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2848
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ma
g
e
s
a
nd
c
o
m
p
ut
i
ng b
o
t
h t
he
m
e
a
n a
nd
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t
s
co
v
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a
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ce
m
at
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i
x
.
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h
e ei
g
en
v
ect
o
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s
o
f
t
h
e co
v
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i
a
n
ce
m
at
r
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x
ar
e o
b
t
ai
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ed
b
y
ei
g
e
n
v
al
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e d
eco
m
p
o
s
i
t
i
o
n
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n
o
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er
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ed
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ce t
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e d
i
m
e
n
s
i
o
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al
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h
e s
p
ace,
i
n
p
r
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p
al
co
m
p
o
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e
n
t
an
al
y
s
i
s
(
P
C
A
)
[
4
]
-
[
6]
on
l
y
ei
g
en
v
ec
t
or
s
a
r
e
k
e
pt
,
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or
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pon
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C
C
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V
(
cl
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n
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r
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s
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t
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ons
,
e
.
g
.
,
176x
120,
or
35
2x
240,
or
704x
4
8
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p
ix
e
ls
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n
th
e
lo
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di
um
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on r
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1280x
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108
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x
e
l
s
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hi
g
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[
7
]
.
A
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w
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s
i
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v
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m
at
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x
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s
2
1
1
2
0
x
2
1
1
20
.
W
hi
l
e
c
o
m
p
ut
a
t
i
o
n e
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ge
n
va
l
ue
s
a
nd
ei
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en
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o
r
s
o
f
l
ar
g
e
m
a
t
r
i
x
t
a
k
e a l
o
n
g
t
i
m
e [
8
]
.
T
h
e l
ef
t
s
i
n
g
u
l
ar
v
ect
o
r
at
s
i
n
g
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l
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al
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e d
eco
m
p
o
s
i
t
i
o
n
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f
a
n
o
r
m
al
i
zed
m
at
r
i
x
w
h
i
c
h
r
ep
r
es
en
t
at
i
o
n
v
i
d
eo
w
as
t
h
e
p
r
i
n
ci
p
al
co
m
p
o
n
en
t
.
T
h
er
ef
o
r
e,
t
h
e
s
i
n
g
u
l
ar
v
al
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e d
eco
m
p
o
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n
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el
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p
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o
m
p
o
ne
nt
w
i
t
ho
ut
c
o
m
p
ut
i
n
g t
he
c
o
va
r
i
a
nc
e
m
a
t
r
i
x.
A
s
ub
s
p
a
c
e
o
p
t
i
m
i
z
a
t
i
o
n t
e
c
h
ni
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ue
t
o
s
i
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ul
a
r
va
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d
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m
p
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s
i
t
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o
n
s
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g
n
i
f
i
ca
n
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l
y
accel
er
at
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t
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cl
as
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c
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m
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l
t
a
n
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o
n
m
et
h
o
d
[
9
]
.
W
e
p
r
o
p
o
s
e
L
i
m
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t
ed
m
e
m
or
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oc
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K
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s
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pa
c
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opt
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m
i
z
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t
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on
f
or
c
o
m
pu
t
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ng pr
i
n
c
i
pa
l
c
om
pon
e
n
t
.
I
t
w
il
l b
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u
s
e
d
to
c
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s
tr
u
c
t
ba
c
k
g
r
oun
d e
s
t
i
m
a
t
i
on
.
2.
R
ES
EA
R
C
H
M
ETH
O
D
T
h
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f
o
llo
w
i
n
g
n
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w
ill b
e
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d
:
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s
w
ith
s
u
b
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c
r
ip
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in
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[
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2.
1.
P
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[
9]
pr
opos
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d
m
e
m
or
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bl
oc
k
k
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=
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t
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k
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1
0
]
f
o
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)
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a
n uns
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c
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i
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.,
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n
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m
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l
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(
2)
a
r
e
(
)
a
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(
2
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a
p
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t
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ltip
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ce t
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ead
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o
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t
h
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g
o
al
o
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ci
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g
t
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n
u
m
b
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o
f
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er
a
t
i
on
s
,
w
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pr
opos
e
t
o m
odi
f
y
t
h
e
b
as
i
c S
S
I
f
r
a
m
e
w
o
r
k
a
s
f
o
l
l
o
w
s
.
W
e r
ep
l
ace t
h
e l
a
s
t
i
t
er
at
e
(
)
i
n t
he
r
i
g
ht
-
h
a
n
d s
i
d
e
of
(
2)
by
a
n
“
i
m
p
r
o
v
ed
” i
n
t
er
m
ed
i
at
e i
t
er
at
e
(
)
s
o
t
ha
t
(
+
1
)
∈
or
th
(
)
,
(3
)
w
h
er
e,
f
o
r
a ch
o
s
e
n
s
u
b
s
p
ace
(
)
wi
t
h
a b
l
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ck
K
r
y
l
o
v
s
u
b
s
p
ace s
t
r
u
ct
u
r
e,
(
)
≔
a
rg
ma
x
∈
×
‖
‖
2
, s
.t
.
=
,
∈
(
)
.
(4
)
A
ga
i
n,
∈
(
)
m
e
a
ns
a
l
l
c
ol
um
ns
of
ar
e f
r
o
m
t
h
e s
u
b
s
p
ace
(
)
.
T
h
e s
el
ect
i
o
n
o
f
t
h
e
s
u
b
s
p
ace
(
)
wh
i
c
h
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s
co
n
s
t
r
u
ct
ed
f
r
o
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a l
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m
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t
ed
m
e
m
o
r
y
o
f
t
h
e l
as
t
a f
e
w
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es
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I
t
s
ch
o
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ce i
s
o
f
co
u
r
s
e n
o
t
u
n
i
q
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e.
W
e f
i
r
s
t
co
n
s
i
d
er
t
h
e s
u
b
s
p
ace s
p
an
n
ed
b
y
t
h
e cu
r
r
en
t
i
-
th
ite
r
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te
a
n
d
th
e
p
r
e
v
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u
s
p
ite
r
a
te
s
; i.
e
.
,
(
)
≔
(
)
,
(
−
1
)
,
⋯
,
(
−
)
;
(5
)
w
h
er
e t
h
e
m
em
o
r
y l
en
g
t
h
≥
0
w
ill
b
e
s
p
e
c
if
ie
d
in
la
te
r
.
W
e co
l
l
ect
t
h
e cu
r
r
en
t
an
d
t
h
e o
t
h
er
s
a
v
ed
i
t
er
at
e
b
lo
c
k
s
in
(
5
)
in
to
a
m
a
tr
i
x
=
(
)
≔
(
)
,
(
−
1
)
,
⋯
,
(
−
)
∈
×
;
(6
)
w
h
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=
(
+
1
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i
s
t
h
e
t
ot
a
l
num
be
r
of
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ol
um
n
s
i
n
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)
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o
r
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tio
n
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l s
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m
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y
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f
r
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o
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w
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te
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c
h
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e
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th
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s
u
p
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ip
t
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ip
t
f
r
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q
u
a
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lik
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w
he
ne
ve
r
no
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f
u
s
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w
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ul
d
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r
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e
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l
s
o
n
o
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th
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t th
e
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o
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tio
n
m
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tr
i
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ld
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c
e
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m
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k
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c
t
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lo
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k
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im
i
la
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ly
,
w
e
d
e
f
i
n
e
=
(
)
≔
(
)
,
(
−
1
)
,
⋯
,
(
−
)
∈
×
,
(7
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
:
20
88
-
8708
In
t
J
E
l
e
c
&
C
o
m
p
E
n
g
,
V
o
l.
8
, N
o
.
5
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r
20
18
:
284
7
-
2856
2850
w
h
i
c
h
i
s
al
s
o
s
av
ed
i
n
m
e
m
o
r
y
.
W
e em
p
h
a
s
i
ze t
h
at
S
S
I
al
r
ead
y
co
m
p
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t
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t
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w
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l
y
n
eed
t
o
s
av
e t
h
e
m
o
n
ce co
m
p
u
t
ed
.
I
t is
c
le
a
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y
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h
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t
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{
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i
f
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n
d on
l
y i
f
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f
o
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s
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me
∈
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a
nd
t
he
s
u
b
s
p
ace o
p
t
i
m
i
zat
i
o
n
p
r
o
b
l
em
(
4
)
i
s
eq
u
i
v
al
e
n
t
t
o
a g
e
n
er
a
l
i
zed
ei
g
en
v
al
u
e d
eco
m
p
o
s
i
t
i
o
n
p
r
o
b
l
em
:
ma
x
∈
×
‖
(
)
‖
2
s
.t
.
(
)
=
.
(8
)
H
o
w
e
ve
r
,
nu
m
e
r
i
c
a
l
d
i
f
f
i
c
ul
t
y
m
a
y
a
r
i
s
e
i
n s
o
l
vi
ng (
8
)
a
s
t
he
m
a
t
r
i
x
can
b
eco
m
e n
u
m
er
i
cal
l
y
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n
k
d
e
f
ic
ie
n
t.
A
m
o
r
e
s
ta
b
le
a
p
p
r
o
a
c
h
,
w
h
ic
h
w
e
w
ill i
m
p
le
m
e
n
t
,
is
to
f
in
d
a
n
o
r
t
h
o
n
o
r
m
a
l b
a
s
is
f
o
r
(
)
,
s
a
y,
=
(
)
∈
or
th
(
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,
an
d
t
o
ex
p
r
es
s
a
m
at
r
i
x
∈
(
)
a
s
=
f
or
s
om
e
∈
×
.
H
er
e
w
e as
s
u
m
e t
ha
t
h
as
a
f
u
l
l
r
an
k
an
d
w
il
l la
te
r
r
e
la
x
th
i
s
a
s
s
u
m
p
tio
n
.
W
e
n
o
w
c
o
n
v
e
r
t t
h
e
g
e
n
e
r
a
liz
e
d
e
ig
e
n
v
a
lu
e
p
r
o
b
le
m
(
8
)
in
to
a
n
e
q
u
i
v
a
le
n
t
ei
g
en
v
al
u
e p
r
o
b
l
e
m
ma
x
∈
×
‖
‖
2
s
.t
.
=
,
(9
)
w
h
er
e
=
(
)
≔
(
)
.
(
10)
N
ex
t
w
e d
es
cr
i
b
e h
o
w
t
o
cal
cu
l
at
e t
h
e
m
at
r
i
x
p
r
o
d
u
ct
i
n
(
10)
f
r
om
h
i
s
t
or
i
c
a
l
i
nf
or
m
a
t
i
on
w
i
t
h
out
a
n
y
a
d
d
itio
n
a
l c
o
m
p
u
ta
t
io
n
in
v
o
lv
i
n
g
th
e
m
a
tr
i
x
.
S
i
n
ce
∈
or
th
(
)
an
d
w
e as
s
u
m
e t
h
a
t
ha
s
a
f
ul
l
r
a
n
k,
t
he
r
e
e
xi
s
t
s
a
no
n
s
i
ng
ul
a
r
m
a
t
r
i
x
∈
×
s
uc
h
th
a
t
=
.
H
en
ce,
=
−
1
,
a
nd
i
n
(
10)
c
a
n
be
co
m
p
u
t
ed
as
=
=
−
1
=
−
1
,
(
11)
W
h
er
e
=
i
s
acces
s
i
b
l
e
f
r
o
m
o
u
r
l
i
m
i
t
ed
m
e
m
o
r
y
.
O
n
ce
i
s
av
a
i
l
ab
l
e,
w
e ca
n
s
o
l
v
e (
9
)
b
y
co
m
p
u
t
i
n
g
t
he
l
ead
i
n
g
ei
g
en
v
ect
o
r
s
o
f
t
h
e
×
ma
t
r
i
x
.
L
e
t
a
s
ol
u
t
i
on
t
o (
9)
be
.
T
h
e
m
a
t
r
i
x
pr
oduc
t
i
n
eq
u
at
i
o
n
(
3
)
can
t
h
e
n
b
e as
s
e
m
b
l
ed
as
(
)
=
=
−
1
.
(
12)
T
h
e r
em
ai
n
i
n
g
i
s
s
u
e i
s
h
o
w
t
o
ef
f
i
ci
en
t
l
y
a
n
d
s
t
ab
l
y
co
m
p
u
t
e
a
nd
e
ve
n w
h
e
n
t
he
m
a
t
r
i
x
is
n
u
m
e
r
ic
a
ll
y
r
a
nk d
e
f
i
c
i
e
nt
.
W
e
us
e
t
he
f
o
l
l
o
w
i
ng p
r
o
c
e
d
ur
e
i
n o
ur
i
m
p
l
e
m
e
nt
a
t
i
o
n.
N
o
tin
g
th
a
t
e
a
c
h
b
lo
c
k
in
is
in
d
iv
id
u
a
ll
y
o
r
th
o
n
o
r
m
a
l,
w
e
c
h
o
o
s
e
to
k
e
e
p
t
h
e
la
te
s
t b
lo
c
k
(
)
i
n
t
act
,
a
n
d
p
r
o
j
ect
t
h
e r
es
t
o
f
t
h
e b
l
o
ck
s
on
t
o t
h
e
nu
l
l
s
pa
c
e
of
(
)
,
o
b
ta
in
in
g
=
(
)
≔
−
(
)
(
)
(
−
1
)
(
−
2
)
⋯
(
−
)
.
(
13)
N
e
x
t
w
e
p
e
r
f
o
r
m
a
n
o
r
th
o
n
o
r
m
a
liz
a
tio
n
o
f
v
i
a t
h
e ei
g
en
v
al
u
e d
eco
m
p
o
s
i
t
i
o
n
o
f
i
t
s
G
r
a
m
m
at
r
i
x
=
Λ
.
(
14)
w
h
er
e
i
s
o
r
t
ho
go
na
l
a
nd
Λ
i
s
d
i
ag
o
n
al
.
I
t
can
b
e eas
i
l
y
v
er
i
f
i
e
d
t
h
at
t
h
e
m
at
r
i
x
=
(
)
≔
(
)
,
Λ
−
1
2
∈
ℎ
(
)
,
(
15)
pr
ov
i
de
d t
h
a
t
Λ
i
s
i
n
v
er
t
i
b
l
e.
T
h
e ab
o
v
e p
r
o
ced
u
r
e can
b
e s
t
ab
i
l
i
zed
b
y
m
o
n
i
t
o
r
i
n
g
t
h
e
n
u
m
er
i
cal
r
an
k
o
f
,
o
r
s
p
eci
f
i
cal
l
y
t
h
e
ei
g
e
n
v
al
u
e
s
o
n t
he
d
i
a
go
na
l
o
f
t
he
m
a
t
r
i
x
Λ
i
n
(
14)
.
W
e
c
h
oos
e
t
o
i
m
p
l
e
m
e
n
t
t
h
e
f
o
llo
w
in
g
t
w
o
-
s
te
p
s
ta
b
iliz
a
tio
n
s
c
h
e
m
e
:
St
e
p 1
D
el
et
e t
h
e co
l
u
m
n
s
o
f
w
h
o
s
e E
u
c
l
i
d
ean
n
o
r
m
s
ar
e b
el
o
w
a t
h
r
e
s
h
o
l
d
1
>
0
.
St
e
p 2
D
el
et
e t
h
e ei
g
en
v
al
u
es
i
n
Λ
,
a
n
d c
or
r
e
s
p
on
di
n
g
c
ol
um
ns
i
n
,
t
h
at
ar
e l
es
s
t
h
an
2
>
0
.
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t
J
E
l
e
c
&
C
o
m
p
E
n
g
I
S
S
N
:
2088
-
8708
B
ac
k
gr
oun
d E
s
t
i
m
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on U
s
i
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P
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C
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A
nal
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s
B
as
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d on
...
.
(
I
lm
iy
a
ti S
a
r
i)
2851
W
ith
a
s
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f
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ta
tio
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n
u
e
to
u
s
e
,
a
nd
Λ
to
d
e
n
o
te
th
e
ir
s
ta
b
iliz
e
d
v
e
r
s
io
n
s
,
r
es
p
ect
i
v
el
y
,
a
f
t
er
p
o
s
s
i
b
l
e d
el
et
i
o
n
s
.
T
h
er
ef
o
r
e,
a s
t
ab
l
e
co
n
s
t
r
u
ct
i
o
n
o
f
i
s
s
till
g
i
v
e
n
b
y
f
o
r
m
u
la
(
1
5
)
.
A
f
te
r
th
is
s
ta
b
le
o
r
th
o
n
o
r
m
a
li
z
a
tio
n
,
th
e
c
o
r
r
e
s
p
o
n
d
in
g
m
at
r
i
x
can
b
e g
e
n
er
at
ed
as
=
(
)
≔
(
)
,
Λ
−
1
2
,
(
16)
w
h
er
e b
ef
o
r
e t
h
e s
t
ab
i
l
i
za
t
i
o
n
p
r
o
ced
u
r
e w
e
h
ad
=
(
)
≔
(
−
1
)
⋯
(
−
)
−
(
)
(
)
(
−
1
)
⋯
(
−
)
,
(
17)
bu
t
s
o
m
e
o
f
t
h
e
c
ol
um
ns
of
m
a
y
h
a
v
e
be
e
n
de
l
e
t
e
d c
or
r
e
s
pon
di
n
g
t
o t
h
os
e
de
l
e
t
e
d c
ol
um
ns
of
du
r
i
ng
t
h
e s
t
ab
i
l
i
zat
i
o
n
s
t
ep
s
.
A
f
t
er
t
h
e r
e
m
o
v
al
o
f
n
u
m
er
i
cal
r
a
n
k
d
ef
i
ci
en
c
y
,
t
h
e
m
a
tr
ix
i
n
(
1
6
)
is
w
e
ll d
e
f
in
e
d
a
s
is
th
e
m
a
t
ri
x
i
n
(1
5
).
I
n
s
um
m
a
r
y
,
t
h
e
a
l
g
or
i
t
hm
p
e
r
f
or
m
s
e
i
g
e
nv
a
l
u
e
de
c
o
m
pos
i
t
i
on
s
on
t
w
o
s
m
a
l
l
s
ym
m
e
t
r
i
c
pos
i
t
i
v
e
d
e
f
in
i
te
m
a
tr
ic
e
s
:
i
n
(
14)
a
n
d
i
n
(
9
)
.
T
h
e s
i
zes
o
f
t
h
e
t
w
o
m
at
r
i
ces
ar
e
a
nd
(
+
1
)
,
r
es
p
ect
i
v
el
y
,
a
n
d
f
r
eq
u
en
t
l
y
s
m
al
l
er
d
u
e
to
d
e
le
tio
n
s
.
O
u
r
c
o
m
p
u
ta
tio
n
a
l e
x
p
e
r
ie
n
c
e
in
d
ic
a
te
s
th
a
t in
g
e
n
e
r
a
l
s
h
ou
l
d be
s
e
t
t
o 2 or
3,
or
a
t
m
o
s
t
4 bu
t
n
ot
g
r
e
a
t
e
r
.
C
ons
e
qu
e
n
t
l
y
,
w
h
e
n
is
s
u
f
f
ic
ie
n
t
l
y
s
m
a
l
le
r
th
a
n
,
it
h
o
ld
s
th
a
t
(
+
1
)
≪
<
.
2.
1.
1.
M
em
o
ry
L
en
g
t
h
T
he
m
e
m
o
r
y
l
e
n
gt
h
, u
s
ed
f
o
r
co
n
s
t
r
u
ct
i
n
g
t
h
e s
u
b
s
p
ace
(
)
in
(
5
)
,
is
a
c
r
u
c
ia
l p
a
r
a
m
e
te
r
to
th
e
p
e
r
f
o
r
m
a
nc
e
o
f
o
ur
a
l
go
r
i
t
h
m
.
T
he
s
i
m
p
l
e
s
t
w
a
y
i
s
t
o
a
s
s
i
gn a
c
o
ns
t
a
nt
i
nt
e
ge
r
va
l
ue
to
at
ev
er
y
ite
r
a
tio
n
o
n
c
e
t
h
e
ite
r
a
tio
n
c
o
u
n
te
r
r
each
es
; th
a
t is
,
a
t ite
r
a
ti
o
n
,
=
(
,
)
.
(
18)
I
n
g
en
er
al
a l
ar
g
er
le
a
d
s
to
a
s
m
a
lle
r
n
u
m
b
e
r
o
f
ite
r
a
tio
n
s
,
b
u
t in
c
r
e
a
s
in
g
al
s
o
i
n
cr
eas
es
t
h
e
co
m
p
u
t
at
i
o
n
al
co
s
t
s
p
er
i
t
er
at
i
o
n
.
O
u
r
co
m
p
u
t
at
i
o
n
al
e
x
p
e
r
i
m
en
t
s
i
n
d
i
cat
e t
h
at
u
s
u
al
l
y
a g
o
o
d
b
al
an
ce i
s
a
tta
in
e
d
f
o
r
∈
{
2
,
3
,
4
}
.
W
e h
av
e
al
s
o
f
o
u
n
d
t
h
at
a
n
a
d
ap
t
i
v
e s
t
r
at
e
g
y
o
n
s
el
ect
i
n
g
i
s
u
s
e
f
ul
t
o i
m
pr
ov
i
n
g t
h
e
pe
r
f
or
m
a
n
c
e
o
f
L
M
S
V
D
.
A
s
t
h
e i
t
er
at
e s
eq
u
en
ce co
n
v
er
g
e
s
,
t
h
e
n
ei
g
h
b
o
r
i
n
g
i
t
er
at
e
s
t
en
d
t
o
b
eco
m
e
m
o
r
e an
d
m
o
r
e
l
i
n
ear
l
y
d
ep
en
d
en
t
.
T
h
er
ef
o
r
e,
o
n
ce
j
u
d
g
ed
a
p
p
r
o
p
r
i
at
e
i
t
i
s
b
en
ef
i
ci
a
l
t
o
s
h
r
i
n
k
t
h
e
m
e
m
o
r
y
b
y
d
el
et
i
n
g
a
b
l
o
ck
f
r
o
m
t
h
e
m
e
m
o
r
y
,
r
ed
u
ci
n
g
t
h
e s
i
ze o
f
l
at
er
s
u
b
s
p
a
c
e
o
p
tim
iz
a
tio
n
p
r
o
b
le
m
s
.
S
p
e
c
if
ic
a
ll
y
,
a
f
te
r
i
t
er
at
i
o
n
s
,
w
e act
i
v
at
e t
h
e f
o
l
l
o
w
i
n
g
ad
ap
t
i
v
e
m
e
m
o
r
y
s
i
ze
s
t
r
at
eg
y
:
=
(
)
−
1
,
(
19)
w
h
er
e
⌈
⌉
is
th
e
s
m
a
lle
s
t in
te
g
e
r
g
r
e
a
te
r
th
a
n
o
r
e
q
u
a
l to
,
a
nd
(
)
i
s
t
h
e
num
be
r
of
c
ol
um
ns
i
n
wh
i
c
h
can
b
e s
m
al
l
er
t
h
an
(
+
1
)
d
u
e
to
p
o
s
s
ib
le
d
e
le
tio
n
s
d
o
n
e
i
n
th
e
t
w
o
s
ta
b
iliz
a
tio
n
s
te
p
s
.
C
o
m
b
in
i
n
g
(
1
8
)
an
d
(
1
9
)
,
w
e r
each
o
u
r
f
o
r
m
u
l
a f
o
r
s
el
ect
i
n
g
t
h
e
m
e
m
o
r
y
l
e
n
g
t
h
a
t th
e
-
t
h
ite
r
a
tio
n
:
=
,
(
)
−
1
,
,
(
20)
w
h
i
c
h
i
s
no
nne
ga
t
i
ve
.
G
e
ne
r
a
l
l
y
,
i
n
i
t
i
al
l
y
i
n
cr
eas
e
s
t
o
r
each
,
t
he
n b
e
c
o
m
e
s
no
n
-
i
nc
r
e
a
s
i
n
g
w
i
t
h a
p
r
o
b
a
b
i
l
i
t
y
t
o
d
ecr
eas
e t
o
a
s
m
al
l
er
v
al
u
e,
e
v
en
p
o
s
s
i
b
l
y
t
o
zer
o
.
O
f
co
u
r
s
e,
w
h
e
n
t
h
e
m
e
m
o
r
y
l
e
n
g
t
h
b
eco
m
e
s
zer
o
,
o
u
r
m
et
h
o
d
r
ed
u
ces
t
o
t
h
e cl
a
s
si
c
S
S
I
.
2.
1.
2.
L
M
S
VD Al
g
o
r
i
t
h
m
B
as
ed
o
n
t
h
e d
e
s
cr
i
p
t
i
o
n
ab
o
v
e,
w
e
s
t
at
e o
u
r
f
u
l
l
A
l
g
o
r
i
t
h
m
.
F
o
r
eas
e o
f
r
e
f
er
en
ce,
t
h
e
al
g
o
r
i
t
h
m
w
i
l
l
b
e r
ef
er
r
ed
t
o
as
L
MS
V
D
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
:
20
88
-
8708
In
t
J
E
l
e
c
&
C
o
m
p
E
n
g
,
V
o
l.
8
, N
o
.
5
,
O
c
t
obe
r
20
18
:
284
7
-
2856
2852
A
l
g
or
i
t
hm
L
M
S
V
D
:
L
i
m
i
t
e
d M
e
m
or
y
B
l
oc
k
S
u
bs
pa
c
e
K
r
y
l
ov
O
pt
i
m
i
z
a
t
i
on
f
or
S
V
D
1
I
np
ut
,
a
nd
.
I
n
itia
liz
e
=
(
0
)
∈
×
,
=
(
0
)
=
(
0
)
,
a
nd
=
=
0
;
2
w
h
ile
“
no
t
c
o
nve
r
ge
d
”
do
/
*
B
l
o
ck
S
u
b
s
p
ace O
p
t
i
m
i
zat
i
o
n
*
/
3
C
o
m
put
e
b
y
(
13)
a
n
d pe
r
f
or
m
s
t
a
bi
l
i
z
a
t
i
on
St
e
p 1
;
4
C
o
m
put
e
b
y
(
17)
w
i
t
h
t
h
e
s
a
m
e
c
ol
um
n
de
l
e
t
i
on
s
a
s
f
o
r
;
5
C
o
m
p
u
t
e t
h
e ei
g
e
n
v
al
u
e d
eco
m
p
o
s
i
t
i
o
n
o
f
i
n
(1
4
);
6
P
e
r
f
o
r
m
s
ta
b
iliz
a
tio
n
St
e
p 2
t
o pos
s
i
bl
y
s
h
r
i
nk
Σ
a
nd
;
7
C
o
m
put
e
b
y
(
16)
a
n
d e
i
g
e
nv
a
l
u
e
de
c
o
m
pos
i
t
i
on
of
;
8
L
e
t
s
o
l
ve
(
9
)
,
c
o
ns
i
s
t
i
ng o
f
t
h
e
l
ead
i
n
g
ei
g
en
v
ect
o
r
s
o
f
;
9
C
o
m
put
e
(
)
=
a
nd
(
)
=
(
w
hi
c
h e
q
ua
l
s
(
)
);
/
*
S
i
m
u
lta
n
e
o
u
s
I
te
r
a
tio
n
*
/
10
C
o
m
put
e
(
+
1
)
∈
or
th
(
)
a
nd
(
+
1
)
=
(
+
1
)
;
11
I
nc
r
e
m
e
nt
,
u
p
d
at
e
,
a
nd
,
a
nd
c
o
nt
i
n
ue
.
O
u
tp
u
t
,
Σ
,
a
nd
2.
2.
B
ac
k
gr
ou
n
d
E
s
t
i
m
at
i
on
O
n
ce p
r
i
n
ci
p
al
co
m
p
o
n
e
n
t
(
) a
n
d
t
h
e
m
e
a
n
ba
c
kg
r
oun
d (
)
a
r
e
c
o
m
p
ut
e
d
,
t
he
i
np
ut
i
m
a
ge
(
)
w
i
t
h
f
o
r
eg
r
o
u
n
d
o
b
j
ect
s
w
as
s
u
b
t
r
act
ed
b
y
t
h
e
m
ea
n
b
ack
g
r
o
u
n
d
.
D
ef
i
n
i
n
g
an
p
r
i
n
ci
p
al
co
m
p
o
n
en
t
m
a
t
r
i
x
as
=
[
1
,
2
,
⋯
,
]
.
I
t
f
o
l
l
o
w
s
t
ha
t
t
he
c
o
o
r
d
i
na
t
e
(
w
e
i
g
ht
)
i
n e
i
ge
ns
p
a
c
e
o
f
i
np
ut
i
m
a
ge
,
,
can
b
e
c
o
m
p
u
te
d
a
s
f
o
llo
w
s
=
(
−
)
,
(2
1
)
wh
e
n
i
s
b
ack
p
r
o
j
ect
ed
o
n
t
o
t
h
e i
m
a
g
e s
p
ace,
a b
ack
g
r
o
u
n
d
es
t
i
m
at
i
o
n
i
s
cr
eat
ed
=
+
.
(2
2
)
N
o
t
i
n
g
t
h
at
s
i
n
ce t
h
e p
r
i
n
ci
p
al
co
m
p
o
n
e
n
t
m
at
r
i
x
d
es
cr
i
b
es
t
h
e g
e
n
er
al
b
ack
g
r
o
u
n
d
ap
p
ear
an
ces
w
el
l
ho
w
e
ve
r
no
t
t
he
s
m
a
l
l
m
o
vi
n
g
o
bj
e
c
t
s
,
d
o
e
s
n
o
t c
o
n
ta
in
s
m
a
ll o
b
j
e
c
ts
.
2.
3.
M
e
t
ri
cs
T
h
e m
et
r
i
cs
ad
o
p
t
ed
t
o
ev
al
u
at
e t
h
e accu
r
ac
y
o
f
t
h
e es
t
i
m
at
e
d
b
ack
g
r
o
u
n
d
m
o
d
el
s
h
a
v
e b
een
ch
o
s
e
n
a
m
o
n
g t
ho
s
e
u
s
e
d
i
n
t
he
l
i
t
e
r
a
t
ur
e
f
o
r
b
a
c
k
gr
o
und
e
s
t
i
m
a
t
i
o
n
[
3
]
.
D
e
no
t
i
ng
w
i
t
h
G
T
(
G
r
o
und
T
r
ut
h)
a
n i
m
a
ge
c
o
nt
a
i
ni
n
g t
he
t
r
ue
b
a
c
k
gr
o
u
nd
a
nd
w
i
t
h
C
B
(
C
o
m
p
ut
e
d
B
a
c
kgr
o
und
)
t
he
e
s
t
i
m
a
t
e
d
b
a
c
kgr
o
u
nd
i
m
a
ge
co
m
p
u
t
ed
w
i
t
h
o
n
e o
f
t
h
e b
ack
g
r
o
u
n
d
in
itia
liz
a
tio
n
m
e
th
o
d
s
,
th
e
e
ig
h
t a
d
o
p
te
d
m
e
tr
ic
s
a
r
e
:
a.
A
ve
r
a
ge
G
r
a
y
-
l
e
v
e
l
E
rro
r (A
G
E
):
It
i
s
t
h
e
a
v
e
ra
g
e
o
f
t
h
e
g
r
a
y
-
l
ev
el
ab
s
o
l
u
t
e
d
i
f
f
er
en
ce
b
et
w
ee
n
G
T
an
d
C
B
i
m
a
ge
s
.
I
t
s
va
l
ue
s
r
a
n
ge
i
n [
0
,
L
-
1
]
,
w
he
r
e
L
i
s
t
he
m
a
xi
m
u
m
n
u
m
b
e
r
o
f
gr
e
y l
e
ve
l
s
;
t
he
l
o
we
r
t
h
e
A
G
E
v
al
u
e,
t
h
e b
et
t
er
i
s
t
h
e b
ack
g
r
o
u
n
d
es
t
i
m
at
e.
b.
T
o
t
al
n
u
m
b
er
o
f
E
r
r
o
r
P
i
x
el
s
(
E
P
s
)
:
A
n
er
r
o
r
p
i
x
el
i
s
a p
i
x
el
o
f
C
B
w
h
o
s
e
v
al
u
e d
i
f
f
er
s
f
r
o
m
t
h
e v
al
u
e
of
t
h
e
c
or
r
e
s
pon
di
ng
pi
x
e
l
i
n
G
T
by
m
or
e
t
h
a
n
s
o
m
e
t
h
r
e
s
hol
d
τ
(
i
n
t
h
e
e
x
pe
r
i
m
e
nt
s
t
he
s
ug
ge
s
t
e
d
va
l
ue
τ=
20 h
a
s
be
e
n
a
dopt
e
d)
.
E
P
s
a
s
s
um
e
v
a
l
u
e
s
i
n
[
0;
N
]
,
w
he
r
e
N
i
s
t
h
e
num
be
r
of
i
m
a
g
e
pi
xe
l
s
;
t
h
e
l
o
w
e
r
t
h
e E
P
s
v
al
u
e,
t
h
e b
et
t
er
i
s
t
h
e
b
ack
g
r
o
u
n
d
es
t
i
m
at
e.
c.
P
er
cen
t
ag
e o
f
E
r
r
o
r
P
i
x
el
s
(
p
E
P
s
)
:
I
t
i
s
t
h
e r
at
i
o
b
et
w
ee
n
t
h
e E
P
s
an
d
t
h
e n
u
m
b
er
N
o
f
i
m
ag
e p
i
x
el
s
.
I
t
s
v
al
u
e
s
r
an
g
e i
n
[
0
,
1
]
;
t
h
e l
o
w
er
t
h
e p
E
P
s
v
al
u
e,
t
h
e b
et
t
er
i
s
t
h
e b
ack
g
r
o
u
n
d
es
t
i
m
at
e.
d.
T
o
t
al
n
u
m
b
er
o
f
C
l
u
s
t
er
ed
E
r
r
o
r
P
i
x
el
s
(
C
E
P
s
)
:
A
cl
u
s
t
er
ed
er
r
o
r
p
i
x
el
i
s
d
ef
i
n
ed
as
a
n
y
er
r
o
r
p
i
x
el
w
hos
e
4
-
co
n
n
ect
ed
n
ei
g
h
b
o
r
s
ar
e
al
s
o
er
r
o
r
p
i
xe
l
s
.
C
E
P
s
va
l
ue
s
r
a
n
ge
i
n
[
0
,
N
]
;
t
he
l
ow
e
r
t
he
C
E
P
s
v
al
u
e,
t
h
e b
et
t
er
i
s
t
h
e b
ack
g
r
o
u
n
d
es
t
i
m
a
t
e.
e.
P
er
cen
t
ag
e o
f
C
l
u
s
t
er
ed
E
r
r
o
r
P
i
x
el
s
(
p
C
E
P
s
)
:
I
t
i
s
t
h
e
r
at
i
o
b
et
w
een
t
h
e
C
E
P
s
a
n
d
t
h
e
n
u
m
b
er
N
o
f
i
m
a
ge
p
i
xe
l
s
.
I
t
s
va
l
ue
s
r
a
nge
i
n [
0
,
1
]
;
t
he
l
o
w
e
r
t
he
p
C
E
P
s
v
al
u
e,
t
h
e b
et
t
er
i
s
t
h
e b
ack
g
r
o
u
n
d
es
t
i
m
a
t
e.
f.
P
eak
-
S
i
g
na
l
-
to
-
N
o
i
se
-
R
a
tio
(
P
S
N
R
)
:
I
t
is
d
e
f
in
e
d
a
s
=
1
0
∙
l
og
1
0
(
(
−
1
)
2
/
)
;
w
h
e
r
e
L
is
t
h
e
m
a
x
i
m
u
m
n
u
m
b
er
o
f
g
r
e
y
l
ev
el
s
a
n
d
M
S
E
i
s
t
h
e M
ea
n
S
q
u
ar
ed
E
r
r
o
r
b
et
w
een
G
T
an
d
C
B
i
m
a
g
e
s
.
T
hi
s
f
r
e
q
ue
nt
l
y
ad
o
p
t
ed
m
e
t
r
i
c as
s
u
m
e
s
v
al
u
e
s
i
n
d
eci
b
el
s
(
d
b
)
;
t
h
e h
i
g
h
er
t
h
e P
S
N
R
v
al
u
e,
t
h
e b
et
t
er
i
s
t
h
e b
ack
g
r
o
u
n
d
es
t
i
m
a
t
e.
g.
M
u
lti
S
c
a
le
S
tr
u
c
tu
r
a
l
S
i
m
ila
r
it
y
I
n
d
e
x
(
M
S
-
S
S
I
M
)
: T
h
is
is
th
e
m
e
tr
ic
d
e
f
in
e
d
i
n
[
1
1
]
,
th
a
t u
s
e
s
s
tr
u
c
t
u
r
a
l
d
is
to
r
tio
n
a
s
a
n
e
s
ti
m
a
te
o
f
th
e
p
e
r
c
e
i
v
e
d
v
is
u
a
l
d
is
to
r
tio
n
.
I
t
a
s
s
u
m
e
s
v
a
l
u
e
s
in
[
0
;
1
]
;
th
e
hi
g
he
r
t
he
va
l
ue
o
f
M
S
-
S
S
I
M,
t
h
e b
et
t
er
i
s
t
h
e e
s
t
i
m
at
ed
b
ack
g
r
o
u
n
d
.
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t
J
E
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e
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&
C
o
m
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n
g
I
S
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:
2088
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8708
B
ac
k
gr
oun
d E
s
t
i
m
at
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on U
s
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P
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2853
h.
C
o
l
o
r
i
m
a
g
e Q
u
al
i
t
y
Meas
u
r
e (
C
Q
M
)
:
I
t
i
s
a r
ecen
t
l
y
p
r
o
p
o
s
ed
m
et
r
i
c [
1
2
]
,
b
as
ed
o
n
a r
ev
er
s
i
b
l
e
tr
a
n
s
f
o
r
m
a
tio
n
o
f
t
h
e
Y
U
V
c
o
lo
r
s
p
ace an
d
o
n
t
h
e
P
S
N
R
co
m
p
u
t
ed
i
n
t
h
e
s
i
n
g
l
e Y
U
V
b
an
d
s
.
I
t
as
s
u
m
e
s
v
al
u
e
s
i
n
d
b
an
d
t
h
e
h
i
g
h
er
t
h
e C
Q
M
v
al
u
e,
t
h
e b
et
t
er
i
s
t
h
e b
ack
g
r
o
u
n
d
es
t
i
m
at
e.
W
h
i
l
e t
h
e l
as
t
m
et
r
i
c i
s
d
ef
i
n
e
d
o
n
l
y
f
o
r
co
l
o
r
i
m
ag
e
s
,
m
et
r
i
cs
1
t
h
r
o
u
g
h
7
ar
e ex
p
r
es
s
l
y
d
ef
i
n
ed
f
o
r
gr
a
y
-
s
cal
e
i
m
ag
e
s
.
I
n
t
h
e ca
s
e
o
f
co
l
o
r
i
m
a
g
es
,
t
h
e
y
ar
e
g
e
n
er
al
l
y
ap
p
l
i
ed
t
o
ei
t
h
er
t
h
e
g
r
a
y
-
s
cal
e co
n
v
er
t
ed
i
m
a
g
e o
r
t
h
e l
u
m
i
n
a
n
ce co
m
p
o
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en
t
Y
o
f
a co
l
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s
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as
Y
cb
C
r
.
3.
R
ES
U
LT
S
A
ND AN
AL
Y
S
I
S
T
h
is
s
e
c
tio
n
d
e
s
c
r
ib
e
s
t
h
e
r
e
s
u
lt
s
o
f
t
h
e
i
m
p
le
m
e
n
ta
tio
n
of
t
h
e
pr
opos
e
d m
e
t
h
od
.
T
he
r
e
s
ul
t
is
ba
c
k
g
r
oun
d e
s
t
i
m
a
t
i
on
u
s
i
ng
p
r
i
n
ci
p
al
co
m
p
o
n
e
n
t
.
T
h
e m
et
r
i
cs
ad
o
p
t
ed
t
o
ev
al
u
at
e t
h
e accu
r
ac
y
o
f
t
h
e
es
t
i
m
at
ed
b
ack
g
r
o
u
n
d
m
o
d
el
s
h
a
v
e b
een
ch
o
s
en
a
m
o
n
g
t
h
o
s
e u
s
ed
i
n
t
h
e l
i
t
er
at
u
r
e f
o
r
b
ack
g
r
o
u
n
d
e
s
ti
m
a
tio
n
.
3.
1.
B
ac
k
gr
ou
n
d
E
s
t
i
m
at
i
on
I
n
t
h
i
s
p
ap
er
,
t
h
e S
ce
n
e B
ack
g
r
o
u
n
d
I
n
i
t
i
al
i
zat
i
o
n
(
S
B
I
)
d
at
a s
et
w
as
c
h
o
s
en
f
o
r
t
h
e
b
ack
g
r
o
u
n
d
e
s
t
i
m
a
t
i
o
n.
T
he
d
a
t
a
s
e
t
c
o
nt
a
i
ns
s
e
ve
n
i
m
a
ge
s
e
q
ue
nc
e
s
a
n
d
c
o
r
r
e
s
p
o
nd
i
ng
gr
o
und
t
r
ut
h
(
G
T
)
b
a
c
kgr
o
u
nd
s
a
r
e
gi
ve
n i
n
F
i
g
ur
e
1
.
I
n
T
ab
l
e 1
w
e r
ep
o
r
t
,
f
o
r
each
s
eq
u
en
ce,
t
h
e n
a
m
e,
t
h
e
n
u
m
b
er
o
f
a
v
ai
l
ab
l
e f
r
a
m
es
,
t
h
e
s
ub
s
e
t
o
f
t
he
f
r
a
m
e
s
a
d
o
p
t
e
d
f
o
r
t
e
s
t
i
ng,
a
nd
t
he
o
r
i
gi
na
l
r
e
s
o
l
ut
i
o
n.
T
he
s
ub
s
e
t
s
ha
ve
b
e
e
n s
e
l
e
c
t
e
d
i
n o
r
d
e
r
t
o
a
vo
i
d
t
he
i
nc
l
us
i
o
n i
nt
o
t
he
t
e
s
t
i
ng
s
e
q
ue
nc
e
s
o
f
e
m
p
t
y
f
r
a
m
e
s
(
f
r
a
m
e
s
n
ot
i
n
c
l
u
di
ng
f
or
e
g
r
ou
n
d obj
e
c
t
s
)
.
T
he
gr
o
und
t
r
ut
hs
(
G
T
)
ha
ve
b
e
e
n
m
a
n
ua
l
l
y o
b
t
a
i
ne
d
b
y
e
i
t
he
r
c
ho
o
s
i
n
g o
ne
o
f
t
he
s
e
q
ue
nc
e
f
r
a
m
e
s
f
r
e
e
o
f
f
or
e
g
r
oun
d ob
j
e
c
t
s
(
n
ot
i
n
c
l
u
d
e
d i
n
t
o t
h
e
s
u
b
s
e
t
s
of
u
s
e
d f
r
a
m
e
s
)
or
by
s
t
i
t
c
hi
ng
t
og
e
t
h
e
r
e
m
pt
y
ba
c
kg
r
oun
d
r
eg
i
o
n
s
f
r
o
m
d
i
f
f
er
en
t
s
eq
u
e
n
ce f
r
a
m
es
.
B
o
t
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I
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f
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t
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s
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eq
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b
et
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an
d
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d t
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H
a
l
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M
o
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t
o
r
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ve
n t
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h
t
he
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f
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gr
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t
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m
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nc
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a
V
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s
eq
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F
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ag
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s
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n
ce i
t
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cl
u
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al
m
o
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t
s
t
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c f
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r
o
u
n
d
o
b
j
ect
s
t
h
at
ar
e f
r
eq
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en
t
l
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m
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n
t
er
p
r
et
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as
b
ack
g
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u
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d
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I
t
can
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l
s
o
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v
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d
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B
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s
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sh
o
w
n
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ab
l
e 3
.
T
he
ha
r
d
w
a
r
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m
e
m
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us
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u
f
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ic
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t to
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ta
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th
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to
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tr
ix
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ab
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s
h
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t
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pe
r
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or
m
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m
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t
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d t
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du
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eq
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.
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ab
l
e 3
.
P
er
f
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o
f
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h
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eq
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R
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s
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t
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l
fra
m
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tim
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(
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d
)
H
a
l
l&
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r
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CO
NCL
U
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I
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N
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n
t
h
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s
p
ap
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,
w
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h
a
v
e p
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a b
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s
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t
h
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p
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co
m
p
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.
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h
e
p
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m
p
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n
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n
t is
obt
a
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d
by
c
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m
pu
t
e
t
h
e
dom
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n
a
nt
s
i
n
gu
l
a
r
v
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e
de
c
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pos
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t
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on
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s
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t
h
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l
i
m
i
t
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d
m
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m
o
r
y
K
r
y
lo
v
s
u
b
s
p
a
c
e
o
p
ti
m
iz
a
tio
n
.
T
he
c
ol
um
ns
of
le
f
t s
in
g
u
la
r
m
a
tr
ix
o
f
th
e
d
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m
i
n
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n
t
s
i
n
g
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la
r
v
a
lu
e
de
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om
pos
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t
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o
n
i
s
t
h
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pr
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n
c
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pa
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c
om
pon
e
n
t
.
B
a
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k
g
r
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d
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s
t
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t
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n
i
s
obt
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s
t
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h
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np
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e (
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eq
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)
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o s
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c
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pa
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de
d pr
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n
c
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pa
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c
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m
pon
e
nt
.
T
h
e p
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u
r
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w
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t
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da
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of
8 v
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w
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r
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t
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[
146
150,
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40]
,
t
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[
258,
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0]
.
T
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8
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R
EF
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EN
C
ES
[
1]
A
. S
o
b
r
a
l
,
e
t a
l.
, “
C
om
pa
r
i
s
on of
M
a
t
r
i
x
C
om
pl
e
t
i
on A
l
g
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t
hm
s
f
or
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a
c
kg
r
ound I
n
i
t
i
a
l
i
z
a
t
i
on i
n
V
i
de
os
,
”
Spr
i
n
ge
r
I
nt
e
r
n
at
i
on
al
P
ubl
i
s
hi
ng
,
p
p.
51
0
-
51
7,
20
15
.
[
2]
A.
S
obr
a
l
an
d
A
.
V
a
c
a
v
a
nt
,
“
A
C
om
pr
e
he
ns
i
v
e
R
e
v
i
e
w
of
B
a
c
kg
r
oun
d S
ub
t
r
a
c
t
i
on A
l
g
or
i
t
hm
s
E
v
a
l
ua
t
e
d w
i
t
h
S
y
n
t
h
et
i
c an
d
R
eal
V
i
d
eo
s
,”
E
l
s
evi
e
r
J
our
nal
, p
p
.
4
-
21
,
2
01
4.
[
3]
L
.
M
ad
d
al
en
a
a
nd
A
.
P
e
t
r
os
i
no,
“
T
o
w
ar
d
s
B
en
ch
m
ar
k
i
n
g
S
cen
e B
ack
g
r
o
u
n
d
I
n
i
t
i
al
i
zat
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o
n
,
”
S
pr
i
n
g
e
r
I
nt
e
r
nat
i
on
al
Pu
b
lis
h
in
g
S
w
itz
e
r
la
n
d
, p
p
.
46
9
-
4
76,
20
15
.
[
4]
N.
M
.
O
liv
e
r
,
et
a
l
.
,
“
A
B
a
y
e
s
i
a
n
C
om
put
e
r
V
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s
i
on S
y
s
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f
or
M
ode
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ng
H
um
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n I
nt
e
r
a
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t
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ons
,”
I
E
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E
T
r
ans
ac
t
i
ons
on P
at
t
e
r
n
A
n
al
y
s
i
s
a
nd M
ac
hi
ne
I
nt
e
l
l
i
ge
nc
e
,
v
o
l/is
s
u
e
:
22(
7)
,
pp.
831
-
8
43D
,
20
00
.
[
5]
H
.
S
a
br
ol
an
d
S
.
K
u
m
a
r
,
“
R
e
c
o
g
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itio
n
o
f
T
o
m
a
to
L
a
te
B
lig
h
t b
y
U
s
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ng
D
W
T
a
nd C
om
pon
e
nt
A
na
l
y
s
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s
,
”
I
nt
e
r
nat
i
o
nal
J
our
n
al
of
E
l
e
c
t
r
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c
al
an
d C
om
pue
r
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ng
i
ne
e
r
i
ng
(
I
J
E
C
E
)
,
v
o
l/is
s
u
e
:
7(
1)
,
p
p.
19
4
-
19
9.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
:
20
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In
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.
5
,
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20
18
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6]
V
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h
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d
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9]
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