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I
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C
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g
,
Vo
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10
,
No
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6
,
Dec
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b
er
2
0
2
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0
5
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0
6
0
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e
an
al
y
ze
d
.
2.
RE
S
E
ARCH
M
E
T
H
O
D
T
h
is
w
o
r
k
u
s
es
m
o
d
er
n
m
eth
o
d
s
o
f
i
m
a
g
e
p
r
o
ce
s
s
i
n
g
an
d
i
m
a
g
e
r
ec
o
g
n
itio
n
[
1
2
,
1
3
]
,
p
r
o
b
ab
ilit
y
th
eo
r
y
a
n
d
m
at
h
e
m
atica
l
s
ta
tis
tics
[
1
4
]
,
th
eo
r
y
o
f
elast
i
cit
y
,
m
eth
o
d
s
o
f
p
r
o
g
r
a
m
m
i
n
g
a
n
d
co
m
p
u
ter
s
i
m
u
lat
io
n
[
1
5
]
.
T
h
e
d
ef
o
r
m
at
io
n
o
f
th
e
f
i
n
g
er
p
r
in
t i
m
a
g
e
is
d
eter
m
in
ed
b
y
a
d
is
p
lace
m
e
n
t m
ap
,
w
h
ic
h
ca
n
b
e
in
ter
p
r
eted
as d
is
p
la
y
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n
g
o
n
e
i
m
ag
e
to
a
n
o
th
er
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m
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e:
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1
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er
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1
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m
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-
i
m
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g
es o
f
f
i
n
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er
p
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in
t
s
.
Nex
t,
w
e
u
s
e
th
e
r
ep
r
esen
tati
o
n
o
f
th
e
m
ap
(
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in
th
e
f
o
r
m
o
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a
d
is
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lace
m
e
n
t
m
ap
u
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tio
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e
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ap
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ciate
d
w
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is
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lace
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en
t
s
u
,
ca
n
b
e
r
ep
r
esen
ted
b
y
th
e
f
o
llo
w
i
n
g
e
x
p
r
ess
io
n
:
1
(
,
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=
−
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2
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,
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1
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2
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I
n
d
y
n
a
m
ics
as
s
h
o
w
n
i
n
F
ig
u
r
e
1
,
w
e
ca
n
ass
u
m
e
t
h
a
t
u
i
t
d
e
p
en
d
s
o
n
tim
e.
Su
p
p
o
s
e
th
at
a
f
in
g
er
p
r
in
t
is
an
elas
tic
o
b
ject.
T
h
en
its
d
y
n
a
m
ics
is
d
es
cr
ib
ed
b
y
t
h
e
f
o
llo
w
i
n
g
s
y
s
te
m
o
f
eq
u
atio
n
s
o
f
th
e
th
eo
r
y
o
f
elast
icit
y
:
+
+
=
2
2
;
+
+
=
2
2
(
3
)
=
;
=
;
=
=
1
2
(
+
)
(
4
)
w
h
er
e
u
x
a
n
d
u
y
–
co
m
p
o
n
e
n
t
s
o
f
th
e
d
i
s
p
lace
m
e
n
t
m
ap
alo
n
g
t
h
e
x
a
n
d
y
ax
e
s
r
esp
ec
ti
v
el
y
,
-
ac
tin
g
e
x
ter
n
al
f
o
r
ce
s
,
ɛ
-
ten
s
o
r
o
f
=
(
,
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ten
s
io
n
,
σ
-
p
r
ess
u
r
e
ten
s
o
r
,
ρ
th
e
d
en
s
it
y
.
C
o
m
p
o
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e
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ts
o
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ten
s
o
r
s
ɛ
an
d
σ
ar
e
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elate
d
b
y
a
li
n
ea
r
r
elatio
n
s
h
ip
:
(
)
=
(
,
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(
)
(
5
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So
lu
tio
n
s
o
f
eq
u
atio
n
s
ar
e
d
e
ter
m
i
n
ed
b
y
th
e
v
alu
e
s
o
f
th
e
elasticit
y
m
atr
ix
(
,
)
.
T
h
e
m
atr
ix
i
s
u
n
s
tab
le,
s
in
ce
th
e
s
u
r
f
ac
e
o
f
th
e
f
i
n
g
er
is
n
o
t
u
n
i
f
o
r
m
in
m
ec
h
an
ica
l
p
r
o
p
e
r
ties
.
Hete
r
o
g
en
eit
y
i
s
ass
o
ciate
d
w
it
h
v
ar
io
u
s
m
ec
h
a
n
is
m
s
o
f
d
ef
o
r
m
atio
n
u
n
d
er
th
e
ac
ti
o
n
o
f
f
o
r
ce
s
alo
n
g
an
d
ac
r
o
s
s
t
h
e
d
ir
ec
tio
n
o
f
th
e
p
ap
illar
y
p
atter
n
[
1
6
]
,
as
s
h
o
w
n
i
n
Fig
u
r
e
2
.
I
n
th
e
c
o
o
r
d
in
ates
ass
o
cia
ted
w
i
th
th
e
lo
ca
l
d
ir
ec
tio
n
o
f
th
e
p
ap
illar
y
p
atter
n
,
m
atr
ix
€
h
as f
o
u
r
d
eg
r
ee
s
o
f
f
r
ee
d
o
m
a
n
d
is
eq
u
al
to
1
:
€
(
,
)
=
(
−
1
−
−
1
0
−
−
1
−
1
0
0
0
)
;
−
1
=
−
/
−
1
(
6
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
Dev
elo
p
men
t m
o
d
elin
g
meth
o
d
s
o
f a
n
a
lysi
s
a
n
d
s
yn
th
esis
o
f
...
(
Ha
id
er Ha
s
s
a
n
Ma
jeed
A
l Ka
r
a
a
w
i)
6055
w
h
er
e
,
-
m
o
d
u
le
s
alo
n
g
an
d
ac
r
o
s
s
th
e
d
ir
ec
tio
n
f
ield
,
an
d
-
P
o
is
s
o
n
's r
atio
,
G
-
Sh
ea
r
m
o
d
u
lu
s
.
W
h
en
ch
a
n
g
i
n
g
to
t
h
e
o
r
ig
i
n
al
g
lo
b
al
co
o
r
d
in
ates (
6
)
.
Fig
u
r
e
1
.
T
h
e
p
r
o
ce
s
s
o
f
d
ef
o
r
m
ati
o
n
o
f
f
i
n
g
er
p
r
in
ts
(
s
cr
ee
n
ca
s
t)
Fig
u
r
e
2
.
Dir
ec
tio
n
o
f
th
e
f
lo
w
o
f
p
ap
illar
y
li
n
e
s
3.
RE
SU
L
T
S
A
ND
D
I
SCU
SS
I
O
N
I
n
f
i
n
g
er
p
r
in
t
id
en
t
if
icatio
n
t
h
e
m
ai
n
in
ter
est
i
s
th
e
m
o
m
en
t
o
f
i
m
a
g
e
ca
p
t
u
r
e
[
1
6
,
1
7
]
.
U
s
u
all
y
t
h
i
s
h
ap
p
en
s
,
w
h
e
n
th
e
i
m
a
g
e
is
s
ti
ll,
th
e
ac
tin
g
f
o
r
ce
s
h
a
v
e
alr
ea
d
y
b
alan
ce
d
th
e
te
n
s
io
n
,
ca
u
s
e
d
is
p
lace
m
e
n
t.
Su
c
h
a
co
n
d
itio
n
ca
n
b
e
w
r
itte
n
as t
h
e
f
o
llo
w
i
n
g
eq
u
atio
n
+
+
=
0
;
+
+
=
0
;
(
7
)
T
h
e
s
y
s
te
m
o
f
(
7
)
an
d
(
4
)
d
eter
m
in
e
s
t
h
e
d
ef
o
r
m
atio
n
o
f
t
h
e
f
i
n
g
er
p
r
in
t.
T
h
e
f
o
llo
w
i
n
g
d
if
f
icu
ltie
s
o
f
its
d
i
r
ec
t
s
o
lu
tio
n
ar
e
n
o
ted
.
First,
th
er
e
is
n
o
in
itial
s
tate
o
f
th
e
p
r
in
t,
f
r
o
m
w
h
ic
h
th
e
d
ef
o
r
m
atio
n
b
eg
i
n
s
.
First,
th
er
e
i
s
n
o
i
n
itial st
ate
o
f
th
e
p
r
in
t,
f
r
o
m
w
h
ic
h
th
e
d
e
f
o
r
m
atio
n
b
e
g
in
s
.
De
f
o
r
m
atio
n
i
s
a
co
n
s
eq
u
e
n
ce
o
f
th
e
p
r
o
ce
s
s
o
f
t
w
o
-
d
i
m
en
s
io
n
a
l
s
ca
n
n
in
g
o
f
a
t
h
r
ee
-
d
i
m
en
s
io
n
al
o
b
j
ec
t
s
ee
Fig
u
r
e
3
.
Seco
n
d
l
y
,
th
e
ac
ti
v
e
f
o
r
ce
s
ar
e
u
n
k
n
o
w
n
.
T
h
er
e
is
n
o
en
g
in
ee
r
in
g
w
a
y
to
m
ea
s
u
r
e
th
e
m
.
Fro
m
th
e
th
eo
r
y
o
f
elastic
it
y
,
it
is
k
n
o
w
n
t
h
at
th
e
s
o
l
u
tio
n
o
f
(
4
)
an
d
(
7
)
ca
n
b
e
s
o
u
g
h
t a
s
a
m
in
i
m
u
m
o
f
t
h
e
f
o
llo
w
i
n
g
en
er
g
y
f
u
n
c
tio
n
=
−
∬
(
+
)
+
1
2
∬
(
+
+
)
(
8
)
I
n
co
n
n
ec
tio
n
w
i
th
t
h
e
ab
o
v
e
-
m
en
t
io
n
ed
p
r
o
b
lem
o
f
t
h
e
in
ab
ilit
y
to
est
i
m
ate
th
e
e
f
f
ec
ti
v
e
f
o
r
ce
s
,
th
e
n
eg
a
tiv
e
ter
m
i
n
(
8
)
also
ca
n
n
o
t
b
e
d
i
r
ec
tly
ev
a
lu
ated
.
Fo
r
its
eli
m
in
at
io
n
,
a
m
et
h
o
d
o
f
ap
p
r
o
x
i
m
ate
d
ef
o
r
m
atio
n
ca
lc
u
latio
n
is
p
r
o
p
o
s
ed
.
Fo
r
tw
o
r
an
d
o
m
i
m
a
g
es
o
f
o
n
e
f
i
n
g
er
p
r
in
t,
w
il
l
tr
an
s
f
o
r
m
i
n
g
o
n
e
in
to
an
o
th
er
b
y
d
e
f
o
r
m
atio
n
,
y
o
u
ca
n
f
in
d
co
r
r
esp
o
n
d
in
g
to
ea
c
h
o
th
er
co
n
tr
o
l
p
o
in
t
s
o
f
t
h
e
i
m
ag
e
as
s
h
o
w
n
in
Fig
u
r
e
4
,
w
h
ich
g
i
v
es i
n
f
o
r
m
a
tio
n
o
n
th
e
g
e
n
er
al
d
ir
ec
tio
n
o
f
th
e
ac
t
in
g
f
o
r
ce
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
10
,
No
.
6
,
Dec
em
b
er
2
0
2
0
:
6
0
5
3
-
6
0
6
0
6056
Fig
u
r
e
3
.
T
h
e
ap
p
ea
r
an
ce
o
f
d
ef
o
r
m
atio
n
o
f
f
in
g
er
p
r
in
t
s
Fig
u
r
e
4
.
Ma
tch
in
g
f
i
n
g
er
p
r
in
t
ch
ec
k
p
o
in
t
s
T
h
e
s
ets
o
f
p
air
s
o
f
p
o
in
ts
co
r
r
esp
o
n
d
in
g
to
ea
ch
o
th
er
ar
e
d
e
n
o
ted
b
y
{
}
=
1
an
d
{
}
=
1
r
esp
ec
tiv
el
y
.
As a
m
ea
s
u
r
e
o
f
p
r
o
x
i
m
it
y
o
f
t
w
o
s
et
s
o
f
co
n
tr
o
l p
o
in
ts
,
t
h
e
m
ea
n
s
q
u
ar
e
er
r
o
r
2
(
)
=
1
∑
∥
+
(
)
−
∥
2
=
1
(
9
)
T
h
e
f
u
n
c
tio
n
al
(
9
)
is
q
u
alitati
v
el
y
co
r
r
elate
d
w
ith
t
h
e
w
o
r
k
o
f
th
e
ac
ti
n
g
f
o
r
ce
s
o
f
th
e
e
n
er
g
y
f
u
n
ctio
n
al
(
8
)
.
I
f
a
co
n
tr
o
l
p
o
in
t
s
h
i
f
t
o
cc
u
r
s
,
it
is
a
s
s
u
m
ed
th
a
t
ex
ter
n
al
f
o
r
ce
s
ac
t
in
th
e
d
ir
ec
tio
n
o
f
d
i
s
p
lace
m
e
n
t.
I
n
ad
d
itio
n
,
it
is
also
s
u
g
g
e
s
ted
th
at
th
e
d
ir
ec
tio
n
s
o
f
t
h
e
f
lu
x
e
s
o
f
th
e
p
ap
illar
y
lin
e
s
at
th
e
c
o
n
tr
o
l
p
o
in
ts
m
atc
h
w
it
h
t
h
e
f
o
llo
w
i
n
g
f
u
n
ctio
n
al
:
2
(
)
=
1
∑
∥
(
+
(
)
)
−
(
)
∥
2
=
1
(
1
0
)
w
h
er
e
n
-
f
u
n
ctio
n
a
l
o
f
tak
in
g
th
e
n
o
r
m
al
to
th
e
lo
ca
l
f
lo
w
o
f
p
ap
illa
r
y
lin
es.
W
ith
allo
w
an
ce
f
o
r
(
9
)
an
d
(
1
0
)
,
it
is
s
u
g
g
e
s
ted
to
s
ee
k
th
e
ap
p
r
o
x
i
m
ate
s
o
lu
tio
n
(
8
)
as
a
m
i
n
i
m
u
m
o
f
th
e
f
o
llo
w
i
n
g
f
u
n
ct
io
n
al,
co
n
s
i
s
ti
n
g
o
f
th
e
in
ter
n
al
e
n
er
g
y
o
f
d
ef
o
r
m
a
tio
n
an
d
r
eg
u
lar
izi
n
g
t
h
e
co
r
r
ec
tio
n
s
to
th
e
d
is
cr
ep
a
n
c
y
:
(
)
=
(
)
+
1
2
(
)
+
2
2
(
)
(
1
1
)
w
h
er
e
a
1
,
a
2
-
w
ei
g
h
t c
o
ef
f
ici
en
ts
,
i
n
ter
n
al
s
tr
ain
e
n
er
g
y
E
d
is
ca
lcu
lated
b
y
t
h
e
f
o
r
m
u
la.
=
1
2
∬
(
+
+
)
(
1
2
)
T
h
e
m
i
n
i
m
u
m
o
f
th
e
f
u
n
c
t
io
n
al
(
1
1
)
is
s
o
u
g
h
t
n
u
m
er
icall
y
b
y
t
h
e
f
i
n
ite
ele
m
e
n
t
m
et
h
o
d
.
T
h
e
d
is
p
lace
m
en
t m
ap
i
s
s
p
ec
i
f
ied
b
y
v
al
u
es
i
n
a
r
ec
ta
n
g
u
lar
g
r
id
.
Fo
r
p
o
in
ts
w
it
h
i
n
a
g
r
id
ele
m
e
n
t,
t
h
e
v
al
u
e
s
u
ar
e
in
ter
p
o
lated
b
y
b
ili
n
ea
r
s
p
lin
e
s
.
W
ith
s
u
ch
i
n
ter
p
o
lati
o
n
(
1
1
)
is
a
q
u
ad
r
atic
f
u
n
ct
io
n
al
o
f
t
h
e
v
al
u
e
s
at
th
e
latt
ice
s
ite
s
.
T
h
u
s
,
th
e
m
i
n
i
m
u
m
i
s
s
o
u
g
h
t
f
r
o
m
th
e
co
n
d
itio
n
t
h
at
al
l
p
ar
tial
d
er
iv
ativ
e
s
v
a
n
i
s
h
.
T
h
is
co
n
d
itio
n
is
a
li
n
ea
r
eq
u
a
tio
n
f
o
r
th
e
v
al
u
es
u
i
n
t
h
e
latt
ice
s
ites
.
T
h
e
d
ev
elo
p
ed
alg
o
r
ith
m
o
f
t
h
e
s
o
lu
tio
n
q
u
ick
l
y
co
n
v
er
g
e
s
.
On
a
v
er
ag
e,
th
e
ca
lcu
latio
n
o
f
t
h
e
r
elati
v
e
d
ef
o
r
m
atio
n
tak
e
s
les
s
th
a
n
0
.
1
s
.
E
x
am
p
les
o
f
th
e
r
esu
lts
o
f
d
e
f
o
r
m
atio
n
ca
l
cu
latio
n
s
ar
e
s
h
o
w
n
in
Fig
u
r
e
5
.
Fro
m
th
e
p
o
in
t
o
f
v
ie
w
o
f
th
e
r
esear
ch
tas
k
s
,
th
e
o
p
ti
m
a
l
r
es
u
lt
i
s
to
f
in
d
a
d
ef
o
r
m
atio
n
t
h
at
tr
a
n
s
late
s
o
n
e
i
m
a
g
e
o
f
th
e
p
r
i
n
t
i
n
to
an
o
t
h
er
i
m
a
g
e
o
f
th
e
s
a
m
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
Dev
elo
p
men
t m
o
d
elin
g
meth
o
d
s
o
f a
n
a
lysi
s
a
n
d
s
yn
th
esis
o
f
...
(
Ha
id
er Ha
s
s
a
n
Ma
jeed
A
l Ka
r
a
a
w
i)
6057
p
r
in
t.
T
h
er
ef
o
r
e,
as
o
n
e
o
f
t
h
e
esti
m
ates
o
f
th
e
ac
cu
r
ac
y
o
f
d
ef
o
r
m
atio
n
ca
lcu
latio
n
,
d
ir
ec
t
o
v
er
lap
is
u
s
ed
Im
av
i
m
ag
e
s
:
=
1
2
(
2
+
(
1
)
)
(
1
3
)
E
x
a
m
p
le
s
o
f
s
u
p
er
p
o
s
itio
n
w
i
th
allo
w
an
ce
f
o
r
th
e
d
ef
o
r
m
at
io
n
o
p
ti
m
al
f
o
r
(
1
1
)
in
co
m
p
a
r
is
o
n
w
it
h
th
e
o
p
ti
m
al
m
o
tio
n
ar
e
s
h
o
w
n
i
n
Fi
g
u
r
e
5
.
T
h
e
co
n
tr
ast
p
ar
t
o
f
th
e
r
esu
lts
o
f
s
u
p
er
p
o
s
itio
n
in
d
icate
s
th
e
r
eso
n
a
n
ce
o
f
th
e
p
ap
illar
y
lin
es.
T
h
e
g
r
a
y
p
ar
t
co
r
r
esp
o
n
d
s
to
in
ac
cu
r
ate
g
u
id
a
n
ce
.
I
t
ca
n
b
e
s
ee
n
f
r
o
m
th
e
f
ig
u
r
e
th
at
t
h
e
p
r
o
p
o
s
ed
m
o
d
el
allo
w
s
t
h
e
i
m
a
g
e
o
f
f
i
n
g
e
r
p
r
in
ts
to
b
e
ac
cu
r
atel
y
co
n
v
er
ted
in
to
ea
ch
o
th
er
w
it
h
h
i
g
h
ac
cu
r
ac
y
.
T
h
er
e
ar
e
n
o
ed
g
e
ef
f
ec
ts
ch
ar
ac
ter
is
tic
o
f
em
p
ir
ical
d
ef
o
r
m
atio
n
m
o
d
els
b
ased
o
n
a
th
in
m
etal
p
late2
o
r
th
e
C
ap
p
elli
et
al
.,
3
m
o
d
el.
A
ls
o
,
t
h
e
ad
v
an
ta
g
e
s
o
f
t
h
e
m
o
d
el
i
n
cl
u
d
e
th
e
p
o
s
s
ib
ilit
y
o
f
ca
lcu
lati
n
g
th
e
r
elativ
e
s
tr
ain
f
o
r
ar
b
itra
r
y
d
ac
t
y
lo
s
co
p
y
i
m
a
g
es
f
o
r
w
h
ic
h
t
h
e
co
r
r
esp
o
n
d
in
g
r
ef
er
e
n
ce
p
o
in
ts
ca
n
b
e
f
o
u
n
d
,
an
d
f
o
r
p
r
esen
ti
n
g
v
ar
io
u
s
f
i
n
g
er
p
r
in
ts
[
1
8
]
.
(
a)
(
b
)
(
c)
(
d
)
Fig
u
r
e
5
.
E
x
a
m
p
le
o
f
ca
lc
u
lati
o
n
o
f
th
e
d
ef
o
r
m
atio
n
(
a)
,
(
b
)
t
w
o
i
m
ag
e
s
o
f
t
h
e
p
r
in
t,
(
c)
d
ir
ec
t o
v
er
lap
w
h
e
n
f
itti
n
g
b
y
h
ar
d
m
o
tio
n
,
(
d
)
d
ir
ec
t o
v
er
lap
a
f
ter
f
itti
n
g
th
e
d
ef
o
r
m
ati
o
n
T
h
e
co
n
d
u
cted
s
tatis
tical
a
n
al
y
s
is
also
co
n
f
ir
m
s
th
a
t
th
e
p
r
o
p
o
s
ed
elastic
m
o
d
el
s
i
g
n
i
f
ica
n
tl
y
i
m
p
r
o
v
e
s
th
e
ac
cu
r
ac
y
o
f
i
m
a
g
e
g
u
id
an
c
e
in
co
m
p
ar
is
o
n
w
it
h
k
n
o
w
n
m
o
d
el
s
.
As
an
o
b
j
ec
tiv
e
cr
iter
io
n
f
o
r
th
e
ac
cu
r
ac
y
o
f
m
o
d
elin
g
t
h
e
p
r
o
ce
s
s
o
f
d
ef
o
r
m
atio
n
o
f
f
in
g
er
p
r
in
ts
,
t
h
e
d
ir
ec
t
im
p
o
s
itio
n
(
co
r
r
elatio
n
)
co
ef
f
icie
n
t
f
o
r
b
in
a
r
ized
f
i
n
g
er
p
r
in
t
i
m
a
g
es
is
u
s
ed
[
1
9
]
.
DE
T
cu
r
v
es
o
f
th
e
co
e
f
f
icien
t
o
f
d
ir
ec
t
o
v
er
lap
f
o
r
th
e
b
as
e
FVC
2
0
0
2
DB
1
(
m
o
d
er
ate
d
ef
o
r
m
at
io
n
)
an
d
FV
C
2
0
0
4
DB
1
(
s
ig
n
i
f
ican
t
d
ef
o
r
m
atio
n
s
)
ar
e
s
h
o
w
n
in
Fig
u
r
e
6
.
As ca
n
b
e
s
ee
n
f
r
o
m
t
h
e
f
ig
u
r
e,
th
e
p
r
o
p
o
s
ed
elastic
m
o
d
e
l
s
ig
n
i
f
ica
n
tl
y
i
m
p
r
o
v
e
s
t
h
e
i
m
p
o
s
itio
n
o
f
i
m
ag
e
s
i
n
co
m
p
ar
is
o
n
w
it
h
th
e
r
i
g
id
m
o
t
io
n
an
d
d
ef
o
r
m
atio
n
m
o
d
eli
n
g
b
y
t
h
e
T
P
S m
et
h
o
d
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
10
,
No
.
6
,
Dec
em
b
er
2
0
2
0
:
6
0
5
3
-
6
0
6
0
6058
──
o
p
tim
a
l
m
o
v
e
m
e
n
t
─◊─
ac
co
u
n
ti
n
g
f
o
r
d
ef
o
r
m
at
i
o
n
s
(
m
o
d
el
T
P
S)
─□─
ac
co
u
n
t
in
g
f
o
r
d
ef
o
r
m
a
ti
o
n
s
(
elastic
m
o
d
el)
Fig
u
r
e
6
.
DE
T
o
f
th
e
d
ir
ec
t o
v
er
lap
f
ac
to
r
(
FVC
2
0
0
2
DB
1
)
a
n
d
(
FVC
2
0
0
4
DB
1
)
I
n
th
i
s
s
tu
d
y
d
e
v
o
ted
to
m
eth
o
d
s
o
f
an
al
y
s
i
s
an
d
s
y
n
t
h
esi
s
o
f
d
ef
o
r
m
atio
n
s
o
f
f
i
n
g
er
p
r
in
t
s
.
T
o
d
eter
m
i
n
e
th
e
d
ef
o
r
m
atio
n
s
tr
u
ct
u
r
e,
an
an
al
y
s
is
w
as
m
ad
e
o
f
th
e
n
u
m
er
ica
l
s
o
lu
t
io
n
s
o
f
(
9
)
o
n
p
u
b
licl
y
av
ailab
le
f
in
g
e
r
p
r
in
t
d
atab
ase
s
.
Sin
ce
(
8
)
is
li
n
ea
r
,
it
s
s
o
l
u
tio
n
s
(
d
ef
o
r
m
atio
n
s
)
ca
n
b
e
ad
d
ed
an
d
m
u
ltip
lied
b
y
a
n
u
m
b
er
.
Fo
r
d
ef
o
r
m
atio
n
s
,
o
p
er
atio
n
s
o
f
t
h
e
s
ca
lar
p
r
o
d
u
ct
an
d
p
r
o
j
ec
tio
n
o
n
to
ea
ch
o
th
e
r
ar
e
also
d
ef
in
ed
.
T
h
er
ef
o
r
e,
it
is
p
r
o
p
o
s
ed
to
s
tu
d
y
t
h
e
s
tr
u
ct
u
r
e
o
f
d
ef
o
r
m
atio
n
s
b
y
lin
ea
r
ex
p
a
n
s
io
n
in
ter
m
s
o
f
an
"
o
r
th
o
n
o
r
m
a
l"
s
et
o
f
b
asis
d
e
f
o
r
m
atio
n
s
[
2
0
]
.
B
asic
d
ef
o
r
m
atio
n
s
ca
n
b
e
ca
lcu
lated
b
o
th
f
r
o
m
q
u
al
itati
v
e
co
n
s
id
er
atio
n
s
,
an
d
th
r
o
u
g
h
f
o
r
m
al
s
tatis
t
ical
an
al
y
s
is
.
B
ased
o
n
t
h
e
e
x
p
a
n
s
io
n
(
1
3
)
,
an
ap
p
r
o
x
im
ate
li
n
ea
r
m
o
d
el
is
d
ev
e
lo
p
ed
.
C
o
ef
f
icie
n
t
s
c
i
ar
e
ca
lcu
lated
b
y
m
in
i
m
iz
in
g
t
h
e
d
is
cr
ep
an
c
y
(
9
)
a
n
d
(1
0
).
As
b
asic
d
ef
o
r
m
at
io
n
s
,
it
i
s
s
u
g
g
e
s
ted
to
u
s
e
th
e
"
p
r
in
cip
al"
d
ef
o
r
m
at
io
n
s
o
b
tain
ed
b
y
t
h
e
m
ai
n
co
m
p
o
n
en
t
m
et
h
o
d
o
n
th
e
r
e
f
er
en
ce
f
i
n
g
er
p
r
in
t
ar
r
ay
[
2
1
,
2
2
]
.
T
o
ca
lcu
late
t
h
e
m
ain
co
m
p
o
n
e
n
ts
,
th
r
ee
F
VC
2
0
0
2
d
atab
ases
w
er
e
u
s
ed
,
co
n
tain
i
n
g
i
m
a
g
es
f
r
o
m
o
p
tical
an
d
ca
p
ac
itiv
e
f
in
g
er
p
r
in
t
s
ca
n
n
er
s
[
2
3
,
2
4
]
.
E
ac
h
d
atab
ase
co
n
tain
s
8
s
a
m
p
les
f
o
r
1
0
0
p
eo
p
le,
i.e
.
f
o
r
th
e
an
a
l
y
s
is
o
f
d
ef
o
r
m
i
ties
,
th
er
e
ar
e
th
r
ee
s
et
s
o
f
2
8
0
0
n
atu
r
a
l
d
ef
o
r
m
atio
n
s
o
f
f
i
n
g
er
p
r
in
ts
i
n
to
tal
[
2
5
,
2
6
]
.
I
n
Fi
g
u
r
e
7
s
h
o
w
s
t
h
e
f
ir
s
t
f
o
u
r
b
asic
d
ef
o
r
m
atio
n
s
o
b
tain
ed
b
y
t
h
e
p
r
in
cip
al
co
m
p
o
n
e
n
t
m
eth
o
d
.
T
h
ey
allo
w
a
p
h
y
s
ical
in
ter
p
r
etatio
n
(
t
w
o
t
y
p
es
o
f
r
o
tatio
n
an
d
t
w
o
s
h
i
f
t
s
)
s
ee
F
ig
u
r
e
8
.
Su
c
h
d
ef
o
r
m
atio
n
s
co
r
r
esp
o
n
d
to
th
e
s
u
b
j
ec
tiv
e
co
n
ce
p
t
o
f
th
e
m
ain
w
a
y
s
o
f
ap
p
ly
i
n
g
a
f
i
n
g
er
to
th
e
s
ca
n
n
er
.
I
n
ad
d
itio
n
to
th
e
q
u
alitati
v
e
an
al
y
s
is
o
f
d
ef
o
r
m
atio
n
s
,
a
n
u
m
b
er
o
f
f
o
r
m
al
cr
iter
ia
f
o
r
th
e
ac
cu
r
ac
y
o
f
th
e
d
ef
o
r
m
a
t
io
n
ap
p
r
o
x
im
a
tio
n
w
er
e
co
n
s
id
er
ed
,
w
h
ic
h
s
h
o
w
ed
a
r
ath
er
h
i
g
h
ac
cu
r
ac
y
o
f
t
h
e
li
n
ea
r
d
ef
o
r
m
atio
n
m
o
d
el.
T
h
e
f
ir
s
t
8
-
1
0
m
ain
co
m
p
o
n
en
ts
p
r
o
v
id
e
a
s
u
f
f
icie
n
tl
y
ac
cu
r
a
te
ap
p
r
o
x
im
at
io
n
o
f
t
h
e
o
b
s
er
v
ed
s
tr
ain
s
f
o
r
an
y
o
f
th
e
ab
o
v
e
ac
cu
r
a
c
y
cr
iter
ia.
A
t
th
e
s
a
m
e
ti
m
e
,
th
e
m
ain
co
m
p
o
n
e
n
t
s
o
b
tain
ed
ar
e
p
r
ac
tically
in
d
ep
en
d
en
t
o
f
t
h
e
f
in
g
er
p
r
in
t a
r
r
ay
c
h
o
s
e
n
f
o
r
an
a
l
y
s
is
[
2
7
,
28]
.
Dif
f
er
en
ce
s
in
th
e
n
at
u
r
e
o
f
th
e
d
e
f
o
r
m
atio
n
s
ar
e
in
th
e
v
ar
io
u
s
o
b
s
er
v
ed
d
is
tr
ib
u
tio
n
s
o
f
t
h
e
co
ef
f
icie
n
ts
c
i
o
f
th
e
ex
p
a
n
s
io
n
(
1
2
).
Fro
m
th
e
d
ata
o
b
tain
ed
,
in
p
ar
ticu
lar
,
th
e
f
o
llo
w
i
n
g
co
n
clu
s
io
n
s
w
er
e:
T
h
e
s
tatis
tical
p
r
o
p
er
ties
o
f
n
atu
r
al
d
ef
o
r
m
at
io
n
s
ar
e
p
r
ac
ticall
y
in
d
ep
en
d
en
t
o
f
t
h
e
t
y
p
e
o
f
s
ca
n
n
er
m
o
d
el
(
ca
s
es
a
an
d
b
)
.
S
y
n
th
e
tic
d
ef
o
r
m
atio
n
s
o
b
tain
ed
b
y
m
et
h
o
d
s
k
n
o
w
n
in
th
e
p
ast
d
if
f
er
in
th
e
ir
ch
ar
ac
ter
is
tics
(
c)
.
A
ls
o
,
th
e
q
u
a
n
titati
v
e
d
if
f
er
en
ce
b
et
w
ee
n
th
e
d
ef
o
r
m
atio
n
s
in
th
e
r
o
llin
g
o
f
a
p
r
in
t
an
d
t
h
e
d
ef
o
r
m
atio
n
i
n
elec
tr
o
n
ic
s
ca
n
n
i
n
g
(
liv
e
s
ca
n
)
is
es
tab
lis
h
e
d
.
T
h
en
d
ea
ls
w
ith
th
e
ap
p
licatio
n
o
f
t
h
e
d
ev
elo
p
ed
m
et
h
o
d
s
o
f
an
al
y
s
is
an
d
s
y
n
th
e
s
is
o
f
d
ef
o
r
m
atio
n
s
t
o
r
ea
l
p
r
o
b
lem
s
o
f
f
i
n
g
er
p
r
in
t
id
e
n
ti
f
icatio
n
:
S
y
n
t
h
esi
s
o
f
ar
ti
f
icial
d
ef
o
r
m
atio
n
s
o
f
f
in
g
er
p
r
in
ts
a
n
d
s
y
n
th
e
s
is
o
f
"
n
o
t
-
d
ef
o
r
m
ed
"
f
in
g
er
p
r
in
t
t
o
in
c
r
e
ase
th
e
ac
cu
r
a
cy
o
f
f
in
g
e
r
p
r
in
t
i
d
en
tif
ic
ati
o
n
[
2
9
]
.
T
h
e
cr
ea
t
io
n
o
f
a
"
n
o
t
-
d
ef
o
r
m
ed
"
av
e
r
ag
e
d
im
ag
e
f
r
o
m
s
ev
e
r
al
f
in
g
e
r
p
r
in
ts
is
a
s
p
e
cia
l
ca
s
e
o
f
th
e
s
y
n
th
esis
o
f
ar
tif
ici
al
d
ef
o
r
m
atio
n
.
L
et
th
e
r
e
b
e
k
+
1
im
ag
es:
Im
0
,
I
m
1
,
….
I
m
k
.
R
ela
tiv
e
d
ef
o
r
m
atio
n
s
Im
i
in
Im
0
ar
e
d
en
o
t
e
d
b
y
u
i
.
T
w
o
a
p
p
r
o
ac
h
es
t
o
th
e
s
y
n
th
esis
o
f
m
ea
n
s
t
r
ain
ar
e
co
n
s
i
d
er
ed
.
T
h
e
f
i
r
s
t
is
t
o
f
o
r
m
all
y
ca
l
cu
lat
e
th
e
av
e
r
ag
e
d
is
p
la
ce
m
en
t m
ap
u
av
:
T
h
e
av
er
ag
e
i
m
a
g
e
i
s
d
eter
m
i
n
ed
as
Im
av
=u
av
(
I
m
0)
.
T
h
e
s
ec
o
n
d
ap
p
r
o
ac
h
is
to
ca
lcu
late
t
h
e
s
tate
o
f
th
e
p
r
in
t,
i
n
w
h
ich
t
h
e
i
n
tr
i
n
s
ic
en
er
g
y
o
f
t
h
e
d
ef
o
r
m
atio
n
s
to
th
e
i
m
a
g
e
s
f
r
o
m
th
e
co
lle
ctio
n
w
as
m
i
n
i
m
al:
T
h
e
av
er
ag
e
f
o
r
t
h
is
co
n
d
it
io
n
is
d
ef
i
n
ed
as
Im
m
i
n
=u
m
i
n
(
I
m
0)
.
T
h
e
r
esu
ltin
g
"
n
o
t
-
d
e
f
o
r
m
ed
"
im
a
g
e
is
u
s
ed
to
in
cr
ea
s
e
th
e
ac
cu
r
ac
y
o
f
id
en
t
i
f
icatio
n
.
W
h
en
r
eg
is
ter
i
n
g
o
n
th
e
b
asis
o
f
s
ev
er
al
f
i
n
g
er
p
r
in
t
s
,
th
e
av
er
ag
e
s
tate
is
ca
lcu
la
ted
s
h
o
w
n
Fi
g
u
r
e
9
.
T
h
e
s
o
lu
tio
n
(
1
2
)
d
ep
en
d
s
o
n
ly
o
n
t
h
e
m
u
t
u
al
ar
r
an
g
e
m
e
n
t
o
f
co
n
tr
o
l
p
o
in
ts
i
n
v
ar
io
u
s
ap
p
licatio
n
s
o
f
th
e
f
i
n
g
er
.
T
h
er
ef
o
r
e,
th
e
n
o
t
-
d
ef
o
r
m
ed
s
tate
ca
n
b
e
ca
lcu
lated
n
o
t
o
n
ly
f
o
r
th
e
i
m
a
g
e
o
f
th
e
f
i
n
g
er
p
r
in
t,
b
u
t
al
s
o
f
o
r
th
e
f
in
g
er
p
r
in
t
te
m
p
late.
T
h
u
s
,
th
e
s
y
n
t
h
esi
s
o
f
t
h
e
"
n
o
t
-
d
e
f
o
r
m
ed
"
s
tate
ca
n
b
e
in
tr
o
d
u
ce
d
in
to
f
u
n
ctio
n
in
g
au
to
m
atic
d
ac
t
y
lo
s
co
p
ic
v
er
if
ica
tio
n
an
d
id
en
ti
f
icat
io
n
s
y
s
te
m
s
[
3
0
,
3
1
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
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lec
&
C
o
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p
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I
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N:
2
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(
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6059
(
a)
(
b
)
(
c)
(
d
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Fig
u
r
e
7
.
Ma
p
o
f
th
e
d
is
p
lace
m
en
ts
o
f
t
h
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m
ain
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e
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t f
in
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p
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r
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c
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d
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r
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s
h
i
f
ts
(
a)
(
b
)
(
c)
(
d
)
Fig
u
r
e
8
.
Sch
e
m
atic
r
ep
r
esen
t
atio
n
o
f
t
h
e
m
ai
n
d
ef
o
r
m
atio
n
s
,
"
H
"
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r
elativ
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y
f
i
x
ed
ar
ea
,
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e
ar
r
o
w
i
n
d
icate
s
th
e
m
a
in
d
ir
ec
tio
n
s
o
f
d
is
p
lace
m
en
t
,
(a
)
,
(
b
)
d
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o
r
m
atio
n
r
o
tatio
n
,
(
c
)
,
(
d
)
d
ef
o
r
m
atio
n
s
h
i
f
t
s
Fig
u
r
e
9
.
Av
er
ag
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ef
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m
ati
o
n
f
i
n
g
er
p
r
in
t i
m
a
g
e
(
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m
m
in
)
4.
CO
NCLU
SI
O
N
A
m
o
d
el
o
f
elastic
f
i
n
g
er
p
r
in
t
d
ef
o
r
m
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n
s
b
ased
o
n
th
e
p
ic
tu
r
e
o
f
th
e
p
r
in
t
as
an
a
n
is
o
tr
o
p
ic
elastic
m
ater
ial
i
s
s
u
g
g
ested
ta
k
i
n
g
in
to
co
n
s
id
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n
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e
h
eter
o
g
en
ei
t
y
o
f
f
i
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p
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t
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h
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n
ical
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r
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ties
i
n
th
e
s
e
n
s
e
o
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t
h
e
lo
ca
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j
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ti
o
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o
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th
e
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ef
o
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m
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n
d
ir
ec
tio
n
in
t
h
e
lo
ca
l
d
ir
ec
tio
n
o
f
t
h
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ap
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y
li
n
e
f
lo
w
s
.
An
ap
p
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m
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te
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o
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ith
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s
h
a
v
e
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ee
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ed
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o
r
f
i
n
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er
p
r
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t
d
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o
r
m
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n
ca
lcu
latio
n
s
b
a
s
ed
o
n
s
o
lu
tio
n
o
f
elastic
d
ef
o
r
m
a
tio
n
eq
u
atio
n
s
t
h
at
h
elp
th
e
m
ec
h
an
ica
l
ch
ar
ac
ter
is
tic
s
o
f
f
in
g
er
p
r
in
ts
.
Me
th
o
d
s
ar
e
b
u
ilt
f
o
r
th
e
s
tu
d
y
an
d
s
y
n
t
h
esi
s
o
f
f
i
n
g
er
p
r
in
t
i
m
ag
e
d
ef
o
r
m
atio
n
s
b
ased
o
n
th
e
ex
p
an
s
i
o
n
o
f
d
ef
o
r
m
at
io
n
s
b
y
m
aj
o
r
ty
p
es o
f
ap
p
lied
f
o
r
c
e
(
d
ef
o
r
m
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n
m
o
v
e
m
e
n
ts
a
n
d
r
o
tatio
n
s
)
.
A
f
ea
tu
r
e
s
y
s
te
m
h
as b
ee
n
d
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