet
f
ilter
[
1
6
]
.
T
h
e
Me
y
er
's
w
a
v
elet
eq
u
atio
n
g
e
n
er
all
y
ac
ts
a
s
a
s
o
lv
e
n
t
m
eth
o
d
f
o
r
s
o
l
v
i
n
g
th
e
t
w
o
-
s
ca
l
e
eq
u
atio
n
.
B
ased
o
n
th
e
ap
p
r
o
x
i
m
a
tio
n
s
p
ac
e
b
asis
,
th
e
Me
y
er
e
m
p
lo
y
ed
th
e
Fo
u
r
ier
tr
an
s
f
o
r
m
in
o
r
d
er
to
d
er
iv
e
th
e
co
ef
f
icie
n
t
s
t
w
o
-
s
ca
le
ed
u
ca
ti
o
n
.
2
.
2
.
3
.
SYM
L
E
T
Wa
v
elet
F
ilte
r
T
h
e
s
y
m
let
w
a
v
elet
f
ilter
d
ef
i
n
es
t
h
e
f
a
m
il
y
o
f
o
r
th
o
g
o
n
al
w
a
v
elet
s
an
d
is
also
ca
lled
as
th
e
least
as
y
m
m
etr
ic
w
a
v
elet
b
as
is
[
1
6
]
.
T
h
e
s
y
m
let
w
a
v
elet
f
u
n
ct
io
n
is
u
s
u
al
l
y
d
e
f
i
n
ed
f
o
r
a
n
y
p
o
s
iti
v
e
i
n
te
g
er
n
w
h
er
ea
s
t
h
e
w
av
ele
t
f
u
n
ctio
n
(
)
an
d
th
e
s
ca
lin
g
f
u
n
ctio
n
(
)
th
at
s
u
p
p
o
r
ts
th
e
len
g
t
h
o
f
2
n
.
T
h
e
s
y
m
let
ca
n
b
e
u
s
ed
as
t
h
e
f
u
n
ctio
n
s
s
u
ch
a
s
w
av
ele
t p
h
i a
n
d
d
is
cr
ee
t
w
a
v
elet
tr
a
n
s
f
o
r
m
s
.
Usi
n
g
t
h
ese
f
ilter
s
,
th
e
f
ea
tu
r
es
ar
e
ex
tr
ac
ted
f
r
o
m
t
h
e
tr
ai
n
in
g
i
m
a
g
es
a
n
d
ar
e
s
av
ed
as
th
e
tr
ain
ed
d
atab
ase
w
h
ich
i
s
later
u
s
ed
.
W
h
er
ea
s
th
e
s
a
m
e
s
et
o
f
f
ilter
s
ar
e
u
s
ed
f
o
r
th
e
te
s
ti
n
g
i
m
a
g
es
a
n
d
ar
e
u
s
ed
as
th
e
in
p
u
ts
f
o
r
th
e
clas
s
i
f
ier
th
a
t p
er
f
o
r
m
s
th
e
r
ec
o
g
n
it
io
n
p
r
o
ce
s
s
.
2
.
3
.
Cla
s
s
if
ica
t
io
n
T
h
e
o
u
tp
u
t
o
f
t
h
e
p
r
o
p
o
s
ed
f
ac
e
r
ec
o
g
n
itio
n
s
y
s
te
m
m
ain
l
y
d
ep
en
d
s
o
n
t
h
e
cla
s
s
i
f
icatio
n
s
tep
th
at
i
s
ca
r
r
ied
o
u
t
f
o
r
t
h
e
d
ec
is
io
n
-
m
ak
in
g
p
r
o
ce
s
s
b
y
u
s
i
n
g
a
n
e
f
f
ec
tiv
e
cla
s
s
i
f
ier
w
i
th
it.
I
n
o
u
r
p
r
o
p
o
s
ed
s
y
s
te
m
th
e
d
ec
is
io
n
-
m
ak
in
g
p
r
o
ce
s
s
is
m
ad
e
b
y
u
s
in
g
th
e
K
-
Nea
r
es
t
Neig
h
b
o
r
(
KNN)
class
if
ier
al
g
o
r
ith
m
.
T
h
e
KNN
h
elp
s
i
n
class
if
y
i
n
g
t
h
e
f
ea
t
u
r
es b
ased
o
n
th
e
tr
ain
in
g
ex
a
m
p
l
es in
t
h
e
clo
s
est
f
ea
t
u
r
e
v
ec
to
r
.
T
h
e
class
if
icatio
n
i
s
m
ad
e
s
u
cc
ess
f
u
l
l
y
b
ased
o
n
t
h
e
m
aj
o
r
it
y
o
f
t
h
e
v
o
te
b
y
i
ts
n
eig
h
b
o
r
s
.
T
h
e
k
r
ef
er
s
to
th
e
v
al
u
es
th
at
ar
e
d
e
cid
ed
b
ased
o
n
th
e
d
ata
s
ize
u
s
ed
f
o
r
class
if
ica
tio
n
.
W
h
e
n
k
is
s
et
to
1
,
(
k
=
1
)
,
th
en
t
h
e
f
ea
t
u
r
es
ar
e
ass
i
g
n
ed
to
its
n
ea
r
est
n
ei
g
h
b
o
r
class
.
W
h
en
t
h
e
s
ize
o
f
k
is
i
n
cr
ea
s
e
d
th
en
t
h
e
ef
f
ec
t
s
o
f
n
o
is
e
i
s
al
s
o
in
cr
ea
s
ed
,
a
n
d
al
s
o
th
e
b
o
u
n
d
ar
ies
b
et
w
ee
n
t
h
e
class
e
s
ar
e
d
ec
r
ea
s
ed
.
T
h
e
p
r
ed
ictio
n
f
o
r
t
h
e
te
s
t
s
a
m
p
les
ar
e
m
ad
e
b
y
f
o
llo
w
i
n
g
th
e
s
tep
s
li
k
e
co
m
p
u
ti
n
g
t
h
e
d
is
ta
n
ce
o
f
tes
t
v
ec
to
r
s
al
o
n
g
w
i
th
t
h
e
tr
ain
v
ec
to
r
s
.
T
o
f
in
d
th
e
clo
s
est
v
e
cto
r
s
o
f
k
an
d
also
to
ar
r
an
g
e
th
e
d
is
ta
n
ce
in
a
s
ce
n
d
i
n
g
o
r
d
er
an
d
to
ch
o
o
s
e
th
e
clo
s
est
lab
el.
I
n
th
is
w
o
r
k
th
e
KNN
alg
o
r
ith
m
i
s
u
s
ed
w
i
th
th
e
E
u
cl
id
ea
n
d
is
ta
n
ce
m
e
asu
r
es
is
u
s
ed
f
o
r
class
i
f
icatio
n
.
E
q
u
atio
n
1
s
h
o
w
s
th
e
E
u
clid
ea
n
d
is
tan
ce
f
o
r
m
u
la
as:
2
1
1
2
)
,
(
m
i
i
i
y
x
y
x
y
x
d
(
1
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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N
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5
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d
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&
C
o
m
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Sci,
Vo
l
.
1
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,
No
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2
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e
m
b
er
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8
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2
4
–
83
1
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h
er
e
x
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n
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te
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u
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lid
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to
r
.
Usi
n
g
th
i
s
E
u
cli
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ea
n
d
is
ta
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m
ea
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r
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t
h
e
cl
ass
i
f
icatio
n
is
d
o
n
e
b
y
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s
i
n
g
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r
e
in
p
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g
i
v
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to
t
h
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cla
s
s
i
f
ier
.
T
h
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f
ea
t
u
r
es
o
b
tain
ed
f
r
o
m
d
i
f
f
er
en
t
f
ilter
s
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f
th
e
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-
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a
n
d
tr
an
s
f
o
r
m
f
r
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m
t
h
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ai
n
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g
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p
les
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e
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p
u
ts
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th
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class
i
f
ier
.
T
h
en
t
h
e
class
i
f
ier
co
m
p
ar
es
b
o
th
t
h
e
f
ea
t
u
r
es
o
b
tai
n
ed
f
r
o
m
t
h
e
tr
ain
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n
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f
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s
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ll
y
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3.
RE
SU
L
T
AND
DI
SCUS
SI
O
N
T
o
illu
s
tr
ate
th
e
p
er
f
o
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m
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itio
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te
m
,
th
e
ex
p
er
i
m
e
n
tal
r
es
u
lt
s
o
b
tain
ed
f
r
o
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t
h
e
m
e
th
o
d
s
e
x
p
lain
ed
in
t
h
e
ab
o
v
e
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ec
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ce
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cu
s
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ed
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Am
o
n
g
m
a
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y
o
f
f
ac
e
i
m
a
g
e
d
atab
ase
th
a
t
i
s
av
ailab
le
in
w
o
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ld
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w
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i
n
o
u
r
s
y
s
te
m
,
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e
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s
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s
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t
co
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s
a
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f
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f
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4
0
d
is
tin
ct
s
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b
j
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ts
o
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n
d
if
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h
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A
l
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e
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m
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p
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s
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r
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ased
o
n
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d
th
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class
if
ica
tio
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r
es
u
lts
o
f
v
ar
io
u
s
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u
tp
u
ts
o
b
tain
ed
b
y
u
s
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n
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t
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d
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f
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b
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m
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ar
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w
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th
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ch
o
th
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also
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it
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P
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p
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C
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m
p
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n
t
An
al
y
s
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P
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A
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al
g
o
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ith
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tp
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t th
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s
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est r
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f
t
h
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g
o
r
ith
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s
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icatio
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r
o
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th
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r
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lts
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i
t
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p
r
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o
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ce
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p
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w
it
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P
C
A
al
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ith
m
a
n
d
ar
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clu
d
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at
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ed
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te
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ca
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b
etter
r
esu
lt
s
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d
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n
p
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ed
ict
th
e
f
ac
e
r
ec
o
g
n
i
tio
n
at
t
h
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r
ate
o
f
9
5
% o
f
r
ec
o
g
n
itio
n
ac
c
u
r
ac
y
.
RE
F
E
R
E
NC
E
S
[1
]
Yin
X,
L
iu
X
.
“
M
u
lt
i
-
tas
k
c
o
n
v
o
lu
ti
o
n
a
l
n
e
u
ra
l
n
e
tw
o
rk
f
o
r
p
o
se
-
i
n
v
a
rian
t
f
a
c
e
re
c
o
g
n
it
io
n
”
.
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Ima
g
e
Pro
c
e
ss
in
g
.
2
0
1
7
;
1
-
12
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esia
n
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4752
A
n
a
lysi
s
o
f D
iffer
en
t
M
-
B
a
n
d
W
a
ve
let
F
il
ters
fo
r
F
a
ce
R
ec
o
g
n
itio
n
u
s
in
g
N
ea
r
est
…
(
C
.
H
ema
la
th
a
)
831
[2
]
Ch
e
n
g
Y,
Jia
o
L
,
T
o
n
g
Y,
L
i
Z,
Hu
Y,
Ca
o
X
.
“
Dire
c
ti
o
n
a
l
il
lu
m
in
a
ti
o
n
e
stim
a
ti
o
n
se
ts
a
n
d
m
u
lt
il
e
v
e
l
m
a
tch
in
g
me
tri
c
f
o
r
il
lu
m
in
a
ti
o
n
-
ro
b
u
st
f
a
c
e
re
c
o
g
n
it
io
n
”
.
IEE
E
Acc
e
ss
.
2
0
1
7
;
5
:
2
5
8
3
5
-
2
5
8
4
5
.
[3
]
Hu
a
n
g
P
,
G
a
o
G
,
Qia
n
C,
Ya
n
g
G
,
Ya
n
g
Z.
“
F
u
z
z
y
li
n
e
a
r
re
g
re
ss
io
n
d
isc
rim
in
a
n
t
p
r
o
jec
ti
o
n
f
o
r
f
a
c
e
re
c
o
g
n
it
io
n
”
.
IEE
E
Acc
e
ss
.
2
0
1
7
;
5
:
4
3
4
0
-
4
3
4
9
.
[4
]
Ca
o
F
,
F
e
n
g
X
,
Z
h
a
o
J
.
“
S
p
a
r
se
r
e
p
re
se
n
tatio
n
f
o
r
ro
b
u
st
f
a
c
e
re
c
o
g
n
it
io
n
b
y
d
ictio
n
a
ry
d
e
c
o
m
p
o
siti
o
n
”
.
J
o
u
rn
a
l
o
f
Vi
su
a
l
Co
mm
u
n
ica
ti
o
n
a
n
d
Im
a
g
e
Rep
re
se
n
ta
ti
o
n
.
2
0
1
7
;
4
6
:
2
6
0
-
2
6
8
.
[5
]
L
iu
W
,
W
e
n
Y,
Yu
Z,
L
i
M
,
R
a
j
B,
S
o
n
g
,
L
.
“
S
p
h
e
re
f
a
c
e
:
D
e
e
p
h
y
p
e
rsp
h
e
re
e
m
b
e
d
d
in
g
f
o
r
fa
c
e
re
c
o
g
n
it
io
n
”
.
IEE
E
Co
n
fer
e
n
c
e
o
n
Co
mp
u
ter
V
isio
n
a
n
d
P
a
tt
e
rn
Rec
o
g
n
it
io
n
.
2
0
1
7
;
1
:
1
-
9
.
[6
]
Hu
a
n
g
P
,
L
a
i
Z,
Ga
o
G
,
Ya
n
g
G
,
Ya
n
g
Z.
“
A
d
a
p
ti
v
e
li
n
e
a
r
d
isc
rim
in
a
n
t
re
g
re
s
sio
n
c
las
sif
i
c
a
ti
o
n
f
o
r
f
a
c
e
re
c
o
g
n
it
io
n
”
.
Dig
it
a
l
S
ig
n
a
l
Pro
c
e
ss
in
g
.
2
0
1
6
;
5
5
:
78
-
84
.
[7
]
M
a
si
I,
Ra
w
ls
S
,
M
e
d
io
n
i
G
,
Na
tara
jan
P
.
“
P
o
se
-
a
w
a
r
e
f
a
c
e
re
c
o
g
n
it
io
n
i
n
th
e
w
il
d
”
.
In
Pro
c
e
e
d
i
n
g
s
o
f
t
h
e
IEE
E
Co
n
fer
e
n
c
e
o
n
Co
m
p
u
ter
Vi
si
o
n
a
n
d
Pa
tt
e
rn
Rec
o
g
n
it
io
n
.
2
0
1
6
;
4
8
3
8
-
4
8
4
6
.
[8
]
P
u
n
n
a
p
p
u
ra
th
A
,
Ra
jag
o
p
a
lan
AN
,
T
a
h
e
ri
S
,
Ch
e
ll
a
p
p
a
R,
S
e
e
th
a
ra
m
a
n
G
.
“
F
a
c
e
re
c
o
g
n
it
io
n
a
c
r
o
ss
n
o
n
-
u
n
if
o
rm
m
o
ti
o
n
b
l
u
r,
il
lu
m
in
a
ti
o
n
,
a
n
d
p
o
se
”
.
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Im
a
g
e
Pro
c
e
ss
in
g
.
2
0
1
5
;
24
(7
)
:
2
0
6
7
-
2
0
8
2
.
[9
]
Ba
sa
ra
n
E,
G
o
k
m
e
n
M
.
“
A
n
e
ff
i
c
ien
t
f
a
c
e
re
c
o
g
n
it
io
n
sc
h
e
m
e
u
sin
g
lo
c
a
l
Zer
n
ik
e
m
o
m
e
n
ts
p
a
tt
e
rn
s”
.
In
Asia
n
Co
n
fer
e
n
c
e
o
n
Co
m
p
u
ter
Vi
si
o
n
.
2
0
1
4
;
7
1
0
-
7
2
4
.
S
p
rin
g
e
r,
C
h
a
m
.
[1
0
]
Qia
n
J,
L
u
o
L
,
Ya
n
g
J,
Zh
a
n
g
F
,
L
in
Z.
“
Ro
b
u
st
n
u
c
lea
r
n
o
rm
re
g
u
lariz
e
d
re
g
re
ss
io
n
f
o
r
f
a
c
e
re
c
o
g
n
it
io
n
w
it
h
o
c
c
lu
sio
n
”
.
Pa
tt
e
rn
Rec
o
g
n
it
io
n
.
2
0
1
5
;
4
8
(
1
0
)
:
3
1
4
5
-
3
1
5
9
.
[1
1
]
Ra
ss
e
m
T
H,
M
a
k
b
o
l
NM,
Ye
e
S
Y.
“
F
a
c
e
re
c
o
g
n
it
io
n
u
si
n
g
c
o
m
p
l
e
ted
lo
c
a
l
tern
a
r
y
p
a
tt
e
rn
tex
tu
re
d
e
sc
rip
to
r”
.
In
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
E
lec
trica
l
a
n
d
C
o
mp
u
ter
En
g
in
e
e
rin
g
(
IJ
ECE
).
2
0
1
7
;
7
(3
):
1
5
9
4
-
1
6
0
4
.
[1
2
]
Ra
h
im
N
AA
,
G
h
a
n
i
NA
M
,
M
o
h
a
m
e
d
N,
Ha
sh
im
H,
M
u
sirin
I
.
“
T
h
e
A
p
p
li
c
a
ti
o
n
o
f
M
o
d
if
ied
L
e
a
st
T
ri
m
m
e
d
S
q
u
a
re
s
w
it
h
G
e
n
e
ti
c
A
l
g
o
rit
h
m
s
M
e
th
o
d
i
n
F
a
c
e
Re
c
o
g
n
it
i
o
n
”
.
I
n
d
o
n
e
si
a
n
J
o
u
rn
a
l
o
f
E
lec
trica
l
E
n
g
i
n
e
e
rin
g
a
n
d
Co
mp
u
ter
S
c
ien
c
e
(
IJ
EE
CS
)
.
2
0
1
7
;
8
(
1
):
1
5
4
-
1
5
8
.
[1
3
]
El
M
e
slo
u
h
i
O,
El
g
a
rra
i
Z,
Ka
rd
o
u
c
h
i
M
,
A
ll
a
li
H.
“
Un
im
o
d
a
l
M
u
lt
i
-
F
e
a
tu
re
F
u
sio
n
a
n
d
o
n
e
-
d
im
e
n
sio
n
a
l
Hi
d
d
e
n
M
a
rk
o
v
M
o
d
e
ls
f
o
r
L
o
w
-
Re
so
lu
ti
o
n
F
a
c
e
Re
c
o
g
n
it
i
o
n
”
.
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
Co
m
p
u
ter
En
g
i
n
e
e
rin
g
(
IJ
ECE
)
.
2
0
1
7
;
7
(4
):
1
9
1
5
-
1
9
2
2
.
[1
4
]
S
a
b
le
A
H,
T
a
lb
a
r
S
N,
Dh
ir
b
a
si
HA
.
“
EV
-
S
IF
T
-
A
n
Ex
ten
d
e
d
S
c
a
le
In
v
a
rian
t
F
a
c
e
Re
c
o
g
n
it
i
o
n
f
o
r
P
las
ti
c
S
u
rg
e
r
y
F
a
c
e
Re
c
o
g
n
it
io
n
”
.
I
n
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
C
o
mp
u
t
e
r E
n
g
i
n
e
e
rin
g
(
IJ
ECE
).
2
0
1
7
;
7
(
4
):
1
9
2
3
-
1
9
3
3
.
[1
5
]
S
e
les
n
ick
I
W
,
Ba
ra
n
iu
k
R
G
,
Kin
g
sb
u
ry
NC.
“
T
h
e
d
u
a
l
-
tree
c
o
m
p
lex
w
a
v
e
let
tran
sf
o
r
m
s
”
.
IEE
E
S
ig
n
a
l
Pro
c
e
ss
in
g
M
a
g
a
zin
e
.
2
0
0
5
;
2
2
(
6
):
1
2
3
-
1
5
1
.
[1
6
]
Bh
a
m
id
ip
a
ti
S
L
,
M
i
n
d
a
g
u
d
la
S
S
,
De
v
a
ll
a
HV
,
G
o
o
d
i
HS,
Na
g
H.
“
A
n
a
l
y
sis
o
f
d
iff
e
re
n
t
d
isc
re
te
w
a
v
e
let
tran
sf
o
r
m
b
a
sis f
u
n
c
ti
o
n
s i
n
s
p
e
e
c
h
sig
n
a
l
c
o
m
p
re
ss
io
n
”
.
IOS
R
J
o
u
rn
a
l
o
f
VL
S
I
a
n
d
S
i
g
n
a
l
Pr
o
c
e
ss
in
g
,
2
0
1
4
;
4
(1
):
3
4
-
38
.
Evaluation Warning : The document was created with Spire.PDF for Python.