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(
1
∑∑
∈∈
A
x
,
y
)
=
f
(
x
,
y
)
ϕ
(
x
)
ϕ
(
y
)
(5)
j
+
j
j
x
Z
y
Z
1
∑∑
∈∈
1
D
(
x
,
y
)
=
A
(
x
,
y
)
ϕ
(
x
)
ψ
(
y
)
(6)
j
+
j
j
j
x
Z
y
Z
∑∑
∈∈
2
D
(
x
,
y
)
=
A
(
x
,
y
)
ψ
(
x
)
ϕ
(
y
)
(7)
j
+
1
j
j
j
x
Z
y
Z
1
∑∑
∈∈
3
D
(
x
,
y
)
=
A
(
x
,
y
)
ψ
(
x
)
ψ
(
y
)
(8)
j
+
j
j
j
x
Z
y
Z
Reconstruction of the image can be expressed as the following equations:
~
~
~
~
~
~
~
~
∑∑
1
2
3
F
=
(
A
ϕ
ϕ
+
D
ϕ
ψ
+
D
ψ
ϕ
+
D
ψ
ψ
)
(9)
j
+
1
j
+
1
j
+
1
j
+
1
j
+
1
j
+
1
j
+
1
j
+
1
j
+
1
j
+
1
j
+
1
j
+
1
x
∈∈
Z
y
Z
1
+
A
D
is the approximate coefficient of the image,
is the horizontal detail co-
j
+
j
2
3
D
D
efficient of the image,
is the vertical detail coefficient of the image,
is the
j
+
1
j
+
1
diagonal detail coefficient of the image.
Show as the Figure 1 below:
Fig. 1.
Image decomposition and reconstruction
3 Image Fusion
1
2
+
3
+
j
D
are carried out edge detection using canny operator. In this way, the horizontal and
vertical detail information of them are extracted. Meanwhile, make a convolution be-
tween a 3 × 3 template and the each frequency domain to acquire the diagonal edge
information. Then the low- frequency coefficients' edge information
A
D
D
Low-frequency component
and high-frequency components
,
,
j
+
j
+
j
EA
,
EA
,
EA
1
2
3
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