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(m
2
,n
2
)
j
(r
r = max(|(m
2
− m
1
|, |n
2
− n
1
|)
δ =(r, θ)
θ
(m
1
,n
1
)
i
Fig. 3
Illustration of
P
δ
(
i
,
j
)
2nd order statistics, statistics derived from run length matrix the amount is higher
order statistics.
In this work, Co-occurrence matrix is adopted.
3.2
Co-occurrence Matrix
In Fig. 3Assuming
P
δ
(
i
,
j
)
is the brightness probability of pixel
j
=
b
(
m
2
,
n
2
)
which
has a displacement
δ
=(
r
,
θ
)
from pixel
i
=
b
(
m
1
,
n
1
)
, the co-occurrence matrix of
(
can be derived. by calculating 11 types of feature value from
co-occurrence matrix, the texture can be characterized by these values.
Let
P
x
i
,
j
=
1
,
2
,···,
n
−
1
)
(
)
(
)
(
+
)
(
|
−
|
)
i
,
P
y
j
,
P
x
+
y
i
j
and
P
x
−
y
i
j
defined as following,
n
1
j
=
0
P
δ
(
i
,
j
)
−
P
x
(
i
)=
i
=
0
,
1
, ...,
n
−
1
(1)
n
1
i
=
0
P
δ
(
i
,
j
)
−
P
y
(
j
)=
j
=
0
,
1
, ...,
n
−
1
(2)
−
i
=
0
n
n
1
j
=
0
P
δ
(
i
,
j
)
−
P
x
+
y
(
i
+
j
)=
k
=
0
,
1
, ...,
2
n
−
2
(3)
n
−
i
=
0
n
−
1
j
=
0
P
δ
(
i
,
j
)
P
x
−
y
(
|
i
−
j
|
)=
k
=
0
,
1
, ...,
n
−
1
(4)
Angular second moment is given by
n
−
1
i
=
0
n
−
1
j
=
0
P
δ
(
i
,
j
)
2
ASM
=
(5)
Contrast is given by
n
1
k
=
0
k
2
−
CNT
=
·
P
x
−
y
(
k
)
(6)
Correlation is given by
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