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image fusion. As the development of the wavelet theory, wavelet transform has been
paid much attention due to its good time-frequency characteristic[5] . After the emer-
gency of fast algorithm of orthogonal wavelet transform, wavelet transform becomes
more efficient[6], the fusion method based on DWT has been a hot research topic. This
paper select Daubechies, bi-orthogonal wavelet to make wavelet transform, multi-scale
decomposing the images.
The traditional rules, such as averaging low frequency coefficients and selecting
maximum or absolute maximum of high frequency coefficients and so on, have a
common defect that the improvement of fuzzy domain quality is at the expense of the
debasement of clear domain quality. This fusion effect and ideal effect exist certain
deviation. This article introduces canny operator to detect low-frequency and
high-frequency components' edges and makes comparison of the energy of each pixel
and consistency verification to determine the edge points and ensure the clarity of the
fusion image.
2 Image Multiscale Decomposition
Wavelet analysis provides an self-adaptive and localized analysis, which is applicable
to time domain and frequency domain. This analysis can focus on any details of the
time domain and frequency domain. Multi-scale decomposition of the image based on
DWT extract low frequency information, as well as, horizontal, vertical and diagonal
directions of the high frequency details.
When it comes to using DWT to Multi-scale decomposition, Mallat fast algorithm is
most people's first choice. This algorithm requires a two-dimensional scaling func-
tion
ϕ
(
x
,
y
)
ψ
1
(
x
,
y
)
2
and three-dimensional wavelet functions
,
ψ
(
x
,
y
)
and
3
ψ
(
x
,
y
)
. The Fourier Transform of scaling function has low-pass filter characteristic,
while the Fourier Transform of wavelet function has high-pass filter characteristic.
Constructing low-pass filter and high-pass filter by the scaling function and wavelet
function[7], and then you can decompose the image. In this way, a separable scaling
function is constructed:
ϕ
(
x
,
y
)
=
ϕ
(
x
)
ϕ
(
y
)
(1)
And three direction-sensitive wavelet functions are constructed too:
1
ψ
(
x
,
y
)
=
ϕ
(
x
)
ψ
(
y
)
(2)
2
ψ
(
x
,
y
)
=
ψ
(
x
)
ϕ
(
y
)
(3)
3
ψ
(
x
,
y
)
=
ψ
(
x
)
ψ
(
y
)
(4)
1
2
ψ
(
x
,
y
)
ψ
(
x
,
y
)
corresponds to the change of horizontal direction,
corresponds
3
ψ
(
x
,
y
)
to the change of vertical direction,
corresponds to the change of diagonal
direction. Decomposition of the image by two-dimensional Mallat algorithm[8] can be
expressed as the following equations.
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