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I
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(
C
NN)
an
d
r
an
d
o
m
s
am
p
le
co
n
s
en
s
u
s
(
R
ANSA
C
)
f
o
r
o
b
ject
r
ec
o
g
n
itio
n
[
1
0
]
,
an
d
o
th
er
r
elev
an
t
ar
ea
s
in
th
e
f
ield
o
f
co
m
p
u
te
r
v
is
io
n
an
d
im
a
g
e
an
aly
s
is
[
1
1
]
–
[
2
0
]
h
av
e
b
ee
n
s
tu
d
ie
d
.
2.
M
AT
E
R
I
AL
S AN
D
M
E
T
H
O
D
2
.
1
.
Alg
o
rit
hm
o
rient
ed
F
A
ST
a
nd
ro
t
a
t
ed
B
RI
E
F
(
O
RB
)
[
6
]
T
h
e
m
eth
o
d
o
l
o
g
y
p
r
o
p
o
s
ed
in
th
is
s
tu
d
y
i
n
v
o
lv
es
c
o
n
v
er
tin
g
in
p
u
t
im
a
g
es
in
t
o
v
ec
to
r
r
ep
r
esen
tatio
n
s
b
y
e
x
tr
ac
tin
g
k
ey
in
f
o
r
m
ativ
e
f
ea
t
u
r
es
u
s
in
g
th
e
OR
B
alg
o
r
ith
m
[
1
0
]
.
O
R
B
co
m
b
in
es
two
f
o
u
n
d
atio
n
al
alg
o
r
ith
m
s
:
f
ea
tu
r
es
f
r
o
m
ac
ce
ler
ate
d
s
eg
m
e
n
t
test
(
FAST)
f
o
r
id
en
tify
in
g
k
ey
p
o
in
ts
,
an
d
b
in
ar
y
r
o
b
u
s
t
in
d
ep
e
n
d
en
t
elem
en
tar
y
f
ea
tu
r
es
(
B
R
I
E
F)
f
o
r
co
m
p
u
tin
g
d
escr
ip
to
r
s
[
2
1
]
.
T
h
e
p
r
o
ce
s
s
b
eg
in
s
with
th
e
d
etec
tio
n
o
f
in
f
o
r
m
ativ
e
p
o
in
ts
ac
r
o
s
s
th
e
im
ag
e
u
s
in
g
th
e
FAST
alg
o
r
ith
m
.
Fo
r
ea
ch
ca
n
d
id
ate
p
ix
el,
th
e
s
u
r
r
o
u
n
d
in
g
1
6
-
p
ix
el
cir
cu
lar
n
ei
g
h
b
o
r
h
o
o
d
is
e
v
alu
ated
to
d
eter
m
in
e
wh
eth
er
it
co
n
s
titu
tes
a
k
ey
p
o
in
t
[
2
2
]
.
A
p
i
x
el
is
class
if
ied
as
in
f
o
r
m
ativ
e
if
th
e
f
o
llo
wi
n
g
co
n
d
itio
n
is
m
et
f
o
r
a
n
y
s
u
b
s
et
o
f
c
o
n
tig
u
o
u
s
p
ix
els o
n
th
e
cir
cle
[
1
1
]
:
let,
(
)
−
b
e
t
h
e
in
ten
s
ity
i
n
p
ix
els.
I
f
cir
cle
co
n
tain
s
ad
jace
n
t
s
ets
o
f
p
ix
els,
th
e
n
p
ix
el
is
co
n
s
id
er
ed
th
e
b
ase
p
o
in
t.
(
)
−
(
)
>
,
o
r
(
)
−
(
)
>
(
1
)
h
er
e,
is
ea
ch
p
ix
el
in
s
id
e
th
e
c
ir
cle.
T
h
e
OR
B
alg
o
r
ith
m
is
d
esig
n
ed
to
tr
a
n
s
f
o
r
m
im
ag
es
i
n
to
f
ea
tu
r
e
v
ec
t
o
r
s
,
en
a
b
lin
g
task
s
s
u
ch
as
o
b
ject
r
ec
o
g
n
itio
n
an
d
im
ag
e
m
atch
in
g
.
T
h
is
co
n
v
er
s
io
n
p
r
o
ce
s
s
is
s
tr
u
ctu
r
ed
in
to
f
o
u
r
k
ey
s
tag
es,
ea
ch
b
u
ild
in
g
u
p
o
n
th
e
p
r
ev
i
o
u
s
o
n
e
to
g
en
e
r
ate
r
eliab
le
b
in
a
r
y
d
escr
ip
to
r
s
.
T
h
e
o
v
er
all
w
o
r
k
f
lo
w
o
f
t
h
e
OR
B
alg
o
r
ith
m
is
d
ep
icted
in
Fig
u
r
e
1
.
I
t star
ts
with
an
in
p
u
t im
ag
e
an
d
m
o
v
es th
r
o
u
g
h
th
e
f
ea
t
u
r
e
d
etec
tio
n
p
h
ase,
wh
ich
lev
er
a
g
es
th
e
F
AST
co
r
n
er
d
etec
to
r
to
ef
f
icien
tly
i
d
en
tify
p
o
te
n
tial
k
ey
p
o
in
ts
.
Fr
o
m
th
is
in
itial
s
et,
th
e
Har
r
is
co
r
n
er
m
ea
s
u
r
e
is
ap
p
li
ed
to
r
ef
in
e
th
e
s
elec
tio
n
,
is
o
l
atin
g
th
e
m
o
s
t
s
tab
le
a
n
d
d
is
tin
ctiv
e
p
o
in
ts
.
Af
ter
p
in
p
o
in
tin
g
th
ese
o
p
tim
al
k
e
y
p
o
in
ts
,
th
e
B
R
I
E
F
d
escr
ip
to
r
is
co
m
p
u
ted
at
ea
c
h
lo
ca
tio
n
,
r
esu
ltin
g
i
n
a
co
m
p
ac
t
a
n
d
r
o
b
u
s
t
b
in
ar
y
r
e
p
r
esen
tatio
n
.
T
h
e
en
d
p
r
o
d
u
ct
is
a
f
ea
tu
r
e
v
e
cto
r
r
ep
r
esen
ta
tio
n
o
f
th
e
im
ag
e
,
r
ea
d
y
f
o
r
u
s
e
in
task
s
lik
e
m
at
ch
in
g
o
r
r
ec
o
g
n
itio
n
.
T
h
is
s
tep
-
by
-
s
tep
a
p
p
r
o
ac
h
e
n
h
an
ce
s
OR
B
's
ef
f
icien
cy
in
r
ea
l
-
tim
e
ap
p
licatio
n
s
,
lev
er
ag
in
g
th
e
co
m
p
u
tatio
n
al
s
im
p
licity
o
f
b
o
th
FAST
an
d
B
R
I
E
F
alg
o
r
ith
m
s
.
T
h
ei
r
in
teg
r
atio
n
p
r
o
d
u
ce
s
a
f
ea
tu
r
e
d
escr
ip
to
r
th
at
is
n
o
t
o
n
ly
r
esis
tan
t
to
n
o
is
e
b
u
t
also
r
o
tatio
n
-
in
v
ar
ia
n
t,
m
ak
in
g
it
id
ea
l
f
o
r
d
iv
er
s
e
co
m
p
u
ter
v
is
io
n
task
s
s
u
ch
as o
b
ject
tr
a
ck
in
g
,
im
a
g
e
s
titch
in
g
,
an
d
v
is
u
al
o
d
o
m
etr
y
.
Fig
u
r
e
1
.
C
o
n
v
er
tin
g
a
n
im
ag
e
to
a
v
ec
to
r
u
s
in
g
OR
B
alg
o
r
ith
m
I
n
p
u
t im
a
g
e
Fin
d
k
ey
p
o
in
t b
y
FAST
Select
b
est p
o
in
t b
y
Har
r
is
Ex
trac
t
b
i
n
a
ry
d
e
sc
rip
to
r
b
y
BRI
EF
Ou
tp
u
t im
ag
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
1
6
,
No
.
1
,
Feb
r
u
ar
y
20
2
6
:
2
5
6
-
277
258
Har
r
is
co
r
n
er
m
ea
s
u
r
e
is
u
s
ed
to
ass
ess
th
e
s
tab
ilit
y
o
f
d
ata
p
o
in
ts
.
Har
r
is
an
g
u
lar
m
ea
s
u
r
e
is
ca
lcu
lated
as
(
2
)
[
1
2
]
:
=
(
)
−
(
(
)
)
2
(
2
)
wh
er
e,
−
g
r
ad
ien
ts
ar
e
th
e
co
v
ar
ian
ce
m
atr
ix
an
d
а
i
s
a
co
n
s
tan
t
(
u
s
u
ally
b
etwe
en
0
.
0
4
-
0
.
0
6
)
.
T
h
e
o
r
ien
tatio
n
o
f
th
e
OR
B
in
f
o
r
m
ativ
e
g
r
ad
ien
t
p
o
in
ts
is
u
s
ed
to
d
eter
m
in
e
th
e
f
o
r
m
u
la
(
3
)
[
2
3
]
:
=
(
∑
(
)
∑
(
)
)
(
3
)
wh
er
e,
is
th
e
weig
h
t f
u
n
ctio
n
,
an
d
(
)
is
th
e
p
ix
el
in
ten
s
ity
.
Fo
r
d
escr
ip
to
r
co
m
p
u
tatio
n
,
B
R
I
E
F
p
er
f
o
r
m
s
b
in
a
r
y
c
o
m
p
ar
is
o
n
s
b
etwe
en
p
air
s
o
f
p
i
x
els
in
a
s
m
o
o
th
ed
im
ag
e
p
atch
.
T
o
en
s
u
r
e
r
o
tatio
n
in
v
ar
ian
ce
,
t
h
e
d
escr
ip
to
r
co
o
r
d
in
ates
ar
e
r
o
tated
ac
co
r
d
i
n
g
to
t
h
e
k
ey
p
o
i
n
t o
r
ien
tatio
n
[
2
4
]
:
(
,
)
=
(
−
,
+
)
,
(
4
)
wh
er
e,
τ
is
th
e
r
o
tatin
g
c
o
o
r
d
i
n
ates
o
f
th
e
d
escr
ip
to
r
p
atch
,
is
th
e
o
r
ien
tatio
n
o
f
th
e
k
ey
p
o
in
t,
an
d
ar
e
th
e
co
o
r
d
in
ates o
f
p
ai
r
s
o
f
p
i
x
els
[
1
3
]
.
W
h
en
g
en
er
atin
g
d
escr
ip
to
r
s
,
t
h
e
v
ec
to
r
is
ex
p
r
ess
ed
as a
b
it
s
tr
in
g
:
(
)
=
∑
2
−
1
(
(
)
+
(
,
)
<
(
)
+
(
,
)
=
1
wh
er
e,
s
th
e
len
g
th
o
f
th
e
d
escr
ip
to
r
(
f
o
r
ex
am
p
le,
2
5
6
b
its
)
,
is
th
e
p
ix
el
in
ten
s
ity
,
an
d
an
d
ar
e
th
e
co
o
r
d
in
ates
o
f
th
e
p
ix
el
p
air
s
.
OR
B
d
escr
ip
to
r
s
ar
e
3
2
b
its
(
2
5
6
b
its
)
lo
n
g
,
ea
ch
b
it
is
p
ar
t
o
f
a
d
escr
ip
to
r
an
d
r
ep
r
esen
ts
a
tex
tu
r
e
a
n
d
o
t
h
er
p
r
o
p
er
ties
ar
o
u
n
d
an
in
f
o
r
m
ati
v
e
p
o
in
t
[
2
5
]
.
2
.
2
.
F
r
a
ct
a
l dim
ens
io
n
[
7
]
I
n
f
o
r
m
ativ
e
f
ea
tu
r
es
r
ef
e
r
to
f
u
n
d
am
e
n
tal
attr
ib
u
tes
with
in
an
im
ag
e
th
at
ca
r
r
y
ess
en
tial
in
f
o
r
m
atio
n
ab
o
u
t
its
co
n
ten
t.
T
h
ese
f
ea
tu
r
es
ar
e
cr
itical
in
task
s
s
u
ch
a
s
im
ag
e
r
ec
o
g
n
itio
n
,
class
if
icatio
n
,
an
d
an
al
y
s
is
[
1
4
]
.
I
n
co
n
tex
tu
al
im
ag
e
r
e
co
g
n
itio
n
s
y
s
tem
s
,
s
u
ch
f
ea
t
u
r
es
ar
e
p
ar
ticu
lar
ly
v
ital,
as
th
eir
id
en
tific
atio
n
en
ab
les
m
o
r
e
e
f
f
ec
tiv
e
an
d
ac
cu
r
ate
im
ag
e
p
r
o
ce
s
s
in
g
[
2
6
]
.
I
n
f
o
r
m
ativ
e
f
ea
tu
r
es
ar
e
wid
el
y
em
p
lo
y
ed
ac
r
o
s
s
d
o
m
ain
s
s
u
ch
as a
g
r
ic
u
ltu
r
e,
e
n
v
ir
o
n
m
en
tal
m
o
n
ito
r
in
g
,
an
d
E
ar
th
r
em
o
te
s
en
s
in
g
[
2
7
]
.
So
m
e
ty
p
ical
in
f
o
r
m
ativ
e
im
a
g
e
f
ea
tu
r
es in
clu
d
e
[
1
5
]
:
−
E
d
g
es
an
d
b
o
r
d
er
s
:
T
h
e
lin
es,
b
o
r
d
er
s
,
a
n
d
co
n
to
u
r
s
o
f
o
b
jec
ts
in
an
im
ag
e
ca
n
b
e
im
p
o
r
ta
n
t
s
ig
n
s
o
f
th
eir
r
ec
o
g
n
itio
n
[
1
6
]
.
−
C
o
r
n
er
s
an
d
f
ac
et
p
o
in
ts
:
C
er
tain
p
o
in
ts
in
an
im
a
g
e,
s
u
ch
a
s
co
r
n
er
s
,
lin
e
in
ter
s
ec
tio
n
s
,
o
r
tex
tu
r
e
n
o
d
es,
s
er
v
e
as p
r
im
ar
y
m
ar
k
er
s
f
o
r
h
ig
h
lig
h
tin
g
a
n
d
r
ec
o
g
n
izin
g
o
b
jects
[
1
7
]
.
−
C
o
lo
r
p
r
o
p
er
ties
:
I
n
f
o
r
m
atio
n
ab
o
u
t
t
h
e
co
lo
r
an
d
co
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p
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tes
[
1
8
]
.
−
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ex
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p
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:
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[
2
8
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.
−
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ap
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ize
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I
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f
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ab
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[
2
0
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.
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d
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im
en
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s
[
3
0
]
.
T
h
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r
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lated
as f
o
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s
.
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:
2088
-
8
7
0
8
Meth
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fo
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Mir
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259
Fra
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[
3
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3
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[
3
3
]
.
I
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h
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to
(
8
)
[
3
4
]
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
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&
C
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p
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g
,
Vo
l.
1
6
,
No
.
1
,
Feb
r
u
ar
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20
2
6
:
2
5
6
-
277
260
∞
−
(
8
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wh
er
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f
icien
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,
∞
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f
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ca
lin
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co
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ir
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e
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f
(
8
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b
y
c
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g
in
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(
9
)
[
3
5
]
:
l
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=
−
l
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(
9
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Fig
u
r
e
3
.
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2
.
3
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No
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[
8
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Fo
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r
ep
r
esen
t
th
ese
f
ea
tu
r
es
in
a
s
tan
d
ar
d
ized
f
o
r
m
at
s
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itab
le
f
o
r
s
u
b
s
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en
t a
n
aly
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is
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d
class
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icatio
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s
.
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h
is
s
ec
t
io
n
o
u
tlin
es th
e
p
r
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s
s
b
y
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ich
o
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ject
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ea
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d
t
h
eir
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r
r
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o
n
d
in
g
in
f
o
r
m
ativ
e
f
ea
tu
r
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ar
e
q
u
an
tifie
d
a
n
d
n
o
r
m
alize
d
f
o
r
co
n
s
is
ten
t
u
s
e
in
m
ac
h
in
e
lea
r
n
in
g
p
i
p
elin
es
[
3
6
]
.
T
h
e
f
o
ll
o
win
g
m
etr
ics
ar
e
co
m
p
u
ted
f
o
r
ea
ch
im
a
g
e
an
d
s
er
v
e
as d
escr
ip
to
r
s
o
f
its
g
eo
m
etr
ic
an
d
s
tr
u
ctu
r
al
co
n
ten
t:
a.
C
o
n
tr
ast
:
A
m
ea
s
u
r
e
o
f
in
ten
s
i
ty
v
ar
iatio
n
ac
r
o
s
s
th
e
im
ag
e.
b.
Nu
m
b
er
o
f
co
n
t
o
u
r
s
(
_
)
:
T
o
tal
n
u
m
b
er
o
f
d
is
tin
ct
o
b
ject
b
o
u
n
d
ar
ies d
etec
ted
.
c.
Me
an
co
n
to
u
r
ar
ea
(
_
_
)
:
T
h
e
av
e
r
ag
e
ar
ea
e
n
clo
s
ed
b
y
id
en
tifie
d
co
n
to
u
r
s
.
d.
Stan
d
ar
d
d
e
v
iatio
n
o
f
co
n
t
o
u
r
ar
ea
(
_
_
)
:
Var
iab
ilit
y
in
th
e
s
ize
o
f
d
etec
ted
r
eg
io
n
s
.
e.
Me
an
co
n
to
u
r
p
e
r
im
eter
(
_
_
)
:
Av
er
ag
e
len
g
th
o
f
th
e
p
e
r
im
eter
s
o
f
all
co
n
to
u
r
s
.
f.
Stan
d
ar
d
d
e
v
iatio
n
o
f
co
n
t
o
u
r
p
er
im
eter
(
_
_
)
:
Dis
p
er
s
io
n
in
th
e
p
er
im
eter
len
g
th
s
.
g.
Me
an
ar
ea
-
to
-
p
er
im
eter
r
atio
(
_
_
_
_
)
:
A
s
h
ap
e
d
escr
ip
to
r
ca
p
t
u
r
in
g
o
b
ject
co
m
p
ac
tn
ess
.
h.
Fra
ctal
d
im
en
s
io
n
:
A
co
m
p
lex
ity
m
ea
s
u
r
e
th
at
q
u
an
tifie
s
th
e
s
elf
-
s
im
ilar
ity
o
r
ir
r
eg
u
lar
i
ty
o
f
th
e
o
b
ject'
s
s
h
ap
e
.
Fig
u
r
e
4
d
is
p
lay
s
th
e
p
r
o
g
r
e
s
s
io
n
o
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r
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r
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io
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io
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atin
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ip
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n
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lu
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ated
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r
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ig
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r
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n
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ig
u
r
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h
e
s
ca
lin
g
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er
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f
o
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m
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la
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³
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T
h
is
v
is
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aliza
tio
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ef
f
ec
tiv
ely
d
em
o
n
s
tr
ates
th
e
g
en
er
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s
ca
lin
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law
=
,
wh
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er
v
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as
th
e
m
ath
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atica
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asis
f
o
r
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s
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g
th
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b
o
x
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c
o
u
n
ti
n
g
m
eth
o
d
.
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:
2088
-
8
7
0
8
Meth
o
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fo
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ma
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Mir
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261
Fig
u
r
e
4
.
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tr
ad
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in
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0
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1
0
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[
3
7
]
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,
=
,
−
,
,
−
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(
1
0
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e,
,
is
n
o
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ately
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s
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ain
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el
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ess
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o
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tim
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at
asets
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2
.
4
.
Su
pp
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rt
v
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t
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r
ma
chine
[
9]
I
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tu
d
y
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th
e
s
u
p
p
o
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t
v
ec
to
r
m
ac
h
in
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(
SVM)
alg
o
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ith
m
was
em
p
lo
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ed
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r
th
e
class
if
icatio
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o
f
f
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im
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ac
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o
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OR
B
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d
etec
tio
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d
f
r
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tal
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im
en
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aly
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is
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e
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r
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s
u
lated
b
o
th
g
eo
m
etr
ic
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d
tex
t
u
r
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r
o
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er
ties
o
f
th
e
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g
et
o
b
jects.
T
h
e
r
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ltin
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f
ea
tu
r
e
v
ec
to
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s
wer
e
s
u
b
s
eq
u
en
tly
n
o
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alize
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,
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o
u
tlin
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in
s
ec
tio
n
2
.
3
,
an
d
s
er
v
ed
as in
p
u
t to
th
e
SVM
class
if
ier
.
SVM
is
a
well
-
estab
li
s
h
ed
s
u
p
er
v
is
ed
lear
n
in
g
alg
o
r
ith
m
p
ar
ticu
lar
ly
s
u
ited
f
o
r
b
in
a
r
y
cl
ass
if
icatio
n
task
s
.
T
h
e
co
r
e
id
ea
b
eh
i
n
d
S
VM
is
th
e
id
en
tific
atio
n
o
f
an
o
p
tim
al
s
ep
a
r
atin
g
h
y
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e
r
p
lan
e
with
in
th
e
f
ea
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r
e
s
p
ac
e
th
at
m
ax
im
izes
th
e
m
ar
g
in
b
etwe
en
d
ata
p
o
in
ts
b
elo
n
g
i
n
g
to
d
if
f
e
r
en
t
cla
s
s
es.
T
h
is
m
ar
g
in
m
ax
im
izatio
n
s
tr
ateg
y
co
n
tr
i
b
u
tes
s
ig
n
if
ican
tly
to
th
e
m
o
d
el'
s
g
en
er
aliza
tio
n
p
e
r
f
o
r
m
an
ce
.
T
h
e
SVM
o
p
er
ates
th
r
o
u
g
h
th
e
f
o
llo
win
g
s
eq
u
en
ce
o
f
s
tep
s
,
en
ab
lin
g
ef
f
ec
tiv
e
class
if
icatio
n
o
f
im
ag
es
b
ased
o
n
th
e
ex
tr
ac
ted
f
ea
tu
r
es:
2
.
4
.
1
.
L
inea
r
s
up
po
rt
v
ec
t
o
r
m
a
chine
Giv
en
a
lab
eled
tr
ain
i
n
g
d
ataset:
{
(
,
)
}
,
=
1
,
2
,
…
,
,
ℝ
,
{
−
1
,
+
1
}
(
1
0
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
1
6
,
No
.
1
,
Feb
r
u
ar
y
20
2
6
:
2
5
6
-
277
262
wh
er
e
is
a
f
ea
tu
r
e
v
ec
to
r
ex
t
r
ac
ted
f
r
o
m
an
im
ag
e
a
n
d
is
th
e
co
r
r
esp
o
n
d
in
g
class
lab
el,
SVM
s
ee
k
s
t
o
f
in
d
th
e
o
p
tim
al
s
ep
ar
atin
g
h
y
p
er
p
lan
e,
is
n
u
m
b
e
r
o
f
tr
ain
in
g
ex
am
p
les
[
3
8
]
.
T
h
e
g
o
al
o
f
SVM
is
to
f
in
d
a
h
y
p
er
p
lan
e:
+
=
0
(
1
1
)
th
at
m
ax
im
izes th
e
m
ar
g
i
n
b
et
wee
n
th
e
two
class
es.
T
h
e
o
p
ti
m
izatio
n
p
r
o
b
lem
is
f
o
r
m
u
late
d
as:
min
,
1
2
‖
‖
2
(
1
2
)
s
u
b
ject
to
th
e
co
n
s
tr
ain
t:
(
+
)
≥
1
,
⩝
(
1
3
)
T
h
is
en
s
u
r
es
th
at
all
d
ata
p
o
in
ts
ar
e
co
r
r
ec
tly
class
if
ied
with
a
m
a
r
g
in
o
f
at
least
1
.
Fig
u
r
e
5
illu
s
tr
atio
n
o
f
a
lin
ea
r
SVM.
T
h
e
d
ec
is
io
n
b
o
u
n
d
ar
y
s
ep
ar
ates
two
d
ata
cla
s
s
es
an
d
is
p
lace
d
m
id
way
b
etwe
en
th
e
n
ea
r
est
d
ata
p
o
in
ts
(
s
u
p
p
o
r
t v
ec
to
r
s
)
.
Dash
ed
lin
es in
d
icate
th
e
m
ax
i
m
u
m
m
ar
g
in
.
Fig
u
r
e
5
.
T
wo
-
d
im
en
s
io
n
al
s
ca
tter
p
lo
t w
ith
a
lin
ea
r
s
ep
ar
ati
n
g
h
y
p
er
p
la
n
e
o
f
th
e
SVM
2
.
4
.
2
.
So
f
t
m
a
r
g
in SVM
I
n
r
ea
l
-
wo
r
l
d
s
ce
n
ar
io
s
,
p
e
r
f
ec
t sep
ar
atio
n
m
ay
n
o
t b
e
p
o
s
s
ib
le.
T
h
er
ef
o
r
e,
s
lack
v
a
r
iab
les
ɛ
≥
0
ar
e
in
tr
o
d
u
ce
d
to
allo
w
s
o
m
e
m
is
class
if
icatio
n
.
T
h
e
m
o
d
if
ied
o
p
t
im
izatio
n
p
r
o
b
lem
b
ec
o
m
es
[
3
9
]
:
min
,
1
2
‖
‖
2
+
∑
ɛ
=
1
(
1
4
)
s
u
b
ject
to
:
(
+
)
≥
1
−
ɛ
,
ɛ
≥
0
(
1
5
)
wh
er
e
>
0
is
a
r
eg
u
lar
izatio
n
p
ar
am
eter
th
at
c
o
n
tr
o
ls
t
h
e
tr
ad
e
-
o
f
f
b
etwe
en
m
ax
im
izin
g
th
e
m
ar
g
in
an
d
m
in
im
izin
g
class
if
icatio
n
er
r
o
r
s
.
Fig
u
r
e
6
two
-
d
im
e
n
s
io
n
al
p
lo
t
illu
s
tr
atin
g
th
e
s
o
f
t
m
ar
g
in
SVM,
wh
er
e
s
o
m
e
d
ata
p
o
in
ts
ar
e
allo
we
d
with
in
o
r
b
e
y
o
n
d
th
e
m
a
r
g
in
b
o
u
n
d
a
r
ies.
Fig
u
r
e
6
.
T
wo
-
d
im
en
s
io
n
al
p
l
o
t o
f
th
e
s
u
p
p
o
r
t v
ec
to
r
m
ac
h
i
n
e
with
a
s
o
f
t m
ar
g
in
(
s
o
f
t
m
a
r
g
in
SVM)
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:
2088
-
8
7
0
8
Meth
o
d
s
fo
r
id
en
tifyin
g
in
fo
r
ma
tive
fea
tu
r
es in
a
g
r
icu
ltu
r
a
l ima
g
es
(
Mir
z
a
a
kb
a
r
Hu
d
a
yb
e
r
d
iev
)
263
2
.
4
.
3
.
No
n
-
lin
ea
r
SVM
a
nd
k
er
nel t
rick
W
h
en
th
e
d
ata
is
n
o
t
lin
ea
r
ly
s
ep
ar
ab
le
in
th
e
o
r
i
g
in
al
s
p
ac
e,
a
n
o
n
-
lin
e
ar
m
ap
p
in
g
ɸ
(
)
is
ap
p
lied
to
p
r
o
ject
th
e
d
ata
in
to
a
h
i
g
h
er
-
d
im
en
s
io
n
al
f
ea
tu
r
e
s
p
ac
e
wh
er
e
lin
ea
r
s
ep
ar
atio
n
m
a
y
b
e
p
o
s
s
ib
le.
T
h
is
is
ef
f
icien
tly
im
p
lem
en
te
d
u
s
in
g
a
k
er
n
el
f
u
n
ctio
n
(
,
)
d
ef
in
ed
as
[
4
0
]
:
(
,
)
=
ɸ
(
)
ɸ
(
)
(
1
6
)
C
o
m
m
o
n
k
e
r
n
el
f
u
n
ctio
n
s
in
cl
u
d
e:
−
L
in
ea
r
k
er
n
el:
(
,
)
=
−
Po
ly
n
o
m
ial
k
er
n
el:
(
,
)
=
(
+
)
−
R
ad
ial
b
asis
f
u
n
ctio
n
(
R
B
F)
k
er
n
el:
(
,
)
=
e
xp
(
−
‖
−
‖
2
)
I
n
th
is
s
tu
d
y
,
th
e
R
B
F
k
er
n
el
was
u
s
ed
d
u
e
to
its
ab
ilit
y
to
h
an
d
le
n
o
n
-
lin
ea
r
f
ea
tu
r
e
d
is
tr
ib
u
tio
n
s
ty
p
ical
in
ag
r
icu
ltu
r
al
im
ag
e
d
ata
.
Fig
u
r
e
7
v
is
u
aliza
tio
n
o
f
a
n
o
n
-
lin
e
ar
SVM
u
s
in
g
th
e
k
er
n
el
tr
ick
to
p
r
o
ject
d
ata
in
to
a
h
ig
h
er
-
d
im
en
s
io
n
al
s
p
ac
e
f
o
r
lin
ea
r
s
ep
ar
atio
n
.
Fig
u
r
e
7
.
Vis
u
aliza
tio
n
o
f
a
n
o
n
-
lin
ea
r
SVM
an
d
t
h
e
ap
p
licat
io
n
o
f
t
h
e
Ker
n
el
tr
ick
2
.
4
.
4
.
Dec
is
io
n f
un
ct
io
n
T
h
e
f
in
al
d
ec
is
io
n
f
u
n
ctio
n
u
s
ed
f
o
r
class
if
icatio
n
is
d
ef
in
ed
as:
(
)
=
(
∑
(
,
)
+
=
1
)
(
1
7
)
wh
er
e
ar
e
L
ag
r
an
g
e
m
u
ltip
lie
r
s
d
eter
m
in
ed
d
u
r
in
g
th
e
tr
ain
i
n
g
p
h
ase,
a
n
d
(
,
)
co
m
p
u
tes th
e
s
im
ilar
ity
b
etwe
en
th
e
s
u
p
p
o
r
t v
ec
t
o
r
s
a
n
d
th
e
test
in
p
u
t.
T
h
e
ex
tr
ac
ted
f
ea
tu
r
es
f
r
o
m
th
e
ag
r
icu
ltu
r
al
im
ag
es
—
ca
p
tu
r
in
g
te
x
tu
r
e,
g
eo
m
etr
ic
s
tr
u
ctu
r
e,
an
d
k
ey
p
o
i
n
t
-
b
ased
d
escr
ip
to
r
s
—
wer
e
u
s
ed
to
tr
ain
an
SVM
m
o
d
el
with
an
R
B
F
k
er
n
el.
T
h
e
m
o
d
el
p
ar
am
eter
s
an
d
wer
e
o
p
tim
ized
u
s
in
g
k
-
f
o
ld
cr
o
s
s
-
v
alid
atio
n
to
p
r
ev
en
t
o
v
er
f
itti
n
g
an
d
en
s
u
r
e
g
e
n
er
aliza
tio
n
.
T
h
e
SVM
class
if
ier
d
em
o
n
s
tr
ated
h
ig
h
ac
c
u
r
ac
y
an
d
r
o
b
u
s
tn
ess
in
d
is
tin
g
u
is
h
in
g
b
etwe
e
n
d
if
f
er
en
t
im
ag
e
ca
teg
o
r
ies
b
ased
o
n
th
e
in
f
o
r
m
ativ
e
f
ea
tu
r
es.
Fig
u
r
e
8
v
is
u
aliza
tio
n
o
f
t
h
e
SVM
d
ec
is
io
n
f
u
n
ctio
n
a
n
d
t
h
e
m
ar
g
in
b
o
u
n
d
ar
ies d
ef
in
e
d
b
y
(
)
=
±
1
.
Fig
u
r
e
8
.
SVM
d
ec
is
io
n
f
u
n
cti
o
n
an
d
m
ar
g
i
n
b
o
u
n
d
a
r
ies
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
1
6
,
No
.
1
,
Feb
r
u
ar
y
20
2
6
:
2
5
6
-
277
264
2
.
5
.
Ev
a
lu
a
ti
o
n
m
e
tr
ics
T
o
q
u
an
titativ
ely
ass
ess
th
e
p
er
f
o
r
m
an
ce
o
f
th
e
p
r
o
p
o
s
ed
im
ag
e
class
if
icatio
n
ap
p
r
o
ac
h
,
s
ev
er
al
s
tan
d
ar
d
ev
alu
atio
n
m
etr
ics
wer
e
em
p
lo
y
e
d
.
T
h
ese
m
etr
ics
p
r
o
v
id
e
i
n
s
ig
h
t
in
to
b
o
t
h
th
e
o
v
er
all
ac
cu
r
ac
y
an
d
th
e
r
eliab
ilit
y
o
f
th
e
class
if
ier
ac
r
o
s
s
d
if
f
er
en
t c
ateg
o
r
ies.
a.
Acc
u
r
ac
y
Acc
u
r
ac
y
is
th
e
p
r
o
p
o
r
tio
n
o
f
co
r
r
ec
tly
class
if
ied
in
s
tan
ce
s
am
o
n
g
t
h
e
to
tal
n
u
m
b
e
r
o
f
s
am
p
les.
I
t
is
d
ef
in
ed
as:
=
+
+
+
+
(
1
8
)
wh
er
e
(
Tr
u
e
P
o
s
itives)
:
Nu
m
b
er
o
f
co
r
r
ec
tl
y
class
if
ied
p
o
s
itiv
e
s
am
p
les,
(
Tr
u
e
N
eg
a
tives)
:
Nu
m
b
er
o
f
co
r
r
ec
tly
class
if
ied
n
e
g
ativ
e
s
am
p
les,
(
F
a
ls
e
P
o
s
itives)
:
Nu
m
b
er
o
f
n
eg
ativ
e
s
am
p
les
in
co
r
r
ec
t
l
y
class
if
ied
as p
o
s
itiv
e,
(
F
a
ls
e
N
eg
a
tives)
: N
u
m
b
er
o
f
p
o
s
itiv
e
s
am
p
les in
co
r
r
ec
tly
class
if
ie
d
as n
eg
ativ
e.
I
n
th
is
s
tu
d
y
,
th
e
SVM
class
if
ier
ac
h
iev
ed
h
ig
h
ac
cu
r
ac
y
in
th
e
test
d
ataset,
d
em
o
n
s
tr
atin
g
h
ig
h
p
er
f
o
r
m
a
n
ce
in
d
is
tin
g
u
is
h
in
g
im
ag
e
class
es b
ased
o
n
th
e
e
x
tr
ac
ted
in
f
o
r
m
at
iv
e
f
ea
tu
r
es.
b.
Pre
cisi
o
n
,
R
ec
all,
an
d
F1
-
Sco
r
e
I
n
ad
d
itio
n
to
ac
cu
r
ac
y
,
t
h
e
f
o
l
lo
win
g
m
etr
ics we
r
e
ca
lcu
late
d
:
−
Pre
cisi
o
n
:
=
+
(
1
9
)
Me
asu
r
es th
e
p
r
o
p
o
r
tio
n
o
f
p
o
s
itiv
e
id
en
tific
atio
n
s
th
at
wer
e
ac
tu
ally
co
r
r
ec
t.
−
R
ec
all
(
Sen
s
itiv
ity
)
=
+
(
2
0
)
Me
asu
r
es th
e
p
r
o
p
o
r
tio
n
o
f
ac
t
u
al
p
o
s
itiv
es th
at
wer
e
co
r
r
ec
tl
y
id
en
tifie
d
.
−
F1
-
Sco
r
e
1
=
2
+
(
2
1
)
Pro
v
id
es a
h
ar
m
o
n
ic
m
ea
n
o
f
p
r
ec
is
io
n
an
d
r
ec
all,
esp
ec
ially
u
s
ef
u
l in
im
b
alan
ce
d
d
atasets
.
c.
C
r
o
s
s
-
v
alid
atio
n
T
o
en
s
u
r
e
g
e
n
er
aliza
b
ilit
y
an
d
av
o
id
o
v
er
f
itti
n
g
,
k
-
f
o
ld
cr
o
s
s
-
v
alid
atio
n
was
p
er
f
o
r
m
ed
with
=
5
.
T
h
e
m
o
d
el
m
ain
tain
ed
s
tab
le
p
er
f
o
r
m
an
ce
ac
r
o
s
s
all
f
o
ld
s
,
in
d
icatin
g
its
r
o
b
u
s
tn
ess
o
n
u
n
s
ee
n
d
ata.
3.
RE
SU
L
T
S
Usi
n
g
th
e
ab
o
v
e
m
eth
o
d
s
,
th
e
r
esu
lts
o
f
th
e
s
tu
d
y
will
b
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Evaluation Warning : The document was created with Spire.PDF for Python.