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1
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Evaluation Warning : The document was created with Spire.PDF for Python.
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A
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o
v
al
o
f
f
ea
t
u
r
es
f
r
o
m
t
h
e
f
ac
e
r
eg
io
n
,
id
en
ti
f
icatio
n
,
a
n
d
m
atc
h
in
g
.
T
h
e
co
m
m
o
n
f
ac
e
r
ec
o
g
n
itio
n
ta
s
k
t
h
u
s
cr
e
ated
is
a
p
r
im
ar
y
is
s
u
e
in
p
r
o
b
lem
s
s
u
ch
a
s
elec
tr
o
n
ic
li
n
e
u
p
an
d
b
r
o
w
s
i
n
g
th
r
o
u
g
h
a
d
atab
ase
o
f
f
ac
e
s
.
F
ac
e
r
ec
o
g
n
itio
n
i
s
o
n
e
o
f
t
h
e
ch
alle
n
g
i
n
g
ta
s
k
s
.
Mo
s
t
e
x
i
s
ti
n
g
f
ac
e
r
ec
o
g
n
i
tio
n
m
et
h
o
d
s
en
co
u
n
ter
d
i
f
f
ic
u
lties
in
t
h
e
ca
s
e
o
f
lar
g
e
v
ar
iatio
n
,
esp
ec
iall
y
w
h
e
n
o
n
l
y
o
n
e
u
p
r
ig
h
t
f
r
o
n
tal
i
m
a
g
e
av
ailab
le
f
o
r
ea
ch
p
er
s
o
n
a
n
d
th
e
tr
ain
i
n
g
i
m
a
g
es
ar
e
u
n
d
er
ev
en
ill
u
m
i
n
atio
n
a
n
d
n
eu
tr
al
f
ac
ial
ex
p
r
es
s
io
n
.
Mo
s
t
o
f
t
h
e
r
ec
o
g
n
itio
n
tech
n
i
q
u
es
ar
e
b
ased
o
n
s
tatis
tical
a
p
p
r
o
ac
h
.
A
n
d
t
h
ese
tech
n
iq
u
e
s
n
ee
d
m
o
r
e
i
m
a
g
e
s
o
f
a
p
er
s
o
n
w
it
h
d
if
f
er
en
t
p
o
s
es
an
d
d
if
f
er
e
n
t
ill
u
m
in
a
tio
n
co
n
d
itio
n
s
f
o
r
b
etter
r
e
co
g
n
itio
n
ac
cu
r
ac
y
.
P
r
ac
tically
it
n
o
t
p
o
s
s
ib
le.
I
t
n
ee
d
s
to
d
ev
elo
p
a
f
ac
e
r
ec
o
g
n
itio
n
s
y
s
te
m
w
h
ich
r
eq
u
ir
es
o
n
l
y
o
n
e
i
m
a
g
e
o
f
a
p
er
s
o
n
f
o
r
tr
ain
in
g
o
f
t
h
e
s
y
s
t
e
m
a
n
d
ca
n
b
e
i
m
p
le
m
e
n
ted
p
r
ac
ticall
y
.
Her
e
Gab
o
r
w
av
e
le
t
k
er
n
e
ls
alo
n
g
w
it
h
p
r
in
cip
al
co
m
p
o
n
e
n
t
an
al
y
s
is
u
s
ed
f
o
r
ex
tr
ac
tio
n
o
f
f
ac
ial
f
ea
t
u
r
es
an
d
r
ec
o
g
n
itio
n
.
Gab
o
r
w
a
v
elet
k
er
n
els
h
av
e
r
esp
o
n
s
e
s
i
m
i
lar
to
th
at
o
f
th
e
h
u
m
an
v
is
u
al
co
r
tex
(
f
ir
s
t
f
e
w
la
y
er
s
o
f
b
r
ain
ce
lls
)
.
T
h
ese
ca
p
tu
r
es
s
alien
t
v
is
u
al
p
r
o
p
er
ties
s
u
ch
a
s
s
p
ati
al
lo
ca
lizatio
n
,
o
r
ien
tatio
n
s
el
ec
tiv
it
y
,
an
d
s
p
atial
f
r
eq
u
en
c
y
.
T
h
at
is
u
s
in
g
th
e
s
e
k
er
n
el
s
lo
ca
l f
ea
t
u
r
es o
f
f
ac
e
i
m
ag
e
ar
e
o
b
tain
ed
.
Sin
ce
Gab
o
r
w
a
v
e
let
s
an
d
P
C
A
ar
e
u
s
e
d
to
g
et
h
er
,
th
e
r
ec
o
g
n
itio
n
ac
c
u
r
ac
y
ca
n
b
e
g
r
ea
tl
y
i
m
p
r
o
v
ed
.
Du
r
i
n
g
th
e
tr
ai
n
i
n
g
p
h
ase
it
is
e
n
o
u
g
h
to
u
s
e
a
s
in
g
le
f
ac
e
i
m
a
g
e
f
o
r
t
h
e
tr
ain
i
n
g
o
f
t
h
e
s
y
s
te
m
.
Hen
ce
th
e
r
ec
o
g
n
itio
n
s
y
s
te
m
i
s
r
o
b
u
s
t
an
d
is
ea
s
y
to
i
m
p
le
m
en
t
p
ar
tiall
y
.
Face
r
e
co
g
n
itio
n
in
v
o
lv
e
s
co
m
p
u
ter
r
ec
o
g
n
itio
n
o
f
p
er
s
o
n
al
id
en
tit
y
b
ased
o
n
g
eo
m
etr
i
c
o
r
s
tatis
tical
f
ea
t
u
r
es
d
er
iv
ed
f
r
o
m
f
ac
e
i
m
a
g
es
.
E
v
en
t
h
o
u
g
h
h
u
m
an
s
ca
n
d
et
ec
t
an
d
id
en
ti
f
y
f
ac
e
s
in
a
s
ce
n
e
w
it
h
litt
le
o
r
n
o
e
f
f
o
r
t,
b
u
i
ld
in
g
a
n
au
to
m
ated
s
y
s
te
m
th
at
ac
co
m
p
lis
h
es
s
u
ch
o
b
j
ec
tiv
es
is
,
h
o
w
ev
er
v
e
r
y
c
h
alle
n
g
i
n
g
.
T
h
e
ch
al
len
g
es
ar
e
ev
e
n
m
o
r
e
p
r
o
f
o
u
n
d
w
h
en
o
n
e
co
n
s
id
er
s
th
e
lar
g
e
v
ar
iatio
n
s
i
n
t
h
e
v
is
u
al
s
ti
m
u
l
u
s
d
u
e
to
ill
u
m
i
n
atio
n
co
n
d
itio
n
s
,
v
ie
w
i
n
g
d
ir
ec
tio
n
s
o
r
p
o
s
es,
f
ac
ial
ex
p
r
ess
io
n
,
ag
i
n
g
,
an
d
d
is
g
u
i
s
es
s
u
ch
as
f
ac
ial
h
air
,
g
l
ass
es
o
r
co
s
m
etics.
T
h
e
en
o
r
m
it
y
o
f
t
h
e
p
r
o
b
lem
h
as
i
n
v
o
lv
ed
h
u
n
d
r
ed
s
o
f
s
cie
n
tis
ts
i
n
i
n
ter
d
is
cip
lin
ar
y
r
ese
ar
ch
b
u
t
t
h
e
u
l
ti
m
ate
s
o
lu
tio
n
r
e
m
ai
n
s
el
u
s
i
v
e
.
2.
B
ACK
G
RO
UND
R
ec
en
t
l
y
,
t
h
e
ap
p
licatio
n
o
f
th
e
Kar
h
u
n
e
n
-
L
o
e
v
e
(
KL
)
ex
ten
s
io
n
f
o
r
th
e
p
r
ese
n
t
atio
n
an
d
r
ec
o
g
n
itio
n
o
f
f
ac
e
s
h
a
s
g
e
n
er
ated
r
en
e
w
ed
i
n
ter
est.
T
h
e
KL
ex
te
n
s
io
n
h
as
b
ee
n
d
esig
n
ed
f
o
r
i
m
a
g
e
co
m
p
r
es
s
io
n
f
o
r
m
o
r
e
o
r
less
3
0
y
ea
r
s
its
u
s
e
in
p
atter
n
r
ec
o
g
n
itio
n
.
T
h
eir
ap
p
licatio
n
s
h
a
v
e
also
b
ee
n
r
ec
o
r
d
e
d
f
o
r
q
u
ite
s
o
m
e
ti
m
e
.
C
o
m
p
u
tatio
n
al
co
m
p
le
x
it
y
w
a
s
o
n
e
o
f
th
e
r
ea
s
o
n
s
w
h
y
KL
m
eth
o
d
s
,
ev
e
n
th
o
u
g
h
o
p
ti
m
al,
d
id
n
o
t
f
in
d
f
av
o
r
w
ith
i
m
a
g
e
co
m
p
r
ess
io
n
r
esear
ch
er
s
.
Siro
v
ic
h
an
d
Kir
b
y
r
ev
i
s
it
th
e
p
r
o
b
lem
o
f
K
L
d
ep
ictio
n
o
f
i
m
ag
e
s
(
cr
o
p
p
ed
f
ac
es).
On
ce
th
e
eig
e
n
v
ec
to
r
s
(
r
ef
er
r
ed
to
as
“
E
i
g
e
n
p
ic
tu
r
es”)
ar
e
ac
q
u
ir
ed
,
an
y
i
m
a
g
e
i
n
t
h
e
en
s
e
m
b
le
ca
n
b
e
ap
p
r
o
x
i
m
ate
l
y
r
eb
u
ilt
u
s
i
n
g
a
w
ei
g
h
ted
co
m
b
in
at
io
n
o
f
E
i
g
e
n
p
ictu
r
es.
B
y
u
s
in
g
an
i
n
cr
ea
s
in
g
n
u
m
b
er
o
f
E
i
g
en
p
ict
u
r
es,
o
n
e
g
ets
a
b
etter
ap
p
r
o
x
im
atio
n
to
t
h
e
g
i
v
e
n
i
m
a
g
e
T
h
e
s
in
g
u
lar
v
al
u
e
d
ec
o
m
p
o
s
i
tio
n
(
SVD)
o
f
a
m
atr
ix
is
u
tili
ze
d
to
r
ep
r
o
d
u
ce
th
e
f
ea
tu
r
e
s
f
r
o
m
th
e
p
atter
n
.
SVD
ca
n
b
e
o
b
s
er
v
ed
as
a
d
eter
m
in
i
s
tic
co
u
n
ter
p
ar
t
o
f
th
e
K
L
tr
a
n
s
f
o
r
m
.
T
h
e
s
in
g
u
lar
v
al
u
es
(
SV
’
s
)
o
f
an
i
m
a
g
e
ar
e
v
er
y
s
ec
u
r
e
an
d
co
n
s
titu
te
th
e
al
g
eb
r
aic
attr
ib
u
tes
o
f
th
e
i
m
a
g
e,
b
ein
g
i
n
tr
in
s
ic
b
u
t
n
o
t
n
ec
es
s
ar
il
y
v
is
ib
le.
I
t
ca
n
b
e
P
r
o
v
en
th
eir
s
tab
ili
t
y
a
n
d
in
v
a
r
ian
ce
to
p
r
o
p
o
r
ti
o
n
al
v
ar
ia
n
ce
o
f
i
m
a
g
e
i
n
te
n
s
it
y
in
th
e
o
p
ti
m
al
d
is
cr
i
m
i
n
ate
v
ec
to
r
s
p
ac
e,
to
t
r
an
s
p
o
s
itio
n
,
r
o
tatio
n
,
tr
an
s
latio
n
,
an
d
r
ef
lectio
n
w
h
ic
h
ar
e
i
m
p
o
r
tan
t
p
r
o
p
er
ties
o
f
th
e
S
V
f
ea
t
u
r
e
v
ec
to
r
.
L
i
n
ea
r
s
u
b
s
p
ac
e
an
al
y
s
is
,
w
h
ic
h
co
n
s
id
er
s
a
f
ea
tu
r
e
s
p
ac
e
as
a
lin
ea
r
co
m
b
i
n
atio
n
o
f
a
s
et
o
f
b
ases
,
h
as b
ee
n
w
id
el
y
u
s
ed
i
n
f
ac
e
r
ec
o
g
n
i
tio
n
ap
p
licatio
n
s
.
T
h
is
is
m
ai
n
l
y
d
u
e
to
its
ef
f
ec
t
iv
e
n
es
s
an
d
co
m
p
u
tatio
n
a
l
ef
f
ic
ie
n
c
y
f
o
r
f
ea
t
u
r
e
ex
tr
ac
tio
n
a
n
d
r
ep
r
esen
tatio
n
.
Di
f
f
er
e
n
t
cr
iter
i
a
w
il
l
p
r
o
d
u
ce
d
if
f
er
en
t
b
a
s
es
a
n
d
,
co
n
s
eq
u
e
n
tl
y
,
t
h
e
tr
a
n
s
f
o
r
m
ed
s
u
b
s
p
ac
e
w
ill
a
ls
o
h
av
e
d
if
f
er
e
n
t
p
r
o
p
er
ties
.
P
r
in
cip
al
co
m
p
o
n
en
t
an
a
l
y
s
is
(
P
C
A
)
i
s
t
h
e
m
o
s
t
p
o
p
u
lar
tec
h
n
iq
u
e;
i
t
g
en
er
ate
s
a
s
et
o
f
o
r
th
o
g
o
n
al
b
ases
t
h
at
ca
p
tu
r
e
th
e
d
ir
ec
tio
n
s
o
f
m
ax
i
m
u
m
v
ar
ian
ce
i
n
th
e
tr
ai
n
i
n
g
d
ata,
an
d
th
e
P
C
A
co
ef
f
icie
n
ts
in
th
e
s
u
b
s
p
ac
e
ar
e
u
n
co
r
r
elate
d
.
P
C
A
ca
n
p
r
eser
v
e
th
e
g
lo
b
al
s
tr
u
ct
u
r
e
o
f
th
e
i
m
a
g
e
s
p
ac
e,
an
d
is
o
p
ti
m
al
i
n
ter
m
s
o
f
r
ep
r
esen
tatio
n
an
d
r
ec
o
n
s
tr
u
ct
io
n
.
B
ec
au
s
e
o
n
l
y
th
e
s
ec
o
n
d
-
o
r
d
er
d
e
p
en
d
en
cies
in
th
e
P
C
A
co
ef
f
icien
t
s
ar
e
eli
m
i
n
ated
,
P
C
A
ca
n
n
o
t
ca
p
tu
r
e
ev
en
t
h
e
s
i
m
p
le
s
t
i
n
v
ar
ia
n
c
e
u
n
less
th
i
s
i
n
f
o
r
m
atio
n
i
s
e
x
p
licitl
y
p
r
o
v
id
ed
in
th
e
tr
ain
i
n
g
d
ata.
I
n
d
ep
en
d
en
t
co
m
p
o
n
e
n
t
an
al
y
s
i
s
(
I
C
A
)
ca
n
b
e
co
n
s
id
er
ed
a
g
en
er
aliza
ti
o
n
o
f
P
C
A
,
w
h
ic
h
ai
m
s
to
f
in
d
s
o
m
e
in
d
ep
en
d
e
n
t
b
ases
b
y
m
et
h
o
d
s
s
en
s
iti
v
e
to
h
ig
h
-
o
r
d
er
s
tatis
t
ics.
Ho
w
e
v
er
,
r
ep
o
r
ted
th
at
I
C
A
g
i
v
es
th
e
s
a
m
e,
s
o
m
e
ti
m
es
ev
e
n
a
litt
le
w
o
r
s
e,
r
ec
o
g
n
itio
n
ac
cu
r
ac
y
as
P
C
A
.
L
i
n
ea
r
d
is
cr
i
m
i
n
ate
an
al
y
s
is
(
L
D
A
)
s
ee
k
s
to
f
in
d
a
lin
ea
r
tr
an
s
f
o
r
m
atio
n
t
h
at
m
ax
i
m
izes
t
h
e
b
et
w
ee
n
-
clas
s
s
ca
tter
an
d
m
i
n
i
m
ize
s
th
e
w
it
h
i
n
-
c
lass
s
ca
tter
,
w
h
ic
h
p
r
eser
v
e
th
e
d
is
cr
i
m
in
a
tin
g
i
n
f
o
r
m
atio
n
an
d
is
s
u
itab
le
f
o
r
r
ec
o
g
n
itio
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4
864
I
J
R
E
S
V
o
l.
7
,
No
.
2
,
J
u
l
y
201
8
:
1
24
–
130
126
Ho
w
e
v
er
,
th
i
s
m
e
th
o
d
n
ee
d
s
m
o
r
e
t
h
a
n
o
n
e
i
m
a
g
e
p
er
p
er
s
o
n
as
a
tr
ain
i
n
g
s
et;
f
u
r
th
er
m
o
r
e
P
C
A
ca
n
o
u
tp
er
f
o
r
m
L
D
A
w
h
en
t
h
e
tr
ain
i
n
g
s
et
is
s
m
all,
an
d
th
e
f
o
r
m
er
is
less
s
e
n
s
i
tiv
e
to
d
if
f
er
en
t
tr
ain
in
g
s
et
s
L
o
ca
lit
y
p
r
eser
v
in
g
p
r
o
j
ec
tio
n
s
(
L
P
P
)
o
b
tain
s
a
f
ac
e
s
u
b
s
p
ac
e
th
at
b
est
d
etec
ts
th
e
ess
en
tial
f
ac
e
m
an
i
f
o
ld
s
tr
u
ct
u
r
e,
an
d
p
r
eser
v
es
th
e
lo
ca
l
in
f
o
r
m
atio
n
ab
o
u
t
th
e
i
m
ag
e
s
p
ac
e.
W
h
e
n
th
e
p
r
o
p
er
d
im
e
n
s
io
n
o
f
th
e
s
u
b
s
p
ac
e
is
s
elec
ted
,
th
e
r
ec
o
g
n
itio
n
r
ates
u
s
i
n
g
L
P
P
ar
e
b
etter
th
an
th
o
s
e
u
s
i
n
g
P
C
A
o
r
L
DA
,
b
ased
o
n
d
if
f
er
e
n
t
d
atab
ases
.
Ho
w
e
v
er
,
th
is
c
o
n
cl
u
s
io
n
i
s
ac
h
ie
v
ed
o
n
l
y
i
f
m
u
ltip
le
tr
ain
in
g
s
a
m
p
l
es
f
o
r
ea
ch
p
er
s
o
n
ar
e
av
ailab
le;
o
th
er
w
is
e,
L
P
P
w
ill
g
iv
e
a
s
i
m
ilar
p
er
f
o
r
m
an
ce
le
v
el
as
P
C
A
.
Ker
n
a
lized
P
C
A
m
eth
o
d
p
er
f
o
r
m
s
b
etter
g
en
er
aliza
tio
n
w
h
e
n
th
e
tr
ai
n
i
n
g
s
et
is
n
o
n
-
l
in
ea
r
l
y
s
ep
ar
ab
le
an
d
b
y
p
er
f
o
r
m
in
g
a
n
o
n
-
li
n
ea
r
m
ap
p
in
g
,
th
e
a
lg
o
r
it
h
m
is
f
o
u
n
d
to
b
e
s
u
itab
le
f
o
r
cu
r
r
en
t
a
p
p
r
o
ac
h
as
th
e
tec
h
n
iq
u
e
w
o
r
k
s
w
el
l
w
it
h
s
i
n
g
l
e
f
ac
e
i
m
ag
e
p
er
p
er
s
o
n
.
B
y
u
s
in
g
t
h
e
C
o
v
er
’
s
th
eo
r
e
m
,
n
o
n
lin
ea
r
l
y
s
ep
ar
ab
le
p
atter
n
s
in
an
in
p
u
t
s
p
ac
e
w
il
l
g
et
in
to
li
n
ea
r
l
y
s
ep
ar
ab
le
w
ith
an
e
x
ce
s
s
iv
e
p
r
o
b
ab
ilit
y
if
th
e
i
n
p
u
t
s
p
ac
e
is
m
o
d
i
f
ie
d
n
o
n
lin
ea
r
l
y
to
a
h
ig
h
-
d
i
m
en
s
io
n
al
f
ea
t
u
r
e
s
p
ac
e.
T
h
is
p
lo
ttin
g
is
u
s
u
al
l
y
ac
h
ie
v
ed
th
r
o
u
g
h
a
k
er
n
el
f
u
n
ctio
n
a
n
d
,
co
r
r
esp
o
n
d
in
g
to
t
h
e
m
eth
o
d
s
u
s
ed
f
o
r
r
ec
o
g
n
it
io
n
i
n
t
h
e
h
ig
h
-
d
i
m
e
n
s
i
o
n
a
l
f
ea
tu
r
e
s
p
ac
e,
w
e
h
a
v
e
a
s
et
o
f
k
er
n
el
-
b
ased
m
et
h
o
d
s
,
s
u
c
h
as
th
e
k
er
n
el
P
C
A
(
KP
C
A
)
,
o
r
th
e
k
er
n
el
Fi
s
h
er
d
is
cr
i
m
i
n
ate
an
a
l
y
s
is
(
KFD
A
)
.
T
h
e
t
w
o
m
e
th
o
d
s
s
u
c
h
as KP
C
A
a
n
d
KFD
A
ar
e
li
n
ea
r
in
ca
s
e
o
f
h
ig
h
-
d
i
m
e
n
s
io
n
a
l f
ea
t
u
r
e
s
p
ac
e,
b
u
t
n
o
n
li
n
ea
r
in
ca
s
e
o
f
lo
w
-
d
i
m
e
n
s
io
n
al
i
m
a
g
e
s
p
ac
.
I
n
o
th
er
w
o
r
d
s
,
th
ese
tec
h
n
iq
u
es
ca
n
d
etec
t
th
e
n
o
n
li
n
ea
r
s
tr
u
ct
u
r
e
o
f
th
e
f
ac
e
i
m
ag
e
s
,
an
d
en
co
d
e
h
ig
h
er
o
r
d
er
s
tatis
tics
.
W
h
ile
k
er
n
el
-
b
ased
m
eth
o
d
s
ca
n
co
n
tr
o
l
m
an
y
o
f
th
e
li
m
itatio
n
s
o
f
li
n
e
ar
tr
an
s
f
o
r
m
atio
n
,
p
o
in
ted
o
u
t
th
at
n
o
n
e
o
f
th
e
s
e
m
eth
o
d
s
cl
ea
r
l
y
co
n
s
id
er
s
th
e
s
tr
u
ct
u
r
e
o
f
th
e
m
a
n
i
f
o
ld
o
n
w
h
ic
h
t
h
e
f
ac
e
i
m
a
g
es
p
o
s
s
ib
l
y
r
esid
e.
Ho
w
e
v
er
,
th
e
k
er
n
e
l
f
u
n
c
tio
n
s
u
s
ed
ar
e
d
ep
r
iv
ed
o
f
d
ir
ec
t
p
h
y
s
ical
m
ea
n
in
g
,
i.e
.
,
h
o
w
an
d
w
h
y
a
k
er
n
el
f
u
n
ctio
n
is
s
u
itab
le
f
o
r
a
p
atter
n
o
f
a
h
u
m
an
f
ac
e,
an
d
h
o
w
to
o
b
tain
a
n
o
n
lin
ea
r
s
tr
u
ctu
r
e
u
s
e
f
u
l
f
o
r
d
is
cr
i
m
i
n
atio
n
m
ea
n
s
t
h
at,
b
esid
es
th
e
co
n
v
e
n
tio
n
al
k
er
n
el
f
u
n
ctio
n
,
a
n
e
w
m
ap
p
i
n
g
f
u
n
ctio
n
is
a
ls
o
d
ef
i
n
ed
a
n
d
u
s
ed
to
h
ig
h
li
g
h
t
t
h
o
s
e
f
ea
t
u
r
es
h
av
in
g
h
i
g
h
er
s
tatis
t
ical
p
r
o
b
ab
ilit
ies
a
n
d
s
p
atial
i
m
p
o
r
tan
ce
f
o
r
f
ac
e
i
m
ag
e
s
.
Mo
r
e
p
r
ec
is
e,
t
h
is
n
e
w
m
ap
p
in
g
f
u
n
ctio
n
m
ar
k
s
n
o
t
o
n
l
y
t
h
e
s
tati
s
tical
d
is
tr
ib
u
tio
n
o
f
th
e
Gab
o
r
f
ea
t
u
r
es,
b
u
t
also
th
e
s
p
atial
in
f
o
r
m
atio
n
ab
o
u
t
h
u
m
a
n
f
ac
es
[
8
]
-
[
1
1
]
.
Fu
r
t
h
er
n
o
n
li
n
ea
r
m
ap
p
in
g
,
th
e
tr
an
s
f
o
r
m
ed
f
ea
t
u
r
es
h
a
v
e
a
h
i
g
h
er
d
is
cr
i
m
in
ati
n
g
p
o
w
er
,
a
n
d
th
e
i
m
p
o
r
ta
n
ce
o
f
th
e
f
ea
t
u
r
es
tr
an
s
f
o
r
m
s
to
t
h
e
s
p
atial
i
m
p
o
r
tan
ce
o
f
t
h
e
f
ac
e
i
m
a
g
es
.
3.
SYST
E
M
DE
SI
G
N
Her
e
is
th
e
f
o
r
m
u
la
o
f
a
co
m
p
l
ex
Gab
o
r
f
u
n
ctio
n
i
n
s
p
ac
e
d
o
m
ai
n
g (
x,y
)
=
s(
x,y
)
ω
r
(
x,y
)
w
h
er
e
s
(
x
,
y
)
is
a
c
o
m
p
le
x
s
i
n
u
s
o
id
,
k
n
o
w
n
as
th
e
ca
rr
ier,
an
d
ω
r
(
x,
y
)
is
a
2
-
D
Gau
s
s
i
an
-
s
h
ap
ed
f
u
n
ct
io
n
,
k
n
o
w
n
as t
h
e
env
elo
pe.
T
h
e
co
m
p
lex
s
in
u
s
o
id
is
d
ef
i
n
ed
as f
o
llo
w
s
s
(
x,
y
)=
ex
p
(
(
j
(
2
∏
(
u
0
x
+
v
0
y
)+
P
)
)
W
h
er
e
(
u
0
,
v
0
)
an
d
P
d
ef
in
e
th
e
s
p
atial
f
r
eq
u
en
c
y
a
n
d
th
e
p
h
ase
o
f
th
e
s
in
u
s
o
id
r
esp
ec
tiv
el
y
.
W
e
ca
n
th
in
k
o
f
th
is
s
in
u
s
o
id
as
t
w
o
s
ep
ar
ate
r
ea
l
f
u
n
ct
io
n
s
,
co
n
v
e
n
ien
tl
y
allo
ca
ted
in
th
e
r
ea
l
an
d
I
m
ag
in
ar
y
p
ar
t
o
f
a
co
m
p
le
x
f
u
n
ctio
n
s
Fi
g
u
r
e
1
.
Fig
u
r
e
1
.
T
h
e
r
ea
l a
n
d
im
a
g
i
n
ar
y
p
ar
ts
o
f
a
co
m
p
lex
s
in
u
s
o
i
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
R
E
S
I
SS
N:
2089
-
4864
A
N
o
ve
l F
a
ce
R
e
co
g
n
itio
n
A
lg
o
r
ith
m
Usi
n
g
Ga
b
o
r
-
b
a
s
ed
K
P
C
A
(
Uma
s
a
n
ka
r
C
h
)
127
T
h
e
im
a
g
es a
r
e
1
2
8
×
1
2
8
p
ix
els.
T
h
e
p
ar
am
eter
s
ar
e:
u
0
=
v
0
=
1
/8
0
cy
cles
/p
ix
el,
P
=
0
d
eg
.
T
h
e
r
ea
l p
ar
t a
n
d
th
e
im
a
g
i
n
ar
y
p
ar
t o
f
th
i
s
s
i
n
u
s
o
id
ar
e
R
e(
s
(
x,
y
))=
co
s
(
2
∏
(
u
0
x
+
v
0
y
)+
P
)
I
m
(
s
(
x,
y
))=
s
in
(
2
∏
(
u
0
x
+
v
0
y
)+
P
)
T
h
e
p
ar
am
eter
s
u
0
a
n
d
v
0
d
e
f
i
n
e
t
h
e
s
p
atial
f
r
eq
u
e
n
c
y
o
f
th
e
s
in
u
s
o
id
in
C
ar
tesi
a
n
C
o
o
r
d
in
ates.
T
h
i
s
s
p
atia
l
f
r
eq
u
en
c
y
ca
n
also
b
e
ex
p
r
ess
ed
in
p
o
lar
co
o
r
d
in
ates a
s
m
a
g
n
it
u
d
e
F
0
an
d
d
ir
ec
tio
n
ω
0
:
F
0
=
√u
0
2
+
v
0
2
ω
0
=
tan
─1
(v
0
/u
0
)
i.e
u
0
=
F
0
co
s
ω
0
v
0
=
F
0
s
in
ω
0
Usi
n
g
t
h
is
r
ep
r
esen
tatio
n
,
t
h
e
co
m
p
le
x
s
i
n
u
s
o
id
is
s
=
ex
p
(
j
(
2
∏
F
0
(x
0
co
s
ω
0
+
y
s
in
ω
0
)
+
P)
)
3
.
1
.
T
he
Co
m
ple
x
G
a
bo
r
F
un
ct
io
n
T
h
e
co
m
p
lex
Gab
o
r
f
u
n
c
tio
n
i
s
d
ef
i
n
ed
b
y
t
h
e
f
o
llo
w
in
g
p
ar
a
m
eter
s
;
a.
K
:
th
i
s
p
ar
a
m
eter
Scales t
h
e
m
ag
n
i
tu
d
e
o
f
t
h
e
Ga
u
s
s
ian
e
n
v
e
lo
p
e.
b.
(
a,
b
)
:
it is
r
esp
o
n
s
ib
le
f
o
r
Scalin
g
th
e
t
w
o
a
x
is
o
f
t
h
e
Ga
u
s
s
i
an
en
v
elo
p
e.
c.
θ
:
w
h
ic
h
w
ill R
o
tate
a
n
g
le
o
f
t
h
e
Gau
s
s
ia
n
e
n
v
elo
p
e.
d.
(
x
0
,
y
0
):
d
ete
r
m
i
n
es t
h
e
L
o
ca
ti
o
n
o
f
th
e
p
ea
k
o
f
th
e
Ga
u
s
s
ia
n
en
v
elo
p
e.
e.
(
u
0
,
v
0
)
:
th
is
p
ar
a
m
eter
g
i
v
es
t
h
e
s
p
atial
f
r
eq
u
e
n
cies
o
f
t
h
e
s
i
n
u
s
o
id
ca
r
r
ier
in
C
ar
tesi
an
co
o
r
d
in
ates.
I
t
ca
n
also
b
e
ex
p
r
ess
ed
in
p
o
lar
co
o
r
d
in
ates a
s
(
F
0
, ω
0
).
f.
P
: r
ef
er
s
to
th
e
P
h
ase
o
f
t
h
e
s
i
n
u
s
o
id
ca
r
r
ier
.
As
m
e
n
tio
n
ed
ab
o
v
e
ea
ch
co
m
p
lex
Gab
o
r
co
n
s
i
s
ts
o
f
t
w
o
f
u
n
ctio
n
s
i
n
q
u
ad
r
atu
r
e
(
o
u
t
o
f
p
h
ase
b
y
9
0
d
eg
r
ee
s
)
,
ap
p
r
o
p
r
iately
lo
ca
ted
in
th
e
r
ea
l
an
d
im
a
g
i
n
ar
y
p
ar
ts
o
f
a
co
m
p
le
x
f
u
n
c
tio
n
.
Ker
n
el
P
C
A
,
th
r
o
u
g
h
t
h
e
u
s
e
o
f
k
er
n
e
ls
,
p
r
in
cip
le
co
m
p
o
n
e
n
ts
ca
n
b
e
co
m
p
u
ted
ef
f
icie
n
tl
y
i
n
h
ig
h
-
d
i
m
e
n
s
io
n
al
f
ea
tu
r
e
s
p
ac
es
th
at
ar
e
r
elate
d
to
t
h
e
in
p
u
t
s
p
ac
e
b
y
s
o
m
e
n
o
n
li
n
ea
r
m
ap
p
in
g
.
Ker
n
el
P
C
A
f
in
d
s
p
r
in
cip
al
co
m
p
o
n
e
n
t
s
w
h
ic
h
ar
e
n
o
n
l
in
ea
r
l
y
r
elate
d
to
th
e
in
p
u
t
s
p
ac
e
b
y
p
er
f
o
r
m
i
n
g
P
C
A
i
n
th
e
s
p
ac
e
p
r
o
d
u
ce
d
b
y
th
e
n
o
n
li
n
ea
r
m
ap
p
in
g
,
w
h
er
e
th
e
lo
w
-
d
i
m
e
n
s
io
n
al
late
n
t str
u
ctu
r
e
i
s
,
h
o
p
ef
u
ll
y
,
ea
s
ier
to
d
is
co
v
er
.
I
n
an
ex
p
er
i
m
en
tal
f
ac
e
r
ec
o
g
n
itio
n
ap
p
licatio
n
,
t
h
r
ee
cla
s
s
es
o
f
k
er
n
el
f
u
n
ctio
n
s
h
a
v
e
b
ee
n
w
id
el
y
u
s
ed
,
w
h
ic
h
ar
e
th
e
p
o
l
y
n
o
m
ia
l k
er
n
el
s
,
Gau
s
s
ia
n
k
er
n
els,
a
n
d
s
ig
m
o
id
k
er
n
el
s
,
[
1
2
]
,
r
esp
e
ctiv
el
y
.
P
o
ly
n
o
m
ial
Ker
n
el
:
(
)
(
)
d
j
i
j
i
Y
Y
Y
Y
k
,
,
=
Gau
s
s
ia
n
Ker
n
el:
(
)
−
−
=
2
2
2
||
||
e
x
p
,
j
i
j
i
Y
Y
Y
Y
k
Sig
m
o
id
Ker
n
el
:
(
)
(
)
(
)
+
=
j
i
j
i
Y
Y
k
Y
Y
k
.
t
a
n
h
,
W
h
er
e
d
>
0
,
k
>
0
,
an
d
v
<
0
th
e
p
o
l
y
n
o
m
ial
k
er
n
el
s
a
r
e
ex
ten
d
ed
to
in
cl
u
d
e
f
r
ac
tio
n
al.
P
o
w
er
p
o
ly
n
o
m
ia
l (
FP
P
)
m
o
d
els,
i.e
.
0
<
d
<1
w
h
er
e
a
m
o
r
e
r
eliab
le
p
er
f
o
r
m
a
n
ce
ca
n
b
e
ac
h
iev
ed
.
P
ick
an
ap
p
r
o
p
r
iate
k
er
n
el
f
u
n
ctio
n
K
(
th
e
f
o
r
m
o
f
t
h
e
k
er
n
el,
p
lu
s
an
y
p
ar
a
m
eter
s
)
.
1)
o
n
s
tr
u
ct
t
h
e
Ker
n
el
Ma
tr
ix
f
o
r
th
e
m
ap
p
ed
d
ata:
(
)
(
)
(
)
j
i
j
i
ij
x
x
K
x
x
K
,
.
=
2)
Use th
i
s
to
co
n
s
tr
u
ct
th
e
C
o
v
a
r
ian
c
e
Ma
tr
ix
f
o
r
th
e
ce
n
ter
ed
d
ata:
(
)
(
)
=
=
=
+
−
−
=
N
q
p
pq
N
q
qj
N
p
ip
ij
j
i
ij
K
N
K
N
K
N
K
x
x
K
1
,
2
1
1
1
1
1
.
~
~
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4
864
I
J
R
E
S
V
o
l.
7
,
No
.
2
,
J
u
l
y
201
8
:
1
24
–
130
128
3)
So
lv
e
f
o
r
t
h
e
s
et
o
f
ei
g
en
v
ec
to
r
s
M
to
N
to
i
b
i
1
,
1
:
=
=
o
f
th
e
m
a
tr
ix
ij
K
~
w
h
ich
g
i
v
e
u
s
o
u
r
s
et
o
f
b
asis
v
ec
to
r
s
b
in
f
ea
tu
r
e
s
p
ac
e
th
u
s
:
M
to
N
to
i
b
i
1
,
1
:
=
=
4)
T
h
e
u
n
n
o
r
m
alis
ed
KP
C
A
co
m
p
o
n
en
ts
o
f
a
test
p
o
in
t
x
ar
e
th
en
g
i
v
e
n
b
y
:
(
)
(
)
(
)
i
N
i
i
x
x
K
b
x
b
x
p
,
.
1
=
4.
RE
SU
L
T
S AN
D
CO
NC
L
U
S
I
O
N
R
ain
in
g
is
p
er
f
o
r
m
ed
f
o
r
f
ac
e
i
m
a
g
es
o
f
1
2
p
er
s
o
n
s
.
Her
e
o
n
e
f
ac
e
i
m
a
g
e
is
ta
k
e
n
f
o
r
e
a
ch
p
er
s
o
n
.
So
tr
ain
i
n
g
s
et
s
ize=
1
2
.
Fo
ll
o
w
i
n
g
i
s
t
h
e
tr
ain
in
g
s
et
.
T
es
tin
g
is
p
er
f
o
r
m
ed
w
ith
9
6
i
m
ag
es.
Her
e
ea
ch
o
f
ab
o
v
e
p
er
s
o
n
’
s
f
ac
e
i
m
ag
e
s
ar
e
g
iv
e
n
as
in
p
u
t
w
it
h
d
if
f
er
en
t
o
r
ien
tatio
n
s
.
Fo
r
ea
ch
p
er
s
o
n
,
9
f
ac
e
im
ag
e
s
ar
e
g
iv
e
n
as i
n
p
u
t
. T
r
ain
in
g
s
e
t
as
s
h
o
w
n
in
F
ig
u
r
e
2
.
Ov
er
all
ac
c
u
r
ac
y
o
f
s
y
s
te
m
is
ar
o
u
n
d
8
9
.
5
8
%
(
test
ed
o
v
er
9
6
I
m
a
g
e
s
)
.
Fi
n
all
y
to
tes
t
t
h
e
s
u
p
er
io
r
it
y
o
f
th
e
alg
o
r
ith
m
,
i
m
a
g
es
co
n
t
ain
i
n
g
an
i
m
a
ls
o
r
an
y
o
th
er
ar
e
g
iv
e
n
as
in
p
u
t.
I
t
is
f
o
u
n
d
th
at
alg
o
r
ith
m
i
s
ab
le
to
d
is
ca
r
d
th
o
s
e
i
m
ag
e
s
.
Fo
l
lo
w
i
n
g
i
m
a
g
es
ar
e
g
i
v
e
n
as
in
p
u
t
(
i
m
ag
e
s
co
n
tai
n
i
n
g
n
o
n
-
h
u
m
a
n
b
ein
g
s
)
.
Dete
ctio
n
o
f
e
i
g
e
n
f
ac
e
(
P
ass
C
ase)
as
s
h
o
w
n
in
Fi
g
u
r
e
3
.
T
ested
o
u
tp
u
t
m
i
s
m
a
tch
ca
s
e
as
s
h
o
w
n
in
Fig
u
r
e
4
.
A
l
s
o
alg
o
r
it
h
m
is
e
x
p
ec
ted
to
w
o
r
k
f
o
r
an
y
o
th
er
s
e
t
o
f
i
m
a
g
e
s
b
y
t
w
ea
k
i
n
g
th
e
m
o
d
el
p
ar
a
m
eter
s
.
T
h
e
ac
cu
r
ac
y
i
n
d
is
ca
r
d
in
g
i
m
ag
es o
f
n
o
n
h
u
m
a
n
b
ein
g
s
=1
0
0
% (
test
ed
w
ith
ab
o
v
e
a
s
et
o
f
i
m
ag
e
s
)
.
Fig
u
r
e
2
.
T
r
ain
in
g
s
et
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
R
E
S
I
SS
N:
2089
-
4864
A
N
o
ve
l F
a
ce
R
e
co
g
n
itio
n
A
lg
o
r
ith
m
Usi
n
g
Ga
b
o
r
-
b
a
s
ed
K
P
C
A
(
Uma
s
a
n
ka
r
C
h
)
129
Fig
u
r
e
3
.
Dete
ctio
n
o
f
e
i
g
en
f
a
ce
(
p
ass
ca
s
e)
Fig
u
r
e
4
.
T
ested
o
u
tp
u
t
m
is
m
a
tch
ca
s
e
5.
CO
NCLU
SI
O
N
T
h
is
w
o
r
k
u
s
ed
a
n
o
v
el
d
o
u
b
ly
n
o
n
li
n
ea
r
m
ap
p
in
g
Gab
o
r
-
b
ased
KP
C
A
f
o
r
h
u
m
a
n
f
ac
e
r
ec
o
g
n
itio
n
.
I
n
th
is
ap
p
r
o
ac
h
,
th
e
Gab
o
r
w
a
v
elet
s
ar
e
em
p
lo
y
ed
to
s
ep
ar
ate
f
ac
ial
f
ea
tu
r
e
s
,
th
e
n
a
d
o
u
b
ly
n
o
n
li
n
ea
r
m
ap
p
in
g
K
P
C
A
is
u
s
ed
to
p
er
f
o
r
m
f
ea
t
u
r
e
tr
an
s
f
o
r
m
a
ti
o
n
an
d
f
ac
e
r
ec
o
g
n
itio
n
.
W
h
en
e
s
ti
m
ati
n
g
w
i
th
th
e
co
n
v
e
n
tio
n
al
KP
C
A
,
an
ad
d
itio
n
al
n
o
n
li
n
ea
r
l
y
m
ap
p
in
g
is
ac
h
iev
ed
in
th
e
o
r
ig
i
n
al
s
p
ac
e.
T
h
is
n
o
n
li
n
ea
r
m
ap
p
in
g
n
o
t
o
n
l
y
m
ar
k
s
th
e
s
tatis
tica
l
p
r
o
p
er
ty
o
f
t
h
e
in
p
u
t
f
ea
t
u
r
es,
b
u
t
al
s
o
af
f
ec
ts
an
E
ig
e
n
m
a
s
k
t
o
e
m
p
h
a
s
ize
t
h
o
s
e
f
ea
tu
r
e
s
d
er
iv
ed
f
r
o
m
th
e
i
m
p
o
r
tan
t
f
ac
ia
l
f
ea
t
u
r
e
p
o
in
ts
.
T
h
er
ef
o
r
e,
a
f
ter
t
h
e
m
ap
p
i
n
g
s
,
th
e
tr
an
s
f
o
r
m
ed
f
ea
t
u
r
es
h
a
v
e
a
h
ig
h
er
d
is
cr
i
m
i
n
a
n
t
p
o
w
er
,
an
d
th
e
im
p
o
r
tan
ce
o
f
th
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I
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[1
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.
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.
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]
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.
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,
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]
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Ta
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T
.
F
.
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,
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0
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.
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.
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2
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Evaluation Warning : The document was created with Spire.PDF for Python.