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io
n
s
o
f
m
o
u
t
h
,
n
o
s
e,
le
f
t
e
y
e,
an
d
r
ig
h
t
e
y
e.
Feat
u
r
e
s
p
ac
e
d
i
m
en
s
io
n
al
it
y
is
r
e
d
u
ce
d
u
s
i
n
g
p
r
i
n
cip
al
co
m
p
o
n
en
ts
a
n
al
y
s
i
s
,
an
d
m
atc
h
in
g
i
s
b
ased
o
n
m
i
n
i
m
u
m
d
is
ta
n
ce
u
s
i
n
g
b
o
th
g
lo
b
al
a
n
d
lo
ca
l s
h
ap
e
co
m
p
o
n
e
n
ts
.
L
u
et
al.
[
7
]
r
ep
o
r
t o
n
r
esu
lt
s
o
f
an
I
C
P
-
b
a
s
ed
ap
p
r
o
ac
h
to
3
D
f
ac
e
r
ec
o
g
n
itio
n
.
T
h
is
ap
p
r
o
ac
h
ass
u
m
es
t
h
at
th
e
g
aller
y
3
D
i
m
ag
e
i
s
a
m
o
r
e
co
m
p
lete
f
ac
e
m
o
d
el
an
d
th
e
p
r
o
b
e
3
D
i
m
a
g
e
is
a
f
r
o
n
tal
v
ie
w
t
h
at
i
s
li
k
el
y
a
s
u
b
s
et
o
f
th
e
g
aller
y
i
m
a
g
e.
P
an
e
t
al.
[
8
]
ap
p
l
y
P
C
A
,
o
r
ei
g
en
f
ac
e,
m
atc
h
i
n
g
t
o
a
n
o
v
el
m
ap
p
in
g
o
f
t
h
e
3
D
d
ata
to
a
r
a
n
g
e,
o
r
d
ep
th
,
i
m
a
g
e.
Fi
n
d
in
g
t
h
e
n
o
s
e
tip
to
u
s
e
as
a
ce
n
ter
p
o
in
t,
an
d
an
a
x
i
s
o
f
s
y
m
m
etr
y
to
u
s
e
f
o
r
alig
n
m
e
n
t,
t
h
e
f
ac
e
d
ata
ar
e
m
ap
p
ed
to
a
cir
cu
lar
r
an
g
e
i
m
a
g
e.
L
ee
et
al.
[
9
]
p
r
o
p
o
s
e
an
ap
p
r
o
ac
h
to
3
D
f
ac
e
r
ec
o
g
n
i
tio
n
b
ased
o
n
t
h
e
c
u
r
v
a
tu
r
e
v
al
u
e
s
at
ei
g
h
t
f
ea
tu
r
e
p
o
in
ts
o
n
th
e
f
ac
e.
Usi
n
g
a
S
u
p
p
o
r
t
V
ec
to
r
M
ac
h
i
n
e
f
o
r
class
i
f
icatio
n
.
T
h
e
y
u
s
e
a
C
y
b
er
w
ar
e
s
e
n
s
o
r
to
ac
q
u
ir
e
th
e
en
r
o
ll
m
e
n
t
i
m
ag
e
s
an
d
a
Gen
e
x
s
e
n
s
o
r
to
ac
q
u
ir
e
th
e
p
r
o
b
e
i
m
ag
e
s
.
Y.
W
an
g
e
t
al.
[
1
0
]
u
s
ed
I
ter
ativ
e
C
lo
s
e
s
t
P
o
in
t
(
I
C
P
)
alg
o
r
ith
m
.
I
n
3
D
f
ac
e
r
ec
o
g
n
itio
n
,
I
C
P
is
f
r
eq
u
en
tl
y
u
s
ed
f
o
r
s
u
r
f
ac
e
r
eg
i
s
tr
atio
n
.
Sa
m
ir
et
al.
[
1
1
]
r
e
p
r
esen
ted
f
ac
ial
s
u
r
f
ac
es
u
s
i
n
g
a
u
n
io
n
o
f
lev
el
-
s
et
c
u
r
v
e
s
o
f
t
h
e
d
ep
th
f
u
n
ct
io
n
w
it
h
r
esp
ec
t
to
th
e
n
o
s
e
tip
n
a
m
ed
is
o
d
ep
th
cu
r
v
e
s
an
d
co
n
s
tr
u
c
ted
a
s
h
ap
e
s
p
ac
e
o
f
c
u
r
v
es
o
f
in
te
r
est.
Fen
g
et
al.
[
12
]
d
iv
id
ed
th
e
is
o
g
eo
d
esics
i
n
s
m
all
s
e
g
m
en
ts
o
f
eq
u
al
ar
c
len
g
th
t
h
at
f
o
r
m
th
e
b
asi
s
o
f
t
r
ain
ed
f
ac
e
s
i
g
n
at
u
r
es.
So
,
th
e
y
f
o
cu
s
ed
o
n
lo
ca
l
r
eg
io
n
s
to
m
ak
e
t
h
e
s
i
g
n
atu
r
e
in
d
ep
en
d
en
t
o
f
t
h
e
s
tar
ti
n
g
p
o
in
t
o
f
a
cu
r
v
e.
T
h
e
y
u
s
ed
th
e
Fels
-
Olv
er
co
n
s
tr
u
ct
io
n
an
d
th
e
3
D
an
alo
g
o
f
Han
n
-
H
ick
er
m
an
in
te
g
r
al
v
ar
i
ab
les
to
d
er
iv
e
in
teg
r
al
i
n
v
ar
i
an
ts
f
o
r
cu
r
v
e
s
in
3
D
s
u
b
j
ec
ted
to
th
e
E
u
clid
ea
n
g
r
o
u
p
.
J
ah
an
b
in
et
al.
[
13
]
ex
tr
ac
ted
f
r
o
m
ea
ch
is
o
g
eo
d
esic
f
i
v
e
s
h
ap
e
d
escr
ip
to
r
s
:
co
n
v
e
x
it
y
,
r
atio
o
f
p
r
in
cip
al
ax
es,
co
m
p
ac
tn
e
s
s
,
cir
cu
lar
an
d
ellip
tic
v
ar
ian
ce
.
T
h
ese
f
ea
tu
r
es
ar
e
tr
ain
ed
w
i
th
L
i
n
ea
r
Dis
cr
i
m
in
a
n
t
An
al
y
s
i
s
(
L
D
A
)
an
d
S
u
p
p
o
r
t
Vec
to
r
Ma
ch
in
es
(
SVM)
.
Han
et
al.
[
14
]
u
s
in
g
f
i
v
e
m
a
n
u
all
y
id
en
ti
f
ied
lan
d
m
ar
k
p
o
in
ts
w
it
h
in
a
s
u
b
s
u
r
f
ac
e
co
m
p
o
s
in
g
o
f
e
y
e
s
an
d
w
h
o
le
n
o
s
e.
Dr
ir
a
et
al.
[
15
]
p
r
o
j
ec
ted
p
ast
w
o
r
k
i
n
R
ie
m
a
n
n
ian
a
n
a
l
y
s
i
s
o
f
s
h
ap
es
o
f
clo
s
ed
cu
r
v
es
o
n
n
asal
s
u
r
f
ac
es.
T
h
is
c
h
o
ice
is
d
u
e
to
th
e
s
tab
ilit
y
o
f
n
o
s
e
d
ata
co
llecti
o
n
an
d
t
h
e
i
n
v
ar
ia
n
ce
o
f
n
as
al
s
h
ap
e
u
n
d
er
e
x
p
r
ess
io
n
s
.
Ma
alej
et
al.
[
16
]
p
r
esen
ted
a
n
o
t
h
er
ap
p
licatio
n
f
o
r
f
ac
ial
ex
p
r
ess
io
n
r
ec
o
g
n
i
tio
n
,
th
e
y
e
x
tr
ac
ted
s
e
v
er
al
r
e
lev
an
t
r
eg
io
n
s
o
f
a
g
iv
e
n
f
ac
ial
s
u
r
f
ac
e
s
.
T
h
ey
lo
ca
ll
y
p
r
o
j
ec
ted
is
o
g
eo
d
esic
p
ath
id
ea
b
y
r
ep
r
esen
t
in
g
ea
ch
p
atch
w
ith
a
s
et
o
f
clo
s
ed
cu
r
v
es.
I
n
th
is
w
o
r
k
w
e
p
r
esen
t
an
a
u
to
m
a
t
ic
3
D
f
ac
e
r
ec
o
g
n
i
tio
n
s
y
s
te
m
b
ased
o
n
f
ac
ial
s
u
r
f
a
ce
an
al
y
s
i
s
u
s
i
n
g
a
R
ie
m
a
n
n
ia
n
g
eo
m
etr
y
.
Fo
r
th
is
w
e
tak
e
th
e
f
o
llo
w
i
n
g
s
tep
s
:
(
1
)
-
N
o
s
e
t
ip
d
etec
tio
n
a
s
a
r
e
f
er
en
ce
p
o
in
t
o
f
3
D
f
ac
e.
(
2
)
-
G
eo
d
etic
d
is
tan
ce
C
o
m
put
in
g
b
et
w
e
en
th
e
r
e
f
er
en
ce
p
o
in
t
a
n
d
th
e
o
th
er
p
o
in
ts
o
f
t
h
e
3
D
f
ac
ial
s
u
r
f
ac
e
u
s
i
n
g
t
h
e
J
ac
o
b
i
iter
a
tio
n
s
.
(
3
)
-
G
eo
d
esic d
is
tan
ce
s
s
p
ac
e
m
atr
ices
r
ed
u
c
tio
n
u
s
in
g
P
r
in
cip
al
C
o
m
p
o
n
e
n
t
An
al
y
s
is
(
P
C
A
)
or
L
in
ea
r
Di
s
cr
i
m
in
a
n
t
An
al
y
s
i
s
(
L
D
A
)
al
g
o
r
ith
m
s
.
T
h
e
r
est
o
f
th
i
s
p
ap
er
is
o
r
g
an
ized
as
f
o
llo
w
s
:
Sectio
n
2
d
es
cr
ib
es
th
e
m
e
th
o
d
o
lo
g
y
o
f
th
e
p
r
o
p
o
s
ed
m
et
h
o
d
w
i
th
its
s
ta
p
es
.
Sec
tio
n
3
i
n
clu
d
es
th
e
s
i
m
u
latio
n
r
esu
lt
s
a
n
d
m
et
h
o
d
an
al
y
s
is
.
Sectio
n
4
co
n
cl
u
s
io
n
an
d
f
u
tu
r
e
w
o
r
k
s
.
2.
RE
S
E
ARCH
M
E
T
H
O
D
T
h
e
o
b
jec
tiv
e
o
f
th
is
w
o
r
k
is
to
p
e
r
f
o
r
m
an
au
to
m
atic
3
D
f
ac
e
r
e
co
g
n
it
io
n
s
y
s
tem
.
Fo
r
th
is
,
w
e
ch
ar
ac
t
er
iz
e
ea
ch
f
ac
e
b
y
a
m
atr
ix
,
w
h
o
s
e
el
em
en
ts
ar
e
a
s
et
o
f
g
eo
m
etr
i
c
f
ea
tu
r
es
(
g
e
o
d
esic
d
is
tan
c
e
co
m
p
u
tin
g
b
e
tw
ee
n
r
ef
er
en
ce
p
o
in
t
an
d
o
th
e
r
p
o
in
ts
o
f
f
a
ce
s
u
r
f
a
ce
)
.
T
h
ese
m
atr
i
ce
s
ar
e
f
in
ally
u
s
ed
to
r
e
co
g
n
iz
e
3
D
f
ac
es
u
n
d
e
r
th
e
f
r
am
e
w
o
r
k
o
f
s
p
ar
s
e
r
e
p
r
e
s
en
tati
o
n
.
F
ig
u
r
e
(
1
)
i
llu
s
t
r
at
es
th
e
s
te
p
s
o
f
o
u
r
p
r
o
p
o
s
e
d
m
eth
o
d
.
Ou
r
s
y
s
te
m
is
d
iv
id
ed
o
n
th
r
e
e
m
ain
s
tep
s
:
P
r
e
p
r
o
c
ess
in
g
,
i
n
th
is
f
ir
s
t
s
tep
,
w
e
d
is
cr
eti
ze
a
3
D
f
ac
e
s
u
r
f
ac
e
u
s
in
g
a
t
r
ian
g
u
la
r
m
esh
b
y
th
e
id
ea
o
f
d
is
p
la
ce
d
s
u
b
d
iv
is
i
o
n
s
u
r
f
a
ce
s
p
r
o
p
o
s
ed
b
y
L
ee
et
al
[
21
]
an
d
Xia
o
x
in
g
L
i
et
al
[
22
]
,
an
d
w
e
d
e
te
ct
au
t
o
m
atica
lly
th
e
r
ef
e
r
en
c
e
p
o
in
t
(
n
o
s
e
ti
p
)
.
I
n
th
e
s
ec
o
n
d
s
t
ep
(
f
ea
tu
r
e
ex
tr
ac
ti
o
n
)
,
w
e
co
m
p
u
te
th
e
g
eo
d
esi
c
d
is
tan
c
e
b
etw
ee
n
th
e
r
ef
e
r
en
ce
p
o
in
t
an
d
a
l
l
o
th
e
r
p
o
in
ts
o
f
3
D
f
ac
e
s
u
r
f
ac
e
t
o
r
ep
r
es
en
t
th
e
3
D
f
ac
e
im
ag
e
w
ith
a
m
atr
ix
w
h
o
s
e
el
em
en
ts
ar
e
g
eo
d
esic
d
i
s
tan
ce
v
alu
es
.
T
h
e
g
eo
d
esi
c
d
is
tan
c
e
b
etw
ee
n
tw
o
p
o
in
ts
o
n
a
m
esh
s
u
r
f
ac
e
is
co
m
p
u
te
d
as
th
e
len
g
th
o
f
th
e
s
h
o
r
test
p
ath
co
n
n
e
ctin
g
th
e
tw
o
p
o
in
ts
w
h
i
le
r
em
ain
in
g
o
n
th
e
f
a
ci
al
s
u
r
f
ac
e
.
W
e
c
o
m
p
u
te
th
e
g
e
o
d
es
i
c
d
is
tan
c
e
b
e
tw
ee
n
t
w
o
p
o
in
ts
o
n
a
m
esh
s
u
r
f
ac
e
u
s
in
g
th
e
J
ac
o
b
i
ite
r
a
ti
o
n
s
as
a
s
o
lu
ti
o
n
o
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[
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S.
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ase
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3
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I
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N
:
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2
5
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i
.
A
d
is
ta
n
ce
m
ap
U
S(x)
f
o
r
x
Ω
is
ap
p
r
o
x
im
a
ted
n
u
m
er
icall
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b
y
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m
p
u
ti
n
g
a
d
is
cr
ete
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ec
to
r
u
R
N
w
h
er
e
ea
ch
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e
u
i is i
n
te
n
d
e
d
to
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p
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o
x
i
m
ate
th
e
v
al
u
e
o
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T
h
is
d
is
cr
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is
co
m
p
u
ted
as
a
s
o
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n
o
f
a
f
i
n
ite
d
i
m
e
n
s
io
n
a
l
f
ix
ed
p
o
in
t
eq
u
atio
n
t
h
at
d
is
cr
etize
s
(
2
)
.
T
o
th
at
en
d
,
a
co
n
tin
u
o
u
s
f
u
n
ctio
n
u
(
x
)
i
s
o
b
tain
ed
f
r
o
m
t
h
e
d
is
cr
ete
s
a
m
p
les
{u
i
}
i
b
y
li
n
ea
r
in
ter
p
o
latio
n
o
v
er
th
e
tr
ia
n
g
le
s
.
W
e
co
m
p
u
te
t
h
e
m
i
n
i
m
izat
io
n
i
n
(
2
)
at
t
h
e
p
o
in
t
x
=
x
i
o
v
er
t
h
e
b
o
u
n
d
ar
y
o
f
B
ε
(x
i
)
d
ef
in
ed
i
n
(
3
)
w
h
er
e
ε
is
th
e
s
a
m
p
lin
g
p
r
ec
is
io
n
.
Fu
r
t
h
er
m
o
r
e,
th
e
te
n
s
o
r
m
etr
ic
is
ap
p
r
o
x
i
m
ated
b
y
a
co
n
s
ta
n
t
ten
s
o
r
f
ield
eq
u
al
to
T
i o
v
er
B
ε
(x
i
)
.
Un
d
er
th
ese
as
s
u
m
p
tio
n
s
,
t
h
e
d
is
cr
et
e
d
er
iv
ativ
e
f
r
ee
E
ik
o
n
al
eq
u
at
io
n
r
ea
d
s
{
(
)
(
)
(
)
(
3
)
Dec
o
m
p
o
s
in
g
t
h
is
m
i
n
i
m
izati
o
n
in
to
ea
c
h
tr
ian
g
le
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i
n
2D
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o
f
th
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n
ei
g
h
b
o
r
h
o
o
d
,
an
d
u
s
i
n
g
th
e
f
ac
t
th
at
u
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y
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is
a
f
f
i
n
e
o
n
ea
ch
tr
ia
n
g
le,
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n
e
ca
n
r
e
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w
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ite
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h
e
d
is
cr
ete
E
ik
o
n
al
eq
u
at
io
n
as a
f
ix
e
d
p
o
in
t
(
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w
h
er
e
th
e
o
p
er
ato
r
(
)
is
d
ef
in
ed
as:
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)
(
)
w
h
er
e
,
,
-
(
)
(
)
W
e
h
av
e
w
r
itte
n
th
is
eq
u
atio
n
f
o
r
s
i
m
p
licit
y
i
n
th
e
2D
ca
s
e,
s
o
th
at
ea
ch
p
o
in
t
y
is
a
b
ar
y
ce
n
ter
o
f
t
w
o
s
a
m
p
li
n
g
p
o
in
t
s
,
b
u
t
t
h
i
s
ex
ten
d
s
to
a
m
an
i
f
o
ld
o
f
ar
b
it
r
ar
y
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i
m
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n
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io
n
d
b
y
co
n
s
id
er
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g
b
ar
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ce
n
ter
s
o
f
d
p
o
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ts
.
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h
e
d
is
cr
ete
E
ik
o
n
al
eq
u
atio
n
is
a
n
o
n
-
li
n
ea
r
f
ix
ed
p
o
in
t
p
r
o
b
lem
.
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n
e
ca
n
co
m
p
u
te
th
e
s
o
lu
t
io
n
to
th
is
p
r
o
b
le
m
u
s
i
n
g
J
ac
o
b
i iter
atio
n
s
.
On
e
ca
n
p
r
o
v
e
t
h
at
th
e
m
ap
p
i
n
g
Г
is
b
o
th
m
o
n
o
to
n
e
s
an
d
n
o
n
-
e
x
p
an
d
i
n
g
:
{
̃
(
)
(
̃
)
(
)
(
̃
)
̃
̃
(
4)
T
h
ese
t
w
o
p
r
o
p
er
ties
en
ab
le
th
e
u
s
e
o
f
s
i
m
p
le
iter
atio
n
s
t
h
at
co
n
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er
g
e
to
th
e
s
o
lu
t
io
n
u
o
f
th
e
p
r
o
b
lem
,
o
n
e
ca
n
ap
p
l
y
t
h
e
u
p
d
ate
o
p
er
ato
r
Г
to
th
e
w
h
o
l
e
s
et
o
f
g
r
id
p
o
in
ts
.
J
ab
o
b
i
n
o
n
-
li
n
ea
r
iter
atio
n
s
in
itial
ize
u
(0)
= 0
an
d
th
en
co
m
p
u
te:
u
(
k
+
1)
=
Γ
(
u
(
k
)
)
T
h
e
f
ix
ed
p
o
in
t p
r
o
p
er
ty
i
s
u
s
ef
u
l to
m
o
n
ito
r
th
e
co
n
v
er
g
e
n
ce
o
f
iter
ativ
e
al
g
o
r
ith
m
s
,
s
i
n
c
e
o
n
e
s
to
p
s
iter
atio
n
s
w
h
en
o
n
e
h
a
s
co
m
p
u
ted
s
o
m
e
d
is
ta
n
ce
u
w
it
h
(
)
(
5
)
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
-
I
C
T
I
SS
N:
2252
-
8776
Geo
d
esic D
is
ta
n
ce
o
n
R
iema
n
n
ia
n
Ma
n
ifo
ld
u
s
in
g
J
a
co
b
i I
t
era
tio
n
s
…
(
R
a
ch
id
A
h
d
id
)
15
An
d
w
h
er
e
is
s
o
m
e
u
s
er
-
d
e
f
i
n
ed
to
ler
an
ce
.
2
.
5
.
G
eo
des
ic
dis
t
a
nce
T
h
e
g
eo
d
esic
d
is
ta
n
ce
b
et
w
ee
n
t
w
o
p
o
i
n
ts
’
p
0
a
n
d
p
o
f
3D
f
ac
e
s
u
r
f
ac
e
i
s
t
h
e
s
h
o
r
test
p
at
h
b
et
w
ee
n
th
e
t
w
o
p
o
in
t
s
w
h
ile
r
e
m
ai
n
i
n
g
o
n
t
h
e
f
ac
ial
s
u
r
f
ac
e.
I
n
th
e
co
n
tex
t
o
f
ca
lcu
lati
n
g
t
h
e
g
eo
d
esic
d
is
tan
ce
R
.
Ki
m
m
el
a
n
d
J
.
A
.
Seth
ian
[
23
]
p
r
o
p
o
s
e
th
e
m
et
h
o
d
o
f
J
ac
o
b
i
iter
atio
n
as
a
s
o
lu
t
io
n
o
f
t
h
e
E
ik
o
n
al
eq
u
at
io
n
.
T
h
e
g
eo
d
esic
d
is
ta
n
ce
b
et
w
e
en
t
w
o
p
o
in
ts
o
n
a
s
u
r
f
ac
e
i
s
ca
lc
u
lated
as
t
h
e
le
n
g
t
h
o
f
th
e
s
h
o
r
test
p
at
h
co
n
n
ec
ti
n
g
th
e
t
w
o
p
o
in
ts
.
Us
in
g
th
e
J
ac
o
b
i
iter
atio
n
al
g
o
r
ith
m
o
n
t
h
e
tr
ian
g
u
lated
s
u
r
f
a
ce
3D
f
ac
e,
w
e
ca
n
co
m
p
u
te
t
h
e
g
eo
d
esic
d
is
ta
n
c
e
b
et
w
ee
n
th
e
r
e
f
er
en
ce
p
o
in
t
p
0
an
d
th
e
o
th
er
p
o
in
t
’
s
p
co
n
s
tr
u
cti
n
g
t
h
e
f
ac
ial
s
u
r
f
ac
e.
T
h
e
g
eo
d
esic d
is
tan
ce
b
et
w
ee
n
p
0
an
d
p
is
ap
p
r
o
x
im
ated
b
y
th
e
f
o
llo
w
i
n
g
e
x
p
r
es
s
io
n
:
(
(
)
)
(
6
)
w
it
h
:
(
)
is
th
e
p
ath
b
et
w
ee
n
p
0
an
d
ac
co
r
d
in
g
to
th
e
s
u
r
f
ac
e
S
o
f
th
e
3D
f
ac
e,
an
d
(
(
)
)
is
th
e
p
ath
len
g
t
h
.
T
h
e
f
o
llo
w
in
g
Fi
g
u
r
e
4
s
h
o
w
s
th
e
s
tep
s
f
o
r
d
eter
m
i
n
i
n
g
t
h
e
g
eo
d
esic
d
is
tan
ce
u
s
i
n
g
a
3D
f
ac
e
im
a
g
e
o
f
SHR
E
C
2
0
0
8
d
atab
ase.
(
a
)
(
b
)
(
c
)
Fig
u
r
e
4
.
3
D
f
ac
e
g
eo
d
esic d
is
tan
ce
co
m
p
u
tes Step
s
: (
a)
R
ef
er
en
ce
p
o
in
t d
etec
tio
n
; (
b
)
Dis
cr
etiza
tio
n
b
y
tr
ian
g
u
lar
m
esh
; (
c)
Geo
d
esic
d
is
tan
ce
co
m
p
u
ti
n
g
R
ep
ea
tin
g
th
is
co
m
p
u
tatio
n
(
g
eo
d
esic
d
is
tan
ce
)
b
etw
ee
n
th
e
r
ef
er
en
ce
p
o
in
t
p
0
an
d
ea
ch
p
o
in
t
p
o
f
th
e
s
u
r
f
ac
e
S
o
f
th
e
3D
f
a
ce
,
th
en
w
e
co
m
p
u
te
a
g
eo
d
esi
c
d
is
tan
ce
m
atr
ix
Ψ
:
[
Ψ
]
=
δij
=
[
]
w
it
h
,
δ
ij
=
T
o
r
ea
lize
o
u
r
3D
f
ac
e
r
ec
o
g
n
itio
n
s
y
s
te
m
,
w
e
u
s
e
t
h
e
P
r
in
cip
al
C
o
m
p
o
n
en
t
A
n
a
l
y
s
is
(
P
C
A
)
a
n
d
L
i
n
ea
r
Dis
cr
i
m
i
n
an
t
A
n
a
l
y
s
is
(
L
D
A
)
f
o
r
w
r
iti
n
g
s
p
ac
e
o
f
t
h
e
g
eo
d
esic
d
is
ta
n
ce
m
a
tr
ix
[
Ψ
]
.
T
o
r
ea
lize
o
u
r
3
D
f
ac
e
r
ec
o
g
n
itio
n
s
y
s
te
m
,
w
e
u
s
e
t
h
r
ee
t
y
p
e
s
o
f
cla
s
s
i
f
ica
t
io
n
alg
o
r
it
h
m
s
:
t
h
e
Ne
u
r
al
Net
w
o
r
k
s
(
NN)
,
k
-
Nea
r
est Ne
ig
h
b
o
r
(
KNN)
an
d
Su
p
p
o
r
t V
ec
to
r
Ma
ch
in
es (
SV
M)
.
3.
RE
SU
L
T
S
A
ND
AN
AL
Y
SI
S
I
n
th
is
s
ec
tio
n
w
e
m
a
k
e
a
s
er
ies
o
f
s
i
m
u
latio
n
to
ev
al
u
ate
th
e
e
f
f
ec
t
iv
e
n
es
s
o
f
th
e
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
.
T
h
ese
r
esu
lts
w
er
e
p
er
f
o
r
m
ed
b
ased
o
n
SHR
E
C
2
0
0
8
d
atab
ase.
T
h
is
d
atab
ase
c
o
n
tain
s
to
tal
o
f
4
2
7
s
ca
n
s
o
f
6
1
s
u
b
j
ec
ts
(
4
5
m
a
le
s
an
d
1
6
f
e
m
ales)
,
f
o
r
ea
ch
o
f
th
e
s
e
6
1
s
u
b
j
ec
ts
7
d
if
f
er
en
t
s
ca
n
s
,
n
a
m
el
y
t
w
o
“f
r
o
n
tal”,
o
n
e
“
lo
o
k
-
u
p
”,
o
n
e
“
lo
o
k
-
d
o
w
n
”,
o
n
e
“
s
m
ile”,
o
n
e
“
la
u
g
h
”
an
d
o
n
e
“
r
a
n
d
o
m
ex
p
r
ess
io
n
”
[
26
,
27
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8776
IJ
-
I
C
T
Vo
l.
6
,
No
.
1
,
A
p
r
il
20
1
7
:
1
0
~
19
16
Fig
u
r
e
5
.
E
x
a
m
p
le
3
D
f
ac
e
i
m
ag
es o
f
t
h
e
d
atab
ase
SH
R
E
C
2
0
0
8
.
Fig
u
r
e
6
g
iv
e
th
e
s
i
m
u
lat
io
n
r
esu
lt
s
o
b
tain
ed
b
y
t
h
e
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
.
T
h
is
f
ig
u
r
e
(
6
)
s
h
o
w
s
th
e
r
ec
o
g
n
itio
n
r
ate
f
o
u
n
d
b
y
th
e
f
ir
s
t
m
et
h
o
d
u
s
ed
in
o
u
r
3
D
f
ac
e
r
ec
o
g
n
itio
n
s
y
s
te
m
s
u
c
h
as
Geo
d
esic
Dis
tan
c
e
u
s
i
n
g
J
ac
o
b
i
I
ter
atio
n
(
GD
-
J
I
)
an
d
P
r
in
cip
al
C
o
m
p
o
n
e
n
t
An
al
y
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i
s
(
P
C
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o
r
ch
ar
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,
w
it
h
th
r
ee
alg
o
r
ith
m
s
o
f
cla
s
s
i
f
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r
al
Net
w
o
r
k
s
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,
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-
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r
est
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g
h
b
o
r
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n
d
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p
p
o
r
t
Vec
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ch
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te
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d
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ar
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n
d
p
r
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est
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itio
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s
i
n
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r
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R
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atab
ase
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m
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g
es.
Fig
u
r
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6
.
R
ec
o
g
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i
tio
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ate
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s
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ica
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atio
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i
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h
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m
et
h
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ar
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Fi
g
u
r
e
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.
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IJ
-
I
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8776
Geo
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17
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ith
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Fig
u
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s
h
o
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iti
o
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ate
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ica
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ith
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t
w
o
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est
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b
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r
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p
p
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Vec
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h
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as:
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I
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A
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d
GD
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L
DA
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s
in
g
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if
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io
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Fig
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s
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s
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4.
CO
NCLU
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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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2
2
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6
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1
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~
19
18
I
n
th
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w
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a
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d
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t
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er
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o
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ts
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th
e
3
D
f
ac
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s
u
r
f
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s
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J
a
co
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s
.
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o
r
G
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d
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ce
s
s
p
ac
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atr
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ctio
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e
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s
ed
P
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o
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p
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n
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t
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al
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i
s
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C
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)
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n
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s
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in
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n
t
An
al
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is
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g
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ith
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s
.
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r
th
e
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la
s
s
if
y
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s
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e
im
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lem
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te
d
alg
o
r
ith
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s
as
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d
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VM
.
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im
u
latio
n
r
esu
l
ts
s
h
o
w
u
s
a
b
ette
r
r
ec
o
g
n
iti
o
n
r
a
te
(
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8
.
6
%
)
f
o
r
w
as
p
r
esen
t
ed
f
o
r
G
D
-
J
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+
P
C
A
u
s
in
g
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lass
if
i
er
,
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e
n
th
is
m
eth
o
d
w
as
also
b
et
ter
th
an
o
th
e
r
t
r
e
e
a
p
p
r
o
ac
h
es
.
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n
f
u
tu
r
e
w
o
r
k
,
w
e
w
ill
tak
e
a
3
D
f
ac
e
r
e
c
o
g
n
iti
o
n
s
y
s
te
m
b
y
an
aly
zin
g
th
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is
o
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g
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d
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s
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R
iem
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n
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ian
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eo
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etr
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d
co
m
p
a
r
e
th
ese
r
esu
lts
w
ith
th
o
s
e
o
b
tain
ed
b
y
th
is
m
eth
o
d
.
RE
F
E
R
E
NC
E
S
[1
]
C.
Ch
u
a
;
F
.
Ha
n
;
Y.K.
Ho
,
“
3
D
h
u
ma
n
fa
c
e
re
c
o
g
n
i
ti
o
n
u
si
n
g
p
o
i
n
t
sig
n
a
t
u
re
,
”
IEE
E
In
ter
n
a
ti
o
n
a
l
Co
n
fer
e
n
c
e
o
n
Au
to
m
a
ti
c
F
a
c
e
a
n
d
Ge
stu
re
Rec
o
g
n
it
io
n
,
p
p
.
2
3
3
–
2
3
8
,
2
0
0
0
.
[2
]
B.
Ac
h
e
r
m
a
n
n
;
H.
Bu
n
k
e
,
“
Cla
ss
if
y
in
g
ra
n
g
e
ima
g
e
s
o
f
h
u
m
a
n
fa
c
e
s
wit
h
Ha
u
s
d
o
rff
d
ista
n
c
e
,
”
in
:
1
5
th
In
ter
n
a
t
io
n
a
l
C
o
n
fer
e
n
c
e
o
n
P
a
tt
e
rn
Rec
o
g
n
it
io
n
,
p
p
.
8
0
9
–
8
1
3
,
S
e
p
tem
b
e
r
2
0
0
0
.
[3
]
A
.
B.
M
o
re
n
o
;
A
´
n
g
e
l
S
a
´
n
c
h
e
z
;
J.F
.
V
e
´
lez
;
F
.
J.
Dı´
a
z
,
“
Fa
c
e
re
c
o
g
n
i
ti
o
n
u
si
n
g
3
D
s
u
rfa
c
e
-
e
x
tra
c
ted
d
e
sc
rip
to
rs
,
”
i
n
:
Irish
M
a
c
h
i
n
e
V
isio
n
a
n
d
Ima
g
e
Pro
c
e
ss
in
g
Co
n
f
e
re
n
c
e
(
IM
VIP
2
0
0
3
),
S
e
p
tem
b
e
r
2
0
0
3
.
[4
]
Y.
L
e
e
;
K.
P
a
rk
;
J.
S
h
im
;
T
.
Yi
,
“
3
D
f
a
c
e
re
c
o
g
n
i
ti
o
n
u
sin
g
sta
ti
stica
l
mu
lt
i
p
le
fe
a
tu
re
s
f
o
r
t
h
e
lo
c
a
l
d
e
p
t
h
in
fo
rm
a
ti
o
n
,
”
in
:
1
6
th
I
n
ter
n
a
ti
o
n
a
l
C
o
n
fer
e
n
c
e
o
n
V
isio
n
In
ter
f
a
c
e
,
Ju
n
e
2
0
0
3
.
[5
]
G
.
M
e
d
io
n
i;
R.
W
a
u
p
o
ti
tsc
h
,
“
Fa
c
e
re
c
o
g
n
it
io
n
a
n
d
mo
d
e
li
n
g
in
3
D,
”
i
n
:
IEE
E
I
n
ter
n
a
ti
o
n
a
l
W
o
rk
sh
o
p
o
n
An
a
lys
is
a
n
d
M
o
d
e
li
n
g
o
f
Fa
c
e
s a
n
d
Ge
stu
re
s (
AM
FG
2
0
0
3
),
p
p
.
2
3
2
–
2
3
3
,
Oc
t
o
b
e
r
2
0
0
3
.
[6
]
C.
X
u
;
Y.
W
a
n
g
;
T
.
T
a
n
;
L
.
Qu
a
n
,
Au
t
o
ma
ti
c
3
D
fa
c
e
re
c
o
g
n
i
ti
o
n
c
o
mb
in
in
g
g
lo
b
a
l
g
e
o
me
tric
fea
tu
re
s
wit
h
lo
c
a
l
sh
a
p
e
v
a
ri
a
ti
o
n
in
f
o
rm
a
ti
o
n
,
”
i
n
:
S
ixth
I
n
ter
n
a
ti
o
n
a
l
Co
n
fer
e
n
c
e
o
n
Au
to
ma
ted
F
a
c
e
a
n
d
Ge
stu
re
R
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308
–
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1
3
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.
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]
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.
L
u
;
D.
C
o
lb
ry
;
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.
K.
Ja
in
,
“
M
a
tch
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n
g
2
.
5
D
s
c
a
n
s
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r
fa
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e
re
c
o
g
n
it
io
n
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i
n
:
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n
ter
n
a
t
io
n
a
l
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n
fer
e
n
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e
o
n
Pa
tt
e
r
n
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o
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io
n
(
ICPR
2
0
0
4
)
,
p
p
.
3
6
2
–
3
6
6
,
2
0
0
4
.
[8
]
G
.
P
a
n
;
S
.
Ha
n
;
Z.
W
u
;
Y.
Wan
g
,
“
3
D
fa
c
e
re
c
o
g
n
it
io
n
u
sin
g
ma
p
p
e
d
d
e
p
t
h
ima
g
e
s,”
in
:
IEE
E
W
o
rk
sh
o
p
o
n
F
a
c
e
Rec
o
g
n
it
io
n
Gr
a
n
d
C
h
a
ll
e
n
g
e
Ex
p
e
rime
n
ts,
Ju
n
e
2
0
0
5
.
[9
]
Y.
L
e
e
;
H.
S
o
n
g
;
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Ya
n
g
;
H.
S
h
in
;
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S
o
h
n
,
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o
c
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l
fea
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re
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f
a
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n
,
”
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n
:
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ter
n
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ti
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a
l
Co
n
fer
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n
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d
io
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n
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Vi
d
e
o
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se
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Bi
o
me
tric
Per
so
n
Au
th
e
n
ti
c
a
ti
o
n
(
AV
BP
A
2
0
0
5
)
,
L
NCS,
v
o
l.
3
5
4
6
,
p
p
.
909
–
9
1
8
,
Ju
ly
2
0
0
5
.
[1
0
]
Y.
W
a
n
g
;
G
.
P
a
n
;
Z
.
W
u
;
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W
a
n
g
,
“
Ex
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lo
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g
fa
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ts
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re
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in
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p
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rt
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l
IC,
”
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P.
Na
ra
y
a
n
a
n
(
e
d
.
),
Co
mp
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ter
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sio
n
˝
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ACC
V
2
0
0
6
,
(
3
8
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1
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5
8
1
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5
9
0
o
f
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t
u
re
No
tes
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mp
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g
e
r
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/He
id
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e
rg
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2
0
0
6
.
[1
1
]
C.
S
a
m
ir;
A
.
S
riv
a
sta
v
a
;
M
.
Da
o
u
d
i
,
“
T
h
re
e
-
Dim
e
n
sio
n
a
l
F
a
c
e
Re
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o
g
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io
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in
g
S
h
a
p
e
s
o
f
F
a
c
ial
Cu
rv
e
s,”
In
IEE
E
T
ra
n
sa
c
ti
o
n
s O
n
P
a
tt
e
rn
A
n
a
lys
is
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n
d
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a
c
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in
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I
n
telli
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e
,
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p
.
.
1
8
5
8
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1
8
6
3
,
2
0
0
6
.
[1
2
]
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.
F
e
n
g
;
H.
Kri
m
;
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A
Ko
g
a
n
,
“
3
D
fa
c
e
re
c
o
g
n
it
io
n
u
sin
g
e
u
c
li
d
e
a
n
in
teg
r
a
l
in
v
a
ri
a
n
ts
sig
n
a
t
u
re
.
”
In
S
S
P
’0
7
:
IEE
E/
S
P
1
4
th
W
o
rk
sh
o
p
o
n
S
ta
ti
s
ti
c
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l
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l
Pro
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g
,
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6
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6
0
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a
d
iso
n
,
W
I,
USA
,
2
0
0
7
.
[1
3
]
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.
Ja
h
a
n
b
i
n
;
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C
h
o
i
;
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.
L
iu
,
A
.
C.
Bo
v
ik
,
“
T
h
re
e
d
ime
n
si
o
n
a
l
fa
c
e
re
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g
n
it
io
n
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si
n
g
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g
e
o
d
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sic
a
n
d
iso
-
d
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p
t
h
c
u
rv
e
s,”
In
B
T
AS
’0
8
:
Pro
c
e
e
d
in
g
s
o
f
t
h
e
IEE
E
S
e
c
o
n
d
I
n
t
e
rn
a
ti
o
n
a
l
Co
n
fer
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n
c
e
o
n
Bi
o
me
trics
T
h
e
o
ry
,
Ap
p
li
c
a
ti
o
n
s
a
n
d
S
y
ste
ms
,
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rli
n
g
to
n
,
V
i
rg
in
ia,
USA
,
2
0
0
8
.
[1
4
]
X
.
Ha
n
;
H.
Ug
a
il
;
I.
P
a
lm
e
r
,
“
M
e
th
o
d
o
f
Ch
a
ra
c
terisin
g
3
D
F
a
c
e
s
Us
in
g
G
a
u
ss
ian
Cu
rv
a
tu
re
,
”
In
IE
EE
,
2
0
0
9
.
[1
5
]
H.
d
rira
;
B.
Be
n
Am
o
r;
A
.
S
riv
a
st
a
v
a
;
M
.
D
a
o
u
d
i
,
“
A
Ri
e
ma
n
n
ia
n
An
a
lys
is
o
f
3
D No
se
S
h
a
p
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s F
o
r P
a
rtia
l
Hu
m
a
n
Bi
o
me
trics
,
”
In
1
2
th
In
ter
n
a
ti
o
n
a
l
Co
n
fer
e
n
c
e
o
n
C
o
mp
u
ter
Vi
sio
n
(
ICCV),
IEE
E,
2
0
0
9
.
[1
6
]
A
.
M
a
a
lej;
B.
B
e
n
Am
o
r;
M
.
Da
o
u
d
i;
A
.
S
riv
a
sta
v
a
;
S
.
Be
rre
tt
i
,
“
L
o
c
a
l
3
D
S
h
a
p
e
An
a
lys
is
fo
r
Fa
c
ia
l
Exp
re
ss
io
n
Rec
o
g
n
it
io
n
,
”
I
n
IE
EE
,
I
n
ter
n
a
ti
o
n
a
l
C
o
n
fer
e
n
c
e
o
n
P
a
tt
e
rn
Rec
o
g
n
it
io
n
,
2
0
1
0
.
[1
7
]
Bro
n
ste
in
A
.
M
;
,
Bro
n
ste
in
M
.
M
.
;
,
Kim
m
e
l
R.
,
“
Th
re
e
d
i
m
e
n
si
o
n
a
l
f
a
c
e
re
c
o
g
n
it
io
n
,
”
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ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
Co
mp
u
ter
V
isio
n
,
v
o
l.
6
4
,
n
o
.
1
,
p
p
.
5
–
3
0
,
2
0
0
5
.
[1
8
]
C.
X
u
;
Y.
W
a
n
g
;
T
.
Tan
;
L
.
Qu
a
n
,
“
Ro
b
u
st
n
o
se
d
e
tec
ti
o
n
in
3
D
fa
c
ia
l
d
a
ta
u
sin
g
lo
c
a
l
c
h
a
ra
c
te
ristics
,
”
Ima
g
e
Pro
c
e
ss
in
g
,
ICIP
'
0
4
.
2
0
0
4
I
n
ter
n
a
ti
o
n
a
l
Co
n
fe
re
n
c
e
o
n
,
v
o
l.
3
,
p
p
.
1
9
9
5
-
1
9
9
8
,
2
0
0
4
.
[1
9
]
L
.
H.
A
n
u
a
r;
S
.
M
a
sh
o
h
o
r;
M
.
M
o
k
h
tar;
W
.
A
.
W
a
n
A
d
n
a
n
,
“
No
se
T
ip
Re
g
io
n
De
tec
ti
o
n
i
n
3
D
F
a
c
ial
M
o
d
e
l
a
c
ro
ss
L
a
r
g
e
P
o
se
V
a
riatio
n
a
n
d
F
a
c
ial
Ex
p
re
ss
io
n
,
”
IJ
CS
I
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
Co
mp
u
ter
S
c
ien
c
e
Iss
u
e
s
,
v
o
l.
7
,
Is
s
u
e
4
,
n
o
.
4
,
Ju
ly
2
0
1
0
.
[2
0
]
S
.
Ja
h
a
n
b
i
n
;
H.
Ch
o
i;
Y.
L
iu
;
A.
C.
Bo
v
ik
,
“
T
h
re
e
Dim
e
n
sio
n
a
l
Fa
c
e
Rec
o
g
n
it
io
n
Us
in
g
Iso
-
Ge
o
d
e
sic
a
n
d
Iso
-
De
p
th
Cu
rv
e
s,”
Bio
m
e
tri
c
s:
T
h
e
o
ry
,
A
p
p
li
c
a
ti
o
n
s
a
n
d
S
y
ste
m
s
,
2
0
0
8
.
BT
A
S
2
0
0
8
,
2
n
d
IE
E
E
In
tern
a
ti
o
n
a
l
Co
n
f
e
re
n
c
e
o
n
,
2
0
0
8
.
S
S
IA
I
2
0
0
8
,
p
p
.
1
-
6
,
S
e
p
t.
2
9
2
0
0
8
-
Oc
t.
1
2
0
0
8
.
[2
1
]
A
.
S
a
li
m
a
;
S
.
S
a
li
m
;
T
.
A
.
A
b
d
e
l
m
a
li
k
,
“
A
S
u
rv
e
y
o
f
A
p
p
ro
a
c
h
e
s
f
o
r
Cu
rv
e
Ba
se
d
F
a
c
ial
S
u
rf
a
c
e
Re
p
re
se
n
tatio
n
s
F
o
r
T
h
re
e
-
Dim
e
n
sio
n
a
l
F
a
c
e
Re
c
o
g
n
it
io
n
.
”
[2
2
]
R.
Ki
m
m
e
l;
J.
A
.
S
e
th
ian
,
“
Co
mp
u
ti
n
g
g
e
o
d
e
sic
o
n
ma
n
if
o
ld
s,”
i
n
Pro
c
.
US
Na
ti
o
n
a
l
Aca
d
e
my
o
f
S
c
ien
c
e
,
v
o
l.
9
5
,
p
p
.
8
4
3
1
–
8
4
3
5
,
1
9
9
8
.
[2
3
]
X
a
v
ier
De
sq
u
e
sn
e
s;
A
b
d
e
rra
h
im
El
m
o
a
taz
;
Oliv
ier
Léz
o
ra
y
,
”
Ei
k
o
n
a
l
e
q
u
a
ti
o
n
a
d
a
p
tatio
n
o
n
w
e
ig
h
ted
g
ra
p
h
s:
f
a
st
g
e
o
m
e
tri
c
d
iff
u
sio
n
p
ro
c
e
ss
f
o
r
l
o
c
a
l
a
n
d
n
o
n
-
lo
c
a
l
im
a
g
e
a
n
d
d
a
t
a
p
ro
c
e
ss
in
g
,
”
J
o
u
rn
a
l
o
f
M
a
th
e
ma
ti
c
a
l
Ima
g
i
n
g
a
n
d
Vi
si
o
n
4
6
,
v
o
l
.
2
,
p
p
.
2
3
8
-
2
5
7
,
2
0
1
4
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
-
I
C
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I
SS
N:
2252
-
8776
Geo
d
esic D
is
ta
n
ce
o
n
R
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Ma
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s
…
(
R
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id
)
19
[2
4
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Ca
rli
n
i,
E.
;
F
a
lco
n
e
;
M
.
,
F
o
rc
a
d
e
l;
N.,
M
o
n
n
e
a
u
,
“
R.
:
Co
n
v
e
rg
e
n
c
e
o
f
a
g
e
n
e
ra
li
z
e
d
f
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st
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m
a
rc
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in
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m
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f
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ik
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n
a
l
e
q
u
a
ti
o
n
w
it
h
a
v
e
lo
c
it
y
-
c
h
a
n
g
in
g
sig
n
,
”
S
IAM
J
.
N
u
me
r.
A
n
a
l
.
4
6
,
pp.
2
9
2
0
–
2
9
5
2
,
2
0
0
8
.
[2
5
]
F
ra
n
k
B
.
ter
Ha
a
r;
M
o
h
a
m
e
d
D
a
o
u
d
i
;
Re
m
c
o
C
,
V
e
lt
k
a
m
p
:
S
Ha
p
e
REt
riev
a
l
Co
n
tes
t
2
0
0
8
:
3
D
F
a
c
e
S
c
a
n
s
.
“
S
h
a
p
e
M
o
d
e
li
n
g
a
n
d
Ap
p
li
c
a
ti
o
n
s,
2
0
0
8
.
S
M
I
2
0
0
8
.
IEE
E
In
ter
n
a
ti
o
n
a
l
Co
n
fer
e
n
c
e
o
n
,
4
-
6
Ju
n
e
2
0
0
8
.
[2
6
]
Brian
Am
b
e
rg
;
Re
in
h
a
rd
Kn
o
t
h
e
;
T
h
o
m
a
s
V
e
tt
e
r
,
“
S
HREC’
0
8
En
try
:
S
h
a
p
e
Ba
se
d
F
a
c
e
Rec
o
g
n
it
io
n
wit
h
a
M
o
rp
h
a
b
le
M
o
d
e
l
,
”
S
h
a
p
e
M
o
d
e
l
in
g
a
n
d
A
p
p
l
ica
ti
o
n
s,
2
0
0
8
.
S
M
I
2
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