I
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t
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r
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Jou
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lec
t
r
ical
an
d
Com
p
u
t
e
r
E
n
gin
e
e
r
in
g
(
I
JE
CE
)
Vol.
15
,
No.
1
,
F
e
br
ua
r
y
20
25
,
pp.
311
~
318
I
S
S
N:
2088
-
8708
,
DO
I
:
10
.
11591/i
jec
e
.
v
15
i
1
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pp
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11
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318
311
Jou
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bs
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r
or
P
e
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k
s
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to
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s
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a
ti
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r
incipa
l
c
omponent
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ti
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to
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CC
B
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SA
l
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s
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C
or
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pon
din
g
A
u
th
or
:
F
a
ouz
ia
E
nna
a
ma
L
a
bor
a
tor
y
of
M
a
thema
ti
c
s
,
C
omput
e
r
S
c
ienc
e
,
E
l
e
c
tr
ica
l
E
nginee
r
ing
a
nd
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hys
ics
,
M
or
oc
c
a
n
S
c
hoo
l
of
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nginee
r
ing
S
c
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e
s
(
E
M
S
I
-
M
a
r
r
a
ke
s
h)
M
a
r
r
a
ke
s
h,
M
or
oc
c
o
E
mail:
f
a
ouz
ia.
e
nna
a
ma@
c
e
d.
uc
a
.
ma
1.
I
NT
RODU
C
T
I
ON
P
r
incipa
l
c
omponent
a
na
lys
is
,
c
omm
only
known
a
s
p
r
inc
ip
a
l
c
om
po
ne
nt
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na
lys
is
(
P
C
A)
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is
a
powe
r
f
ul
a
nd
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ll
-
e
s
tablis
he
d
mul
ti
va
r
iate
s
tatis
ti
c
a
l
tec
hnique
e
mpl
oye
d
in
pa
tt
e
r
n
r
e
c
ognit
ion,
c
omput
e
r
vis
ion,
a
nd
s
ignal
pr
oc
e
s
s
ing.
I
nit
ially
int
r
oduc
e
d
by
P
e
a
r
s
on
in
1901
a
nd
late
r
r
e
f
ined
by
Hote
ll
ing
in
1933,
P
C
A,
s
ometim
e
s
r
e
f
e
r
r
e
d
to
a
s
the
dis
c
r
e
te
Ka
r
hune
n
-
L
o
è
ve
tr
a
ns
f
or
mation
[
1]
–
[
3
]
,
is
de
s
igned
t
o
e
xtr
a
c
t
e
s
s
e
nti
a
l
inf
or
mation
f
r
om
mul
ti
va
r
iate
da
ta
by
m
a
pping
the
or
igi
na
l
high
-
dim
e
ns
ional
s
pa
c
e
int
o
a
r
e
duc
e
d
-
dim
e
ns
ional
s
pa
c
e
.
T
his
pr
oc
e
s
s
invol
ve
s
c
r
e
a
ti
ng
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omponents
that
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r
e
li
ne
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r
c
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na
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r
ve
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va
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iable
s
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e
f
f
e
c
ti
ve
ly
c
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ptur
ing
the
majo
r
it
y
o
f
the
da
ta’
s
va
r
iabili
ty.
I
n
1991,
T
ur
k
a
nd
P
e
ntl
a
nd
[
4]
a
ppli
e
d
P
C
A
to
f
a
c
ial
r
e
c
ognit
ion,
p
ionee
r
ing
the
e
igenf
a
c
e
s
method.
T
his
a
ppr
oa
c
h
invol
ve
s
de
r
ivi
ng
f
a
c
ial
f
e
a
tur
e
s
a
nd
r
e
pr
e
s
e
nti
ng
them
a
s
a
li
ne
a
r
c
ombi
n
a
ti
on
of
“
e
igenf
a
c
e
s
,
”
whic
h
a
r
e
e
igenve
c
tor
s
obtaine
d
f
r
om
the
c
ova
r
ianc
e
matr
ix
of
the
high
-
dim
e
ns
ional
f
a
c
ial
im
a
ge
s
pa
c
e
.
T
he
numbe
r
o
f
e
igenf
a
c
e
s
c
or
r
e
s
pon
ds
to
the
qua
nti
ty
of
tr
a
ini
ng
im
a
ge
s
,
a
nd
e
a
c
h
f
a
c
e
is
then
mappe
d
int
o
thi
s
r
e
duc
e
d
-
dim
e
ns
ional
s
pa
c
e
to
de
ter
mi
ne
the
c
ontr
ibu
ti
on
o
f
e
a
c
h
e
igenve
c
tor
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2088
-
8708
I
nt
J
E
lec
&
C
omp
E
ng
,
Vol
.
15
,
No.
1
,
F
e
br
ua
r
y
20
25
:
311
-
318
312
Although
the
e
igenf
a
c
e
s
method
is
e
f
f
e
c
ti
ve
f
or
a
li
mi
ted
number
o
f
low
-
r
e
s
olut
ion
im
a
ge
s
,
but
i
t
be
c
omes
les
s
e
f
f
icie
nt
a
s
the
da
tas
e
t
g
r
ows
.
T
he
p
r
oc
e
s
s
ing
ti
me
incr
e
a
s
e
s
,
lea
ding
to
longer
t
r
a
ini
n
g
pe
r
iods
a
nd
higher
c
omput
a
ti
ona
l
c
os
ts
.
R
e
c
e
nt
a
dva
n
c
e
ments
in
int
e
gr
a
ted
c
ir
c
uit
s
a
nd
mi
c
r
oe
lec
tr
onics
,
s
uc
h
a
s
c
e
ntr
a
l
pr
oc
e
s
s
ing
unit
s
(
C
P
Us
)
,
g
r
a
phics
pr
oc
e
s
s
ing
unit
s
(
GPUs
)
,
a
nd
f
ield
pr
ogr
a
mm
a
ble
ga
te
a
r
r
a
y
(
F
P
GA
s
)
,
ha
ve
f
a
c
il
it
a
ted
pa
r
a
ll
e
li
z
a
ti
on
tec
hnique
s
[
5]
,
[
6]
,
s
igni
f
ica
ntl
y
a
c
c
e
ler
a
ti
ng
c
omput
a
ti
ons
.
T
he
us
e
of
GPUs
,
in
pa
r
ti
c
ula
r
,
ha
s
de
mons
tr
a
ted
s
ubs
tantial
s
pe
e
d
-
ups
in
e
igenf
a
c
e
s
a
nd
P
C
A
a
ppli
c
a
ti
ons
thr
ough
pa
r
a
ll
e
l
pr
oc
e
s
s
ing
[
7]
–
[
9]
.
C
omput
e
uni
f
ied
de
vice
a
r
c
hit
e
c
tur
e
(
C
UD
A
)
im
pleme
ntations
,
f
or
e
xa
mpl
e
,
ha
ve
be
e
n
us
e
d
to
e
nha
nc
e
the
pe
r
f
o
r
manc
e
of
thes
e
methods
[
10
]
–
[
16]
,
e
na
bli
ng
r
a
pid
a
nd
e
f
f
icie
nt
pr
oc
e
s
s
ing.
I
n
thi
s
pa
pe
r
,
we
p
r
opos
e
a
n
e
nha
nc
e
ment
to
t
he
e
xis
ti
ng
ge
ometr
ica
l
a
ppr
oxim
a
ti
on
of
P
C
A,
pr
e
vious
ly
va
li
da
ted
on
s
ynthetic
2D
da
ta
with
Ga
us
s
ian
dis
tr
ibut
ion
a
nd
e
f
f
e
c
ti
ve
f
or
hype
r
s
pe
c
tr
a
l
s
a
telli
te
im
a
ge
vis
ua
li
z
a
ti
on.
W
e
c
ompar
e
thi
s
ge
ometr
ica
ll
y
-
a
ppr
oxim
a
ted
P
C
A
method
with
the
c
las
s
ica
l
e
igenf
a
c
e
s
a
ppr
oa
c
h.
T
o
e
va
luate
the
e
f
f
e
c
ti
ve
ne
s
s
of
both
methods
,
we
e
mpl
oy
s
e
ve
r
a
l
qua
li
ty
met
r
ics
:
E
uc
li
de
a
n
dis
tanc
e
,
pe
a
k
s
ignal
-
to
-
noi
s
e
r
a
ti
o
(
P
S
NR
)
,
mea
n
a
bs
olut
e
e
r
r
or
(
M
AE
)
,
s
ignal
-
to
-
nois
e
r
a
ti
o
(
S
NR
)
,
a
nd
s
tr
uc
tur
a
l
s
im
il
a
r
it
y
index
mea
s
ur
e
(
S
S
I
M
)
.
T
he
r
e
s
ult
s
of
thi
s
c
ompar
a
ti
ve
s
tudy
a
r
e
de
tailed
in
s
e
c
ti
on
4,
with
c
onc
lus
ions
pr
ovided
in
the
f
inal
s
e
c
ti
on.
2.
M
E
T
HO
D
T
he
e
igenf
a
c
e
s
method
[
4]
is
a
wide
ly
r
e
c
ogni
z
e
d
tec
hnique
in
f
a
c
ial
r
e
c
ognit
ion
a
nd
im
a
ge
pr
oc
e
s
s
ing.
I
t
tr
a
ns
f
or
ms
f
a
c
ial
im
a
ge
s
int
o
a
s
e
t
of
c
ha
r
a
c
ter
is
ti
c
f
e
a
tur
e
s
,
known
a
s
e
i
ge
nf
a
c
e
s
,
whic
h
r
e
pr
e
s
e
nt
the
pr
incipa
l
c
omponents
of
the
i
mage
da
tas
e
t.
T
his
tec
hnique
e
mpl
oys
P
C
A
to
identif
y
the
ke
y
f
e
a
tur
e
s
that
a
c
c
ount
f
or
the
va
r
ianc
e
in
f
a
c
ial
im
a
ge
s
,
f
a
c
il
it
a
ti
ng
e
f
f
e
c
ti
ve
r
e
c
ognit
ion
a
nd
c
om
pa
r
is
on.
C
onve
r
s
e
ly,
the
a
ppr
oxim
a
te
a
ppr
oa
c
h
to
e
i
ge
nf
a
c
e
s
s
im
pli
f
ies
a
nd
a
c
c
e
ler
a
tes
thi
s
pr
o
c
e
s
s
by
us
ing
ge
ometr
ic
a
ppr
oxim
a
ti
ons
r
a
ther
than
tr
a
dit
ional
P
C
A
c
omput
a
ti
ons
.
T
his
a
ppr
oa
c
h
f
oc
us
e
s
on
identif
ying
ke
y
e
igenve
c
tor
s
ba
s
e
d
on
ge
ometr
ic
p
r
ope
r
ti
e
s
,
s
uc
h
a
s
the
maximu
m
dis
tanc
e
s
be
twe
e
n
im
a
ge
s
in
the
da
tas
e
t,
potentially
of
f
e
r
ing
f
a
s
ter
c
omput
a
ti
on
ti
mes
while
maintaining
r
e
a
s
ona
ble
a
c
c
ur
a
c
y.
B
oth
methods
a
im
to
a
c
hieve
r
e
li
a
ble
f
a
c
e
r
e
c
ognit
ion
but
dif
f
e
r
in
their
unde
r
lyi
ng
p
r
inciples
a
nd
c
omput
a
ti
ona
l
s
tr
a
tegie
s
.
T
he
f
oll
owing
s
e
c
ti
ons
de
tail
thes
e
methods
,
e
xplor
ing
their
methodologi
e
s
,
a
dva
nt
a
ge
s
,
a
nd
li
mi
tations
.
2.
1.
E
igenf
ac
e
ap
p
r
oac
h
T
he
e
igenf
a
c
e
s
tec
hnique,
int
r
oduc
e
d
by
T
ur
k
a
nd
P
e
ntl
a
nd
[
4]
,
is
a
c
las
s
ic
tec
hnique
f
or
f
a
c
e
r
e
c
ognit
ion.
I
t
r
e
pr
e
s
e
nts
f
a
c
e
s
a
s
li
ne
a
r
c
ombi
na
ti
ons
of
“
e
igenf
a
c
e
s
,”
whic
h
a
r
e
pr
incipa
l
c
o
mponents
ge
ne
r
a
ted
f
r
om
the
c
oll
e
c
ti
on
o
f
t
r
a
ini
ng
f
a
c
e
i
mage
s
.
T
he
ke
y
s
tage
s
of
the
e
igenf
a
c
e
s
a
ppr
oa
c
h
a
r
e
o
utl
ined:
a.
Ga
ther
f
a
c
e
im
a
ge
s
1
,
2
,
…
,
a
s
the
tr
a
ini
ng
da
tas
e
t.
E
ns
ur
e
thes
e
im
a
ge
s
a
r
e
s
tanda
r
dize
d
to
ha
ve
identica
l
dim
e
ns
ions
N
×
N
a
nd
c
ons
is
tent
li
ghti
ng
c
ondit
ions
.
b.
C
onve
r
t
the
tr
a
ini
ng
im
a
ge
s
f
r
om
R
GB
c
olor
s
pa
c
e
to
gr
a
ys
c
a
le.
c.
T
r
a
ns
f
or
m
im
a
ge
s
int
o
ve
c
tor
s
=
1
,
2
,
…
,
:
C
onve
r
t
im
a
ge
to
ve
c
tor
with
dim
e
ns
ions
²
×
1
.
d.
C
a
lcula
te
the
a
ve
r
a
ge
f
a
c
e
im
a
ge
:
Ψ
=
1
∑
=
1
(
1)
he
r
e
,
de
notes
the
ove
r
a
ll
c
ount
of
im
a
ge
s
,
a
nd
c
or
r
e
s
ponds
to
the
ve
c
tor
r
e
pr
e
s
e
ntation
of
e
a
c
h
im
a
ge
.
e.
R
e
move
the
a
ve
r
a
ge
f
a
c
e
f
r
om
e
ve
r
y
f
a
c
e
in
the
tr
a
ini
ng
da
tas
e
t
to
obtain
a
s
e
t
of
dif
f
e
r
e
nt
f
a
c
e
s
.
i
=
i
−
(
2)
I
n
thi
s
c
ontext,
r
a
nge
s
f
r
om
1
to
,
a
nd
is
a
n
²
×
matr
i
x
c
ompos
e
d
of
[
1
,
2
,
…
,
]
.
f.
Obta
in
the
c
ova
r
ianc
e
matr
ix
f
r
om
the
dif
f
e
r
e
nc
e
f
a
c
e
s
.
C=
1
∑
=
=
1
(
3)
whe
r
e
de
notes
the
tr
a
ns
pos
it
ion
o
f
the
matr
ix
c
ons
tr
uc
ted
f
r
om
[
1
,
2
,
…
,
]
g.
De
ter
mi
ne
the
pr
incipa
l
e
leme
nts
(
whic
h
a
r
e
a
ls
o
known
a
s
e
igenve
c
tor
s
)
a
nd
their
c
or
r
e
s
ponding
e
igenva
lues
f
r
om
the
c
ova
r
ianc
e
matr
ix.
T
he
e
ige
nf
a
c
e
s
r
e
pr
e
s
e
nt
the
pr
im
a
r
y
c
omponents
de
r
ived
f
r
om
the
s
e
t
of
f
a
c
e
im
a
ge
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
E
lec
&
C
omp
E
ng
I
S
S
N:
2088
-
8708
E
v
aluat
ing
ge
ome
tr
ically
-
appr
ox
imated
pr
incipal
c
ompone
nt
analys
is
v
s
.
c
las
s
ical
…
(
F
aouz
ia
E
nna
ama
)
313
h.
Obta
in
the
e
igenf
a
c
e
s
.
S
e
lec
t
the
top
e
igenve
c
tor
s
to
f
or
m
the
e
igenf
a
c
e
s
.
=
(
−
)
(
4)
whe
r
e
r
a
nge
s
f
r
om
1
to
’
a
nd
indi
c
a
tes
the
c
ount
of
c
hos
e
n
e
igenve
c
tor
s
.
i.
Ge
ne
r
a
te
the
we
ight
ve
c
tor
s
:
Ω
T
K
=
[
ω
1
,ω
2
,
…,
ω
K
]
(
5
)
j.
Us
e
E
uc
li
de
a
n
dis
tanc
e
to
c
ompar
e
we
ight
ve
c
tor
s
:
ε
2
=‖
Ω
-
Ω
k
‖²
(
6)
he
r
e
,
de
notes
the
ve
c
tor
that
c
ha
r
a
c
ter
ize
s
the
ℎ
f
a
c
e
c
las
s
.
A
f
a
c
e
is
c
ons
ider
e
d
‘
k
now
n
’
if
the
s
malles
t
f
a
ll
s
be
low
a
s
pe
c
if
ied
th
r
e
s
hold
;
other
wis
e
,
the
f
a
c
e
is
c
las
s
if
ied
a
s
‘
unk
now
n
’.
2.
2.
Clas
s
ical
ap
p
r
oac
h
I
n
thi
s
s
e
c
ti
on,
we
r
e
vis
it
the
ge
ometr
ica
l
a
ppr
ox
im
a
ti
on
of
P
C
A
p
r
opos
e
d
by
[
17]
.
T
his
method
e
s
ti
mate
s
e
igenf
a
c
e
s
f
or
a
da
tas
e
t
of
f
a
c
e
im
a
ge
s
ba
s
e
d
on
the
obs
e
r
va
ti
on
that
the
dir
e
c
ti
on
given
by
the
f
ur
thes
t
point
s
in
a
mul
t
ivar
iate
da
tas
e
t
is
of
ten
c
los
e
to
the
f
ir
s
t
pr
incipa
l
c
omponent,
de
pe
nding
on
da
ta
c
or
r
e
lation.
T
his
a
ppr
oa
c
h
is
pa
r
ti
c
ular
ly
e
f
f
e
c
ti
v
e
in
c
a
s
e
s
wh
e
r
e
the
da
tas
e
t
e
xhibi
ts
s
tr
ong
c
or
r
e
lations
a
mong
va
r
iable
s
,
a
ll
owing
the
method
to
c
a
ptur
e
t
he
mos
t
s
igni
f
ica
nt
va
r
ianc
e
.
T
he
method
invol
ve
s
s
e
ve
r
a
l
s
teps
.
F
i
r
s
tl
y,
the
tr
a
i
ning
s
e
t
of
f
a
c
e
im
a
ge
s
is
or
ga
nize
d
a
s
a
gr
a
ys
c
a
le
mul
ti
dim
e
ns
ional
a
r
r
a
y,
whe
r
e
e
a
c
h
c
olum
n
r
e
pr
e
s
e
nts
one
of
the
f
a
c
e
im
a
ge
s
of
the
s
e
t
(
c
onve
r
ted
f
r
om
R
GB
to
gr
a
ys
c
a
le
a
nd
r
e
s
ha
pe
d
a
s
a
c
olum
n
ve
c
t
or
)
.
T
his
r
e
s
tr
uc
tur
ing
f
a
c
il
it
a
tes
the
a
ppli
c
a
ti
on
of
matr
ix
ope
r
a
ti
ons
a
nd
e
ns
ur
e
s
c
ons
is
tenc
y
in
the
dim
e
ns
i
ons
of
the
da
ta
be
f
or
e
P
C
A
is
a
ppli
e
d
.
T
he
n,
the
in
it
ial
s
tep
invol
ve
s
identif
ying
the
two
c
omponents
with
in
t
his
s
e
t
of
n
-
dim
e
ns
ional
ve
c
tor
s
1
=
{
11
,
12
,
.
.
.
}
⊂
ℝ
that
a
r
e
s
e
pa
r
a
ted
by
the
maximu
m
dis
tanc
e
.
T
his
maximum
dis
tanc
e
r
e
pr
e
s
e
nts
the
longes
t
s
tr
a
ight
li
ne
that
c
a
n
be
dr
a
wn
be
twe
e
n
two
point
s
in
the
da
tas
e
t.
T
he
s
e
two
point
s
de
f
ine
the
di
r
e
c
ti
on
of
the
f
i
r
s
t
pr
incipa
l
c
omponent.
Onc
e
thes
e
two
point
s
a
r
e
identif
ied,
the
s
e
c
ond
s
t
e
p
invol
ve
s
c
a
lcula
ti
ng
the
c
e
ntr
oid
(
mea
n)
of
the
da
tas
e
t,
whic
h
r
e
pr
e
s
e
nts
the
a
ve
r
a
ge
pos
it
ion
of
a
ll
da
ta
point
s
.
T
he
n,
the
di
r
e
c
ti
on
ve
c
tor
f
r
om
the
c
e
ntr
oid
to
the
point
f
ur
thes
t
a
wa
y
(
maximum
dis
tanc
e
)
is
c
ons
ider
e
d
a
s
the
f
ir
s
t
p
r
incipa
l
c
omponent
:
{
11
,
12
}
=
1
,
1
∈
1
(
1
,
1
)
(
7)
h
e
r
e
,
(
.
,
.
)
de
notes
the
E
uc
li
de
a
n
dis
tanc
e
.
T
he
f
ir
s
t
ba
s
is
ve
c
tor
,
v
1
is
the
ve
c
tor
that
c
onne
c
t
s
the
two
point
s
:
v
1
=e
11
-
e
12
.
T
his
ve
c
tor
r
e
pr
e
s
e
nts
the
dir
e
c
ti
on
of
maximum
va
r
ianc
e
be
twe
e
n
the
t
wo
f
ur
thes
t
point
s
in
the
da
tas
e
t,
whic
h
a
ppr
ox
i
mate
s
the
f
ir
s
t
pr
incipa
l
c
omponent.
T
ypica
ll
y
,
to
c
omput
e
the
−
ℎ
ba
s
is
ve
c
tor
,
the
pr
oc
e
s
s
invol
ve
s
pr
ojec
ti
ng
the
point
s
in
the
s
e
t
P
i
-
1
onto
the
hype
r
plane
H
i
-
1
.
B
y
identif
ying
the
two
pr
ojec
ti
ons
with
the
maximum
s
e
pa
r
a
ti
on
dis
tanc
e
,
the
−
ℎ
ba
s
ic
ve
c
tor
,
v
i
is
de
f
i
ne
d
a
s
the
dif
f
e
r
e
nc
e
be
twe
e
n
thes
e
two
p
r
ojec
ti
ons
,
c
a
ptur
ing
the
ne
xt
mos
t
s
igni
f
ica
nt
di
r
e
c
ti
on
of
va
r
ianc
e
.
T
his
it
e
r
a
ti
ve
pr
oc
e
dur
e
e
ns
ur
e
s
that
e
a
c
h
ba
s
is
ve
c
tor
c
or
r
e
s
ponds
to
a
p
r
incipa
l
c
omponent,
pr
ovidi
ng
a
n
e
f
f
icie
nt
a
ppr
oxim
a
ti
on
of
the
und
e
r
lyi
ng
s
tr
uc
tur
e
of
the
da
tas
e
t.
T
he
f
inal
outcome
is
the
c
oll
e
c
ti
on
of
ba
s
is
ve
c
tor
s
V
=
{v
1
,
v
2
,
…,
v
n
}
,
with
e
a
c
h
ve
c
tor
a
ppr
oxim
a
ti
ng
a
n
e
igenf
a
c
e
.
T
he
s
e
e
igenf
a
c
e
s
f
or
m
a
c
ompac
t
r
e
pr
e
s
e
ntation
of
the
da
ta,
whic
h
is
us
e
f
ul
f
or
tas
ks
s
uc
h
a
s
f
a
c
ial
r
e
c
ognit
ion
or
im
a
ge
c
ompr
e
s
s
ion.
3.
I
M
AGE
QUAL
I
T
Y
M
E
T
R
I
CS
I
mage
qua
li
ty
metr
ics
a
r
e
e
s
s
e
nti
a
l
f
or
qua
nti
f
yin
g
the
dif
f
e
r
e
nc
e
or
s
im
il
a
r
it
y
be
twe
e
n
a
n
or
igi
na
l
im
a
ge
a
nd
a
modi
f
ied
ve
r
s
ion
[
18
]
.
T
h
is
pa
pe
r
e
mpl
oys
s
e
ve
r
a
l
metr
ics
to
a
s
s
e
s
s
the
dis
pa
r
it
y
be
twe
e
n
e
igenf
a
c
e
s
ge
ne
r
a
ted
by
the
c
las
s
ica
l
e
igenf
a
c
e
s
method
a
nd
our
P
C
A
a
pp
r
oxim
a
ti
on.
T
he
e
va
luation
metr
ics
c
ons
is
t
of
S
S
I
M
,
M
AE
,
S
NR
,
P
S
NR
,
a
nd
E
uc
li
de
a
n
d
is
tanc
e
.
C
ons
ider
ing
two
i
mage
s
ha
ving
the
s
a
me
dim
e
ns
i
ons
M
×
N
,
I
(
i,
j
)
r
e
pr
e
s
e
nts
the
ini
t
ial
i
mage
,
a
nd
K
(
i,j
)
,
r
e
pr
e
s
e
nts
the
modi
f
ied
im
a
ge
.
He
r
e
,
s
pa
ns
f
r
o
m
0
to
M
-
1
a
nd
j
s
pa
ns
f
r
om
0
to
N
-
1
,
indi
c
a
ti
ng
that
e
a
c
h
pixel
in
the
i
mage
is
indexe
d
by
it
s
r
ow
a
nd
c
olum
n
pos
it
ions
.
T
his
s
e
tup
e
ns
ur
e
s
that
both
im
a
ge
s
a
r
e
of
identica
l
s
ize
,
a
ll
owing
f
or
a
pixel
-
by
-
pixel
c
ompar
is
on
be
twe
e
n
the
in
it
ial
a
nd
modi
f
ied
im
a
ge
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2088
-
8708
I
nt
J
E
lec
&
C
omp
E
ng
,
Vol
.
15
,
No.
1
,
F
e
br
ua
r
y
20
25
:
311
-
318
314
C
ompar
is
on
is
a
r
e
of
ten
e
s
s
e
nti
a
l
in
tas
ks
li
ke
im
a
ge
pr
oc
e
s
s
ing,
whe
r
e
c
ha
nge
s
a
t
e
a
c
h
pixel
c
a
n
be
a
na
lyze
d
s
ys
tema
ti
c
a
ll
y.
3.
1.
M
e
an
ab
s
olu
t
e
e
r
r
or
M
e
a
n
a
bs
olut
e
e
r
r
or
(
M
AE
)
indi
c
a
tes
the
mea
n
a
b
s
olut
e
dif
f
e
r
e
nc
e
be
twe
e
n
c
or
r
e
s
ponding
pixels
of
a
n
or
igi
na
l
i
mage
a
nd
it
s
mod
if
ied
ve
r
s
ion
[
19]
.
I
t
is
pa
r
ti
c
ular
ly
us
e
f
ul
f
or
a
na
lyzing
unif
or
ml
y
di
s
tr
ibut
e
d
e
r
r
or
s
a
c
r
os
s
the
im
a
ge
.
T
he
M
AE
is
c
a
lcula
ted
a
s
(
8)
:
M
A
E
=
1
∑
∑
|
(
,
)
−
(
,
)
|
−
1
=
0
−
1
=
0
(
8)
M
AE
of
f
e
r
s
a
s
im
ple
metr
ic
f
or
a
s
s
e
s
s
ing
the
a
ve
r
a
ge
s
ize
of
dis
c
r
e
pa
nc
ies
be
twe
e
n
the
two
im
a
ge
s
,
s
howing
how
c
los
e
ly
the
a
lt
e
r
e
d
im
a
ge
matc
he
s
the
or
igi
na
l
.
3.
2.
M
e
an
s
q
u
ar
e
d
e
r
r
or
M
e
a
n
s
qua
r
e
d
e
r
r
or
(
M
S
E
)
is
a
ppli
e
d
to
c
a
lcula
t
e
the
a
ve
r
a
ge
of
the
s
qua
r
e
d
int
e
ns
it
y
dif
f
e
r
e
nc
e
s
be
twe
e
n
two
im
a
ge
s
,
whic
h
is
a
f
unda
menta
l
met
r
ic
us
e
d
in
c
omput
ing
P
S
NR
.
M
S
E
is
c
a
lcula
ted
a
s
in
(
9)
[
20]
:
M
S
E
=
1
∑
∑
|
(
,
)
−
(
,
)
|
−
1
=
0
−
1
=
0
²
(
9)
M
S
E
is
a
n
indi
c
a
tor
of
the
a
ve
r
a
ge
s
ize
of
e
r
r
or
s
be
twe
e
n
the
two
im
a
ge
s
,
with
higher
va
lues
s
i
gnif
ying
lar
ge
r
dif
f
e
r
e
nc
e
s
be
twe
e
n
them.
3.
3.
P
e
ak
s
ign
al
-
to
-
n
ois
e
r
at
io
T
his
metr
ic
is
e
mpl
oye
d
to
a
s
s
e
s
s
the
s
qua
r
e
d
e
r
r
or
be
twe
e
n
a
r
e
f
e
r
e
nc
e
im
a
ge
a
nd
a
modi
f
ied
im
a
ge
[
21]
,
[
22
]
.
A
higher
pe
a
k
s
ignal
-
to
-
nois
e
r
a
ti
o
(
P
S
NR
)
va
lue
indi
c
a
tes
gr
e
a
ter
s
im
il
a
r
i
ty
be
twe
e
n
the
two
im
a
ge
s
,
while
a
lowe
r
P
S
NR
va
lue
s
igni
f
ies
poor
e
r
im
a
ge
qua
li
ty.
P
S
NR
is
de
ter
mi
ne
d
th
r
ough
the
(
1
0)
:
=
1
0
l
o
g
10
(
(
)
²
)
(
10)
whe
r
e
de
notes
the
highes
t
pixel
va
lue
in
the
i
mage
,
f
o
r
ins
tanc
e
,
255
in
the
c
a
s
e
of
8
-
bit
i
mage
s
.
P
S
NR
is
e
xpr
e
s
s
e
d
in
de
c
ibels
(
dB
)
a
nd
pr
ov
id
e
s
a
s
tanda
r
dize
d
mea
s
ur
e
of
im
a
ge
qua
li
ty,
pa
r
ti
c
ular
ly
in
ter
ms
of
how
much
nois
e
or
d
is
tor
ti
on
is
p
r
e
s
e
nt
r
e
lative
to
the
maximum
pos
s
ibl
e
int
e
ns
it
y
of
the
i
mage
s
.
3.
4.
S
ign
a
l
-
to
-
n
ois
e
r
at
io
S
ignal
-
to
-
nois
e
r
a
ti
o
(
S
NR
)
e
va
luate
s
the
pr
opor
ti
on
of
s
ignal
powe
r
,
a
s
s
oc
iate
d
with
the
r
e
s
tor
e
d
im
a
ge
,
to
nois
e
powe
r
,
whic
h
pe
r
tains
to
the
dis
c
r
e
pa
nc
y
be
twe
e
n
the
or
igi
na
l
a
nd
de
gr
a
de
d
im
a
ge
s
[
23]
.
I
t
is
f
r
e
que
ntl
y
us
e
d
a
s
a
pe
r
f
or
manc
e
metr
ic
in
i
mage
r
e
s
tor
a
ti
on.
T
he
f
or
mu
la
is
:
=
1
0
l
o
g
10
[
∑
∑
[
(
,
)
]
−
1
=
0
−
1
=
0
²
∑
∑
|
(
,
)
−
(
,
)
|
−
1
=
0
−
1
=
0
²
]
(
11)
S
NR
is
e
xp
r
e
s
s
e
d
i
n
de
c
i
be
ls
(
d
B
)
a
nd
q
ua
nt
i
f
i
e
s
ho
w
m
uc
h
s
t
r
on
ge
r
t
he
s
i
gna
l
(
o
r
i
gi
na
l
i
mag
e
)
is
c
om
pa
r
e
d
to
t
he
no
is
e
(
d
is
to
r
ti
on
)
in
t
r
o
duc
e
d
by
the
mo
d
if
ic
a
t
io
n
p
r
oc
e
s
s
.
Hi
gh
e
r
S
N
R
va
lu
e
s
i
nd
ica
te
a
be
tt
e
r
r
e
s
to
r
a
t
io
n
p
e
r
f
o
r
m
a
n
c
e
,
w
he
r
e
th
e
r
e
s
t
o
r
e
d
i
ma
ge
c
los
e
l
y
m
a
t
c
h
e
s
t
he
o
r
i
gi
na
l
i
ma
ge
w
i
th
mi
n
im
a
l
dis
to
r
ti
on
.
3.
5.
S
t
r
u
c
t
u
r
al
s
im
i
larit
y
i
n
d
e
x
m
e
as
u
r
e
T
h
e
s
t
r
uc
tu
r
a
l
s
i
m
il
a
r
i
ty
in
de
x
me
a
s
u
r
e
(
S
S
I
M
)
met
r
ic
is
a
qua
l
it
y
m
e
t
r
ic
d
e
v
e
l
op
e
d
b
y
Li
e
t
al
.
[
24
]
,
d
e
s
i
gn
e
d
to
a
s
s
e
s
s
the
s
i
mi
la
r
it
y
o
f
loc
a
l
pa
tt
e
r
ns
o
f
p
i
xe
l
i
nte
ns
it
ies
in
tw
o
i
ma
ge
s
X
a
n
d
Y
.
I
t
c
o
mp
r
is
e
s
th
r
e
e
c
om
po
ne
nts
:
(
,
)
=
2
µ
µ
+
1
µ
2
+
µ
2
+
1
(
12)
(
,
)
=
2
+
2
2
+
2
+
2
(
13)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
E
lec
&
C
omp
E
ng
I
S
S
N:
2088
-
8708
E
v
aluat
ing
ge
ome
tr
ically
-
appr
ox
imated
pr
incipal
c
ompone
nt
analys
is
v
s
.
c
las
s
ical
…
(
F
aouz
ia
E
nna
ama
)
315
(
,
)
=
+
3
+
2
(
14)
whe
r
e
µ
a
nd
µ
a
r
e
their
mea
n
int
e
ns
it
ies
,
a
nd
r
e
pr
e
s
e
nt
their
s
tanda
r
d
de
viations
,
de
notes
the
c
ova
r
ianc
e
be
twe
e
n
them,
while
1
,
2
,
a
nd
C
3
a
r
e
c
ons
tant
pa
r
a
mete
r
s
.
F
inally,
we
obtain
the
S
S
I
M
as
(
15
)
.
S
S
I
M
(
x
,
y
)
=
[
l
(
x
,
y
)
]
⋅
[
c
(
x
,
y
)
]
⋅
[
s
(
x
,
y
)
]
(
15)
F
or
α
>
0,
β
>
0
a
nd
γ
>
0,
thes
e
a
r
e
f
a
c
tor
s
that
inf
luenc
e
the
we
ight
of
the
thr
e
e
e
leme
nts
.
S
S
I
M
pr
ovides
a
s
c
or
e
be
twe
e
n
0
a
nd
1,
whe
r
e
1
indi
c
a
tes
pe
r
f
e
c
t
s
i
mi
lar
it
y
be
twe
e
n
im
a
ge
s
X
a
nd
Y.
4.
RE
S
UL
T
S
AN
D
DI
S
CU
S
S
I
ON
W
e
pe
r
f
or
med
a
c
ompar
a
ti
ve
e
va
luation
be
tw
e
e
n
ge
ometr
ica
ll
y
-
a
ppr
oxim
a
ted
e
igenf
a
c
e
s
a
nd
c
las
s
ica
l
e
igenf
a
c
e
s
us
ing
the
F
E
I
f
a
c
e
da
taba
s
e
[
25]
.
F
o
r
th
is
c
ompar
is
on,
we
e
mpl
oye
d
s
e
ve
r
a
l
im
a
ge
qua
li
ty
metr
ics
:
E
uc
li
de
a
n
d
is
tanc
e
,
M
AE
,
S
S
I
M
,
S
NR
,
a
nd
P
S
NR
.
T
he
F
E
I
da
taba
s
e
include
s
two
types
of
c
olor
f
a
c
e
i
mage
s
:
640×
480
pixels
a
nd
360×
260
pixels
.
Ou
r
s
tudy
f
oc
us
e
d
on
the
360×
260
pixel
im
a
ge
s
,
tot
a
li
ng
200
im
a
ge
s
.
4.
1.
Gener
at
ion
of
e
igenf
ac
e
s
T
he
ini
ti
a
l
pha
s
e
of
ou
r
c
ompar
is
on
invol
ve
d
a
pplyi
ng
both
the
e
igenf
a
c
e
s
method
a
nd
the
ge
ometr
ic
a
ppr
oxim
a
ti
on
of
P
C
A
to
the
F
E
I
da
t
a
ba
s
e
to
e
xtr
a
c
t
the
a
ve
r
a
ge
f
a
c
e
.
B
y
c
ompar
ing
the
two
a
ppr
oa
c
he
s
,
we
a
im
e
d
to
e
va
luate
how
e
a
c
h
me
thod
c
a
ptur
e
d
the
e
s
s
e
nti
a
l
f
a
c
ial
f
e
a
tur
e
s
pr
e
s
e
nt
in
the
da
tas
e
t.
F
igur
e
1
il
lus
tr
a
tes
the
a
ve
r
a
ge
f
a
c
e
s
obta
ined
thr
ough
both
methods
,
highl
igh
ti
ng
the
di
f
f
e
r
e
nc
e
s
in
the
wa
y
e
a
c
h
tec
hnique
pr
oc
e
s
s
e
s
a
nd
r
e
pr
e
s
e
nts
the
ke
y
c
omponents
of
f
a
c
ial
im
a
ge
s
.
F
igur
e
1.
Ave
r
a
ge
f
a
c
e
s
f
r
om
the
F
E
I
da
taba
s
e
,
a
v
e
r
a
g
e
f
a
c
e
us
ing
e
igenf
a
c
e
s
method
(
lef
t
pa
ne
l)
,
a
v
e
r
a
ge
f
a
c
e
us
ing
a
ppr
oxim
a
ted
e
igenf
a
c
e
s
(
r
ight
pa
ne
l)
S
ubs
e
que
ntl
y,
we
ge
ne
r
a
ted
a
ll
pos
s
ibl
e
e
igenf
a
c
e
s
us
ing
both
methods
.
T
he
number
of
e
igenf
a
c
e
s
c
r
e
a
ted
matc
he
s
the
c
ount
of
f
a
c
e
im
a
ge
s
in
the
da
taba
s
e
.
W
e
s
pe
c
if
ica
ll
y
c
hos
e
a
nd
a
na
lyz
e
d
the
f
ir
s
t
7
e
igenf
a
c
e
s
obtaine
d
via
the
c
las
s
ica
l
e
igenf
a
c
e
s
method
a
s
s
hown
in
F
igur
e
2
a
nd
the
a
ppr
oxim
a
ted
e
igenf
a
c
e
s
a
s
s
hown
in
F
igur
e
3.
T
he
s
e
e
igenf
a
c
e
s
a
r
e
a
s
s
oc
iate
d
with
the
lar
ge
s
t
e
igenva
lues
a
nd
thus
c
a
ptur
e
mor
e
in
f
or
mation
f
r
om
the
t
r
a
ini
ng
i
mage
s
[
4]
.
F
igur
e
2.
F
i
r
s
t
7
e
igenf
a
c
e
im
a
ge
s
f
r
om
the
F
E
I
da
taba
s
e
obtaine
d
us
ing
the
c
las
s
ica
l
e
igenf
a
c
e
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2088
-
8708
I
nt
J
E
lec
&
C
omp
E
ng
,
Vol
.
15
,
No.
1
,
F
e
br
ua
r
y
20
25
:
311
-
318
316
F
igur
e
3.
F
i
r
s
t
7
e
igenf
a
c
e
im
a
ge
s
f
r
om
the
F
E
I
d
a
taba
s
e
obtaine
d
us
ing
the
a
ppr
oxim
a
ted
e
igenf
a
c
e
s
4.
2.
Qu
an
t
it
a
t
ive
c
om
p
ar
is
on
r
e
s
u
lt
s
W
e
c
ompar
e
d
the
f
ir
s
t
7
e
igenf
a
c
e
s
ge
ne
r
a
ted
by
both
methods
us
ing
im
a
ge
qua
li
ty
met
r
ics
.
T
he
c
ompar
is
on
invol
ve
d
e
va
luating
e
a
c
h
pa
ir
of
e
igen
f
a
c
e
s
ba
s
e
d
on
E
uc
li
de
a
n
d
is
tanc
e
,
M
AE
,
S
NR
,
P
S
NR
,
a
nd
S
S
I
M
.
T
he
metr
ics
we
r
e
a
ppli
e
d
to
e
a
c
h
pa
ir
in
s
e
que
nc
e
,
s
tar
ti
ng
with
the
f
ir
s
t
two
e
igenf
a
c
e
s
,
f
oll
owe
d
by
the
ne
xt
two,
a
nd
s
o
f
or
th.
T
he
da
ta
in
T
a
ble
1
r
e
ve
a
l
s
igni
f
ica
nt
dif
f
e
r
e
nc
e
s
in
im
a
ge
qua
li
ty
metr
ics
be
twe
e
n
e
igenf
a
c
e
s
ge
ne
r
a
ted
by
the
c
las
s
ica
l
e
igenf
a
c
e
s
method
a
nd
the
a
ppr
oxim
a
ted
e
igenf
a
c
e
s
method.
T
he
E
uc
li
de
a
n
d
is
tanc
e
va
lues
a
r
e
s
igni
f
ica
ntl
y
lar
ge
,
indi
c
a
ti
ng
c
ons
ider
a
ble
dis
c
r
e
pa
nc
ies
be
twe
e
n
e
igenf
a
c
e
s
pr
oduc
e
d
by
the
two
a
ppr
oa
c
he
s
.
M
AE
va
lues
r
a
nge
f
r
om
28
to
64,
h
ighl
ight
ing
va
r
ianc
e
s
in
e
igenf
a
c
e
r
e
pr
e
s
e
ntations
.
S
NR
va
lues
a
r
e
c
ons
is
tently
be
low
32
dB
,
r
e
f
le
c
ti
ng
dif
f
e
r
e
nc
e
s
in
the
qua
li
ty
o
f
e
igenf
a
c
e
s
f
r
om
both
methods
.
P
S
NR
va
lues
,
whic
h
a
r
e
ne
ga
ti
ve
a
nd
b
e
low
30
dB
,
f
ur
ther
unde
r
s
c
or
e
the
va
r
iation
in
e
igenf
a
c
e
f
idelit
y.
Additi
ona
ll
y
,
a
ll
S
S
I
M
va
lues
a
r
e
be
low
1,
c
onf
ir
mi
ng
dif
f
e
r
e
nc
e
s
in
how
the
two
methods
c
a
ptur
e
im
a
ge
s
tr
uc
tur
e
.
T
a
ble
1.
E
va
luation
of
e
igen
f
a
c
e
s
de
r
ived
us
ing
bo
th
the
tr
a
di
ti
ona
l
a
nd
a
ppr
ox
im
a
ted
e
igenf
a
c
e
s
tec
hniques
E
ig
e
nf
a
c
e
s
E
uc
di
s
ta
nc
e
(
×
10
3
)
M
A
E
S
N
R
dB
P
S
N
R
dB
S
S
I
M
1
2.3841
28.0314
10.4224
-
32.7224
0.1943
2
3.5120
63.4315
1.0533
-
39.1457
0.0987
3
3.7018
37.5793
8.4284
-
33.7736
0.1153
4
2.7154
54.9430
4.3333
-
37.2305
0.0571
5
2.6402
45.0207
4.9677
-
36.2332
-
0.0910
6
2.7192
42.6299
5.2446
-
35.8557
-
0.0178
7
3.9907
60.1694
3.0974
-
36.8377
-
0.0847
T
he
s
e
va
r
iations
pr
im
a
r
il
y
r
e
s
ult
f
r
om
di
f
f
e
r
e
nc
e
s
in
e
igenve
c
tor
ge
ne
r
a
ti
on.
T
he
ge
ometr
ica
ll
y
-
a
ppr
oxim
a
ted
P
C
A
f
oc
us
e
s
on
s
e
le
c
ti
ng
e
igenve
c
tor
s
ba
s
e
d
on
the
maximum
dis
tanc
e
s
be
twe
e
n
im
a
ge
s
,
pr
ior
it
izing
ge
ometr
ic
pr
ope
r
ti
e
s
.
I
n
c
ontr
a
s
t,
th
e
c
las
s
ica
l
e
igenf
a
c
e
s
method
de
r
ives
e
igenve
c
t
or
s
f
r
om
c
ova
r
ianc
e
matr
ice
s
,
e
mphas
izing
s
tatis
ti
c
a
l
r
e
latio
ns
hips
.
T
he
s
e
methodologi
c
a
l
di
f
f
e
r
e
nc
e
s
c
ontr
ibu
te
to
the
obs
e
r
ve
d
dis
pa
r
it
ies
in
e
igenf
a
c
e
qua
li
ty
a
nd
f
idelit
y.
5.
CONC
L
USI
ON
I
n
thi
s
wor
k,
we
pe
r
f
o
r
med
a
c
ompar
a
ti
ve
e
va
luation
of
the
ge
ometr
ica
ll
y
-
a
ppr
oxim
a
ted
P
C
A
method
a
nd
the
c
las
s
ica
l
e
igenf
a
c
e
s
tec
hnique,
e
va
luating
their
pe
r
f
or
manc
e
us
ing
s
e
ve
r
a
l
metr
ics
:
E
uc
li
de
a
n
Dis
tanc
e
,
P
S
NR
,
M
AE
,
S
NR
,
a
nd
S
S
I
M
.
T
he
a
na
lys
is
wa
s
pe
r
f
or
med
on
the
F
E
I
f
a
c
e
da
taba
s
e
,
uti
li
z
ing
200
f
r
ontal
im
a
ge
s
f
o
r
tr
a
ini
ng.
B
oth
methods
we
r
e
e
mpl
oye
d
to
e
xtr
a
c
t
e
igenf
a
c
e
s
,
a
nd
the
f
i
r
s
t
7
e
i
ge
nf
a
c
e
s
f
r
om
e
a
c
h
method
we
r
e
a
s
s
e
s
s
e
d.
T
he
r
e
s
ult
s
de
mons
tr
a
te
notable
di
f
f
e
r
e
nc
e
s
be
twe
e
n
the
two
methods
.
S
pe
c
if
ica
ll
y,
the
S
NR
a
nd
P
S
NR
va
lues
f
or
e
igenf
a
c
e
s
ge
ne
r
a
ted
by
the
g
e
ometr
ica
ll
y
-
a
ppr
oxim
a
ted
P
C
A
method
we
r
e
c
on
s
is
tently
be
low
30
dB
,
a
nd
the
S
S
I
M
va
lues
we
r
e
les
s
than
1.
T
he
s
e
f
indi
ngs
indi
c
a
te
a
dis
pa
r
it
y
in
the
qu
a
li
ty
a
nd
f
idelit
y
of
the
e
igenf
a
c
e
s
pr
oduc
e
d
by
the
two
met
hods
.
T
he
dis
c
r
e
pa
nc
ies
obs
e
r
ve
d
s
tem
f
r
o
m
the
di
f
f
e
r
ing
a
pp
r
oa
c
he
s
to
e
igenve
c
tor
c
omput
a
ti
on:
the
ge
ometr
ica
ll
y
-
a
ppr
oxim
a
ted
P
C
A
de
ter
mi
ne
s
e
ige
nve
c
tor
s
ba
s
e
d
on
the
maximum
dis
tan
c
e
s
be
tw
e
e
n
im
a
ge
s
,
while
the
c
las
s
ica
l
e
igenf
a
c
e
s
method
c
omput
e
s
them
us
ing
c
ova
r
ianc
e
mat
r
ice
s
.
T
his
d
iver
g
e
nc
e
in
methodology
ha
s
a
notable
im
pa
c
t
on
the
qua
li
ty
of
the
r
e
s
ult
ing
e
igenf
a
c
e
s
,
a
s
e
videnc
e
d
by
the
va
r
iations
in
pe
r
f
or
manc
e
metr
ics
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
E
lec
&
C
omp
E
ng
I
S
S
N:
2088
-
8708
E
v
aluat
ing
ge
ome
tr
ically
-
appr
ox
imated
pr
incipal
c
ompone
nt
analys
is
v
s
.
c
las
s
ical
…
(
F
aouz
ia
E
nna
ama
)
317
Although
the
ge
ometr
ica
ll
y
-
a
ppr
oxim
a
ted
P
C
A
method
pr
ovides
a
mor
e
c
omput
a
t
ionally
e
f
f
icie
nt
a
lt
e
r
na
ti
ve
to
the
c
las
s
ica
l
e
igenf
a
c
e
s
a
ppr
oa
c
h,
it
may
lea
d
to
e
igenf
a
c
e
r
e
pr
e
s
e
ntations
that
a
r
e
les
s
pr
e
c
is
e
.
F
utur
e
r
e
s
e
a
r
c
h
c
ould
f
oc
us
on
r
e
f
ini
ng
the
ge
om
e
tr
ic
a
ppr
oxim
a
ti
on
tec
hnique
to
e
nha
nc
e
it
s
a
c
c
ur
a
c
y
a
nd
mi
ti
ga
te
the
obs
e
r
ve
d
di
f
f
e
r
e
nc
e
s
in
pe
r
f
or
manc
e
.
RE
F
E
RE
NC
E
S
[
1]
K
.
K
a
r
hune
n,
“
A
bout
li
ne
a
r
me
th
od
s
in
pr
oba
bi
li
ty
th
e
or
y
,”
(
in
G
e
r
ma
n)
,
Se
r
ie
s
A
.
I
.
M
at
he
m
at
ic
s
-
P
hy
s
ic
s
,
vol
.
37,
pp.
1
–
79,
1947.
[
2]
B
.
A
.
D
e
C
a
s
tr
o,
A
.
B
in
ot
to
,
J
.
A
.
A
r
di
la
-
R
e
y,
J
.
R
.
C
.
P
.
F
r
a
ga
,
C
.
S
mi
th
,
a
nd
A
.
L
.
A
ndr
e
ol
i,
“
N
e
w
a
lg
or
it
hm
a
ppl
ie
d
to
tr
a
ns
f
or
me
r
s
’
f
a
il
ur
e
s
de
te
c
ti
on
ba
s
e
d
on
K
a
r
hune
n
-
L
oè
ve
tr
a
ns
f
or
m,”
I
E
E
E
T
r
ans
ac
ti
ons
on
I
ndus
tr
ia
l
I
nf
or
m
at
ic
s
,
vol
.
19,
no. 11, pp. 10883
–
10891, Nov. 2023, d
oi
:
10.1109/T
I
I
.2023.3240590.
[
3]
H
.
C
ha
ng,
C
.
W
a
ng,
Z
.
L
iu
,
B
.
F
e
ng,
C
.
Z
ha
n,
a
nd
X
.
C
he
ng,
“
R
e
s
e
a
r
c
h
on
th
e
K
a
r
hune
n
-
L
oè
ve
tr
a
ns
f
or
m
me
th
od
a
n
d
it
s
a
ppl
ic
a
ti
on
to
hul
l
f
or
m
opt
im
iz
a
ti
on,”
J
our
nal
of
M
ar
in
e
Sc
ie
nc
e
and
E
ngi
ne
e
r
in
g
,
vol
.
11,
no.
1,
p.
230,
J
a
n.
2023,
doi
:
10.3390/j
ms
e
11010230.
[
4]
M
.
T
ur
k
a
nd
A
.
P
e
nt
la
nd,
“
E
ig
e
nf
a
c
e
s
f
or
r
e
c
ogni
ti
on,”
J
our
n
al
of
C
ogni
ti
v
e
N
e
ur
o
s
c
ie
nc
e
,
vol
.
3,
no.
1,
pp.
71
–
86,
J
a
n.
19
91,
doi
:
10.1162/j
oc
n.1991.3.1.71.
[
5]
L
.
G
uo a
nd S
. W
u,
“
F
P
G
A
i
mpl
e
me
nt
a
ti
on of
a
r
e
a
l
-
ti
me
e
dge
de
te
c
ti
on s
ys
te
m ba
s
e
d on a
n i
mpr
ove
d C
a
nny a
lg
or
it
hm,”
A
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li
e
d
Sc
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e
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be
n
F
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e
dj
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gha
ir
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S
oua
ni
,
“
A
n
e
f
f
ic
ie
nt
pa
r
a
ll
e
l
im
pl
e
me
nt
a
ti
on
of
f
a
c
e
de
te
c
ti
on
s
y
s
te
m
us
in
g
C
U
D
A
,”
in
202
0
5t
h
I
nt
e
r
nat
io
nal
C
onf
e
r
e
nc
e
on
A
dv
anc
e
d
T
e
c
hnol
ogi
e
s
fo
r
Si
gna
l
and
I
m
age
P
r
oc
e
s
s
in
g
(
A
T
SI
P
)
,
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[
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Z
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B
oube
gui
r
a
a
nd
S
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G
ha
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mi
,
“
G
P
U
-
a
c
c
e
le
r
a
te
d
im
pl
e
me
nt
a
ti
on
of
E
ig
e
nf
a
c
e
s
(
P
C
A
)
a
lg
o
r
it
hm
us
in
g
me
mor
y
opt
im
iz
a
ti
on,”
P
r
oc
e
e
di
ngs
of
th
e
1
s
t
I
nt
e
r
nat
io
nal
C
onf
e
r
e
nc
e
on
I
nt
e
l
li
ge
nt
Sy
s
te
m
s
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P
at
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r
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R
e
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A
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P
G
A
-
ba
s
e
d
pa
r
a
ll
e
l
im
pl
e
me
nt
a
ti
on
to
c
la
s
s
if
y
hype
r
s
pe
c
tr
a
l
im
a
ge
s
by
us
in
g
a
c
onvolut
io
na
l
n
e
ur
a
l
ne
tw
or
k,”
I
nt
e
gr
at
io
n
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ll
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ha
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ve
e
n,
S
.
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oke
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h,
a
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B
.
S
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J
a
ya
s
r
i,
“
R
e
a
l
-
ti
me
obj
e
c
t
de
te
c
ti
on
a
nd
f
a
c
e
r
e
c
ogni
ti
on
s
ys
te
m
to
a
s
s
is
t
th
e
vi
s
ua
ll
y
im
pa
ir
e
d,”
J
our
nal
of
P
hy
s
ic
s
:
C
onf
e
r
e
nc
e
Se
r
ie
s
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A
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on,
“
F
unda
me
nt
a
ls
of
a
c
c
e
le
r
a
te
d
c
omput
in
g
w
it
h C
U
D
A
C
/C
+
+
,”
(
in
P
or
tu
gue
s
e
)
in
M
in
ic
ur
s
o
s
do
X
X
I
I
I
Si
m
pós
io
e
m
Si
s
te
m
as
C
om
put
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c
io
nai
s
de
A
lt
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e
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J
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X
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“
A
na
ly
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e
nt
e
r
pr
is
e
va
lu
a
ti
on
a
nd
f
ut
ur
e
de
ve
lo
pme
nt
of
N
vi
di
a
,”
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anc
e
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E
c
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ti
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nc
he
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N
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A
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A
r
or
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M
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C
or
c
ha
do,
“
F
a
c
e
de
te
c
ti
on
a
nd
r
e
c
ogni
ti
on,
f
a
c
e
e
mot
io
n
r
e
c
ogni
ti
on
th
r
ough
nvi
di
a
je
ts
on
na
no,”
in
A
dv
anc
e
s
in
I
nt
e
ll
ig
e
nt
Sy
s
te
m
s
and
C
om
put
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g
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I
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e
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d
pr
e
c
is
io
n
a
lg
or
it
hms
in
nu
me
r
ic
a
l
li
ne
a
r
a
lg
e
br
a
,”
A
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ta
N
um
e
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E
.
T
or
ti
,
E
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M
a
r
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nz
i,
G
.
D
a
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,
A
.
J
.
P
la
z
a
,
a
nd
F
.
L
e
por
a
ti
,
“
S
pa
ti
a
l
-
s
pe
c
tr
a
l
f
e
a
tu
r
e
e
xt
r
a
c
ti
on
w
it
h
lo
c
a
l
c
ova
r
ia
nc
e
ma
tr
ix
f
r
om
hype
r
s
pe
c
tr
a
l
im
a
ge
s
th
r
ough
hybr
id
pa
r
a
ll
e
li
z
a
ti
on,”
I
E
E
E
J
our
nal
of
Se
le
c
te
d
T
opi
c
s
in
A
ppl
ie
d
E
ar
th
O
bs
e
r
v
at
io
ns
and
R
e
m
ot
e
Se
ns
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g
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A
R
S
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N
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D
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F
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A
ta
n,
R
.
R
a
hma
de
w
i,
D
.
A
d
z
a
ni
S
us
a
nt
o,
a
nd
W
.
K
u
nc
or
o
J
a
ti
,
“
I
mpl
e
me
nt
a
ti
on
of
a
n
id
e
nt
if
ic
a
ti
on
s
ys
te
m
w
it
h
f
a
c
ia
l
im
a
ge
pr
oc
e
s
s
in
g
(
E
ig
e
nf
a
c
e
)
us
in
g
M
a
tl
a
b
a
ppl
ic
a
ti
on,”
J
u
r
nal
M
e
di
a
E
le
k
tr
ik
,
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no.
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–
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ik
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[
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F
.
E
nna
a
ma
,
K
.
B
e
nhi
da
, a
nd
S
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E
nna
a
ma
,
“
R
obu
s
t
f
a
c
e
r
e
c
og
ni
ti
on
unde
r
a
dva
nc
e
d
oc
c
lu
s
io
n:
pr
opos
a
l
of
a
n a
ppr
oa
c
h
ba
s
e
d
on
s
ki
n
de
te
c
ti
on
a
nd
e
ig
e
nf
a
c
e
s
,
”
in
L
e
c
tu
r
e
N
ot
e
s
in
N
e
tw
or
k
s
and
Sy
s
te
m
s
,
vol
.
455,
S
pr
in
ge
r
I
nt
e
r
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ti
ona
l
P
ubl
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2022,
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[
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K
.
B
a
r
te
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ki
,
“
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la
s
s
ic
a
l
vs
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ne
ur
a
l
ne
twor
k
-
ba
s
e
d
P
C
A
a
ppr
oa
c
he
s
f
or
lo
s
s
y
im
a
g
e
c
ompr
e
s
s
io
n:
S
im
il
a
r
it
ie
s
a
nd
di
f
f
e
r
e
nc
e
s
,”
A
ppl
ie
d Soft
C
om
put
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g
, vol
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i:
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s
oc
.2024.111721.
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Y
.
L
iu
,
B
.
Z
ha
ng,
R
.
H
u, K
.
G
u,
G
.
Z
ha
i,
a
nd
J
.
D
ong,
“
U
nd
e
r
w
a
te
r
im
a
ge
qua
li
ty
a
s
s
e
s
s
me
nt
:
b
e
nc
hma
r
k
da
ta
b
a
s
e
a
nd
obj
e
c
ti
ve
me
th
od,”
I
E
E
E
T
r
ans
ac
ti
ons
on M
ul
ti
m
e
di
a
, vol
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[
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S
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H
a
o
a
nd
S
.
L
i,
“
A
w
e
i
gh
te
d
m
e
a
n
a
b
s
ol
ut
e
e
r
r
or
me
tr
i
c
f
or
im
a
ge
qu
a
l
it
y
a
s
s
e
s
s
m
e
n
t,
”
i
n
2
02
0
I
E
E
E
I
n
t
e
r
na
ti
on
al
C
o
nf
e
r
e
nc
e
on
V
i
s
ua
l
C
om
m
u
ni
c
a
ti
on
s
a
nd
I
m
ag
e
P
r
o
c
e
s
s
in
g
(
V
C
I
P
)
,
D
e
c
.
20
20
,
v
ol
.
1
0,
p
p.
3
30
–
3
33
,
do
i:
1
0.
11
09
/V
C
I
P
49
81
9.
20
20
.9
30
18
89
.
[
20]
B
.
G
ir
od,
“
W
ha
t’
s
w
r
ong
w
it
h
me
a
n
s
qua
r
e
d
e
r
r
or
?
,”
in
D
ig
it
al
I
m
age
s
and
H
um
an
V
is
io
n
,
1993,
pp.
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–
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ds
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[
21]
Y
.
A
l
N
a
jj
a
r
,
“
C
ompa
r
a
ti
ve
a
na
ly
s
is
of
im
a
ge
qua
li
ty
a
s
s
e
s
s
me
nt
me
tr
ic
s
:
M
S
E
,
P
S
N
R
,
S
S
I
M
,
a
nd
F
S
I
M
,”
I
nt
e
r
nat
io
nal
J
our
nal
of
Sc
ie
nc
e
and R
e
s
e
a
r
c
h (
I
J
SR
)
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D
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.
I
.
M
.
S
e
ti
a
di
,
“
P
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N
R
v
s
S
S
I
M
:
im
pe
r
c
e
pt
ib
il
it
y
qua
li
ty
a
s
s
e
s
s
me
nt
f
or
im
a
ge
s
te
g
a
nogr
a
phy,”
M
ul
ti
m
e
di
a
T
ool
s
and
A
ppl
ic
at
io
ns
, vol
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[
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K
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G
.
S
c
hi
ll
in
g
e
t
al
.
,
“
M
in
im
a
l
numbe
r
of
s
a
mpl
in
g
di
r
e
c
ti
o
ns
f
or
r
obus
t
me
a
s
ur
e
s
of
th
e
s
phe
r
ic
a
l
me
a
n
di
f
f
us
io
n
w
e
ig
ht
e
d
s
ig
na
l:
E
f
f
e
c
ts
of
s
a
mpl
in
g
di
r
e
c
ti
ons
,
b
-
va
lu
e
,
s
ig
na
l
-
to
-
no
is
e
r
a
ti
o,
ha
r
dw
a
r
e
,
a
nd
f
it
ti
ng
s
tr
a
te
gy,”
M
agne
ti
c
R
e
s
onanc
e
I
m
agi
ng
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–
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[
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X
.
L
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J
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J
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S
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A
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a
nd
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.
G
a
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,
“
A
n
im
pr
ove
d
bl
in
d/
r
e
f
e
r
e
nc
e
le
s
s
im
a
ge
s
pa
ti
a
l
qua
li
ty
e
v
a
lu
a
to
r
a
lg
or
it
hm
f
or
im
a
ge
qua
li
ty
a
s
s
e
s
s
me
nt
,”
I
nt
e
r
nat
io
nal
J
our
nal
of
C
om
put
at
io
nal
Sc
ie
nc
e
and E
ngi
ne
e
r
in
g
, vol
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C
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homa
z
, “
F
E
I
f
a
c
e
da
ta
ba
s
e
.”
FEI
, 2023.
ht
tp
s
:/
/f
e
i.
e
du.br
/~
c
e
t/
f
a
c
e
da
ta
ba
s
e
.ht
ml
(a
c
c
e
s
s
e
d:
A
ug. 12, 2024
)
.
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15
,
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br
ua
r
y
20
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:
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