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The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B7. Beijing 2008
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using SWT, the original image is transformed into four pieces
which can be labeled as ZZ , LH , HL and HH . The ZZ piece
is the low-band or called approximated component, the
remaining pieces LH , HL and HH are high-bands or called
detail components. All of the components have the same size as
the original image due to shift-invariant character.
In the wavelet domains of the two transformed images,
low-bands coefficients are integrated using the weighted
average, the fusion equation is as below:
LL(x,y) =a *LL\(x,y) + b *LL2(x,y) (16)
3. OUR PROPOSED FUSION ALGORITHM
An important preprocessing step in image fusion is image
registration. It ensures that the information from each of the
images refers to the same physical structure in the environment.
In this paper, we assume that images to be combined have
already been co-registered. The proposed multifocus image
fusion algorithm is composed of computing SML for each
focus image, SWT decomposition, image fusion and inverse
SWT.
where LL represents the new low-band coefficient after
fusion, a and b denote weighted coefficients, their
summation is always 1.
The high-bands coefficients are first integrated using
choose-max as follows:
J HH 1(jc, y) HH l(x, y) > HH2(x, y)
[HH2(x,y) HHl(x,y) < HH2(x,y)
(17)
Firstly, we choose SML as focus measure to compute the
clarity of each focus image. With the SML, we can get two
initial binary decision maps by setting two thresholds to the
SML difference between two focus images, which can be
represented with the following equations:
Map\{x, y)
SML\(x, y) - SML2(x, y) > T1
SML\{x, y) - SML2(x, y) < 7T
(14)
Map2(x, y)
SML\(x,y) - SML2{x,y) < T2
SML\(x,y) - SML2(x,y) > T2
(15)
Then the two SML decision maps are used to refine the fusion
rule.
HH(x,y) = <
HH\(x,y)
HH2{x,y)
HH(x,y)
A/apl(x,y) = 1
AZap2(x, y) = 1
others
(18)
The similar fusion rules are performed on LH and HL
high-bands in each decomposition level.
At last, the fused image will be obtained by reconstructed with
the fused approximate coefficients and detailed coefficients.
where Map1 and Map2 denote two decision maps. SML\
and SML2 represent the SML values of two focused
images respectively. 71 and T2 are two thresholds.
Secondly, two focus images are decomposed into multiscale
coefficients with SWT respectively. Due to the decomposition
The proposed approach is implemented in personal computers
with MATLAB 6.5 programs under Microsoft Windows XP
environment.
4. EXPERIMENTAL RESULT AND EVALUATION
To illustrate the performance of the proposed method, two
groups of different focus but co-registered images are taken as
examples in this paper. In order to compare fusion effect,
discrete wavelet fusion method is performed as reference.
computed to evaluation image quality quantitatively (Wang et
al.,2002). The bigger of the average gradient, the more
The wavelet function sym4 is adopted and the input images are
decomposed to 2 levels in this paper. The thresholds 71 and
T2 are set to 0.2 and -0.2 respectively. Both low-band
weighted coefficients a and b are equal to 0.5. The
simulation experiment results are shown as Figure 1 and Figure
2.
It is difficult to evaluation the quality of a fusion image (Wald
et al., 1997). Generally, the visual perception and quantitative
analysis are used to compare image quality. From the visual
perception, it is obvious form Figure 1 and Figure 2 that the
proposed method has reserved more detail information than the
wavelet transform method. The average gradient of image is
clear-cut of the image is. The equation of the average gradient
is as follows,
J M-\ N-1
If
09)
2 ax. dyj