![](https://csdnimg.cn/release/download_crawler_static/18499741/bg4.jpg)
3. Proposed fusion scheme
3.1. Acquisition of initial and transition fused images
As we know, the MST-based fusion method has the strong
stability and reliability. However, this method may produce a
suboptimal fusion result due to the case of mistaken identity of
pixel focusing properties. Experimental results demonstrate that
the difference between a low-quality fused image and focused
region of one source image is sharper than those generated by
high-quality fused image. Based on this fact, we design two novel
schemes to improve the quality of the transition fused images.
Firstly, we must obtain the initial low-quality and the transition
high-quality fused images.
To obtain a high-quality transition fused result, the MMND is
used as the MST to decompose the source images. For the lowpass
subband coefficients, we can obtain the lowpass subband coeffi-
cients of the fused image by
∑
()= ()(= …)
()
=
fxy
N
fxy l L,
1
,, 1,2, ,,
10
L
F
i
N
Li
1
,
where N is the number of the source images,
(
fxy,
L
F
and
()fxy,
Li,
are the lowpass subband coefficients of fused and the original
image i at the coarsest scale L and location (x,y).
When the source images are decomposed by the MMND, we
obtain a series of highpass subbands which contain the most in-
trinsic geometrical structures of the source image, and these
structures generally correspond to the salient features in the
source image. In addition, the pixel in source image i is with higher
saliency, this pixel is more possible in focus. Therefore, to improve
the fusion performance, the saliency features of the source images
should be extracted and transferred into the fused result. To sup-
port this, the saliency measure must be well-designed.
According to the imaging properties of multifocus images, we
know that the pixel with a sharp change in the gray value corre-
spond to the salient features such as edge lines, region boundaries.
The more intense changes in gray value the pixel is, the more
possible it locates in focus. Based on this analysis, we proposed a
new focus measure (FM) to determine the focusing properties of
the highpass subband coefficients. Let
Ω
be a local region centered
at a given point (x,y), the FM is defined as
∑
()=
|( )|(( )− ( ))
((( )( )))
()
Ω
α
()∈
FM x y
fxy fab fxy
dxy ab
,
,, ,
,,,
,
11
ab,
2
where ‘
(( ) ( )
dab xy,,,
’ denotes the distance from (a,b)to(x,y);
α
is
a constant, which is used to adjust the importance of
‘
(( ) ( )
dab xy,,,
’ in
(
FM x y,
. For convenience,
α
can be set to 1 in
our proposed methods. In fact, when the point
(
ab,
is far from
(
xy,
, its contribution to the saliency of point
(
xy,
will be reduced.
Based on this analysis, in
(
FM x y,
, we employ ‘
(( ) ( )
dab xy,,,
’ to
reflect the influence of distance between (a,b) and (x,y)on
()|(()−())fxy fab fxy,, ,
. In contrast to OD de fi ned in Eq. (1),
‘
(( ) ( )
dab xy,,,
’ is described as
(( ) ( )) = ( − ) + ( − )
()
dab xy a x b y,,,
12
22
To better understand the process, Fig. 2 illustrates the calculation
of distance in a local neighborhood
Ω
.Indefinition of
(
FM x y,
,
(( )− ( ))fab fxy,,
2
is used to describe the change in pixel intensity,
and
()|fxy,
is employed to express the role that the current pixel
plays in determining its focusing property. Based on the definition
of Eq. (11), we developed the following discriminate criterion (DC)
to determine which pixel of l-th scale and p-th direction is focused
in image i.
}
{
)
(
Ω
()=( )∈ ( )≥ ( )
…()()…()
()
−
+
⎡
⎢
⎢
⎤
⎥
⎥
xy xy FMxy FMxy
FM x y FM x y FM x y
DC , , , max , ,
,,,,,,,,
13
lp
i
lp
i
lp
lp
i
lp
i
lp
N
,
0
0
1
,
0
0
,
1
0
0
,
1
0
0
,
1
0
0
,
0
0
where
⌈
denotes the cardinality of set
·}
in a local region
Ω
1
centered at (x,y). In this definition of DC, the idea of major operator
is introduced with the expectation that the distinguishing per-
formance of DC can be improved. Based on the definition of Eq.
(13), we established a decision map (DM) for each source image as
follows:
()=
()>
˜
×
˜
()
⎧
⎨
⎪
⎩
⎪
xy
xy
MN
DM ,
1, if DC ,
2
0, otherwise
14
lp
i
lp
i
,
,
where
˜
×
˜
M
is the size of
Ω
1
. The coeffi cient of the highpass
subband with a higher value of
(
xyDC ,
generally correspond to
the salient features of the focused regions in source image.
Therefore, the selection principle for different directional highpass
Fig. 2. Distance of different position in local region Ω. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this
paper.)
H. Li et al. / Signal Processing 128 (2016) 474–493 477