Image Processing Reference
In-Depth Information
F
k
and the final fused image
F
K
. The correlation coefficient between each of the
k
incrementally fused images (
F
k
) and the final image
F
indicates the degree
of the pixel-level similarity, and thus, it can be used to analyze the consistency
of the fusion technique as well. The correlation coefficient has been defined by
Eq. (
9.9
).
x
=
1
y
=
1
(
F
k
(
x
,
y
)
−
m
(
F
k
)) (
F
(
x
,
y
)
−
m
(
F
))
CC
k
≡
CC
(
F
k
,
F
)
=
x
y
(
2
,
x
y
(
2
F
k
(
x
,
y
)
−
m
(
F
k
))
F
(
x
,
y
)
−
m
(
F
))
(9.9)
where
m
are the mean gray levels of images
F
k
and
F
, respectively.
Similar to the other measures described in this subsection, the similarity between
the incrementally fused images and the final fused image is expected to increase
as
k
(
F
k
)
and
m
(
F
)
K
. The coefficient being a normalized measure, the maximum value it
can attain is 1, which trivially occurs at the final fused image, i.e.,
CC
k
|
k
=
K
→
=
=
CC
K
1. We expect the function
CC
k
to approach unity monotonically.
It should be noted that the measures with an asymptotic reference deal with
the similarity of the incrementally fused images with the final fused image, and
hence the convergence property of the measures. The first two measures indicate
the similarity in terms of the image histograms i.e., the gray scale distributions,
while the last measure of CC computes the degree of the similarity from the
pixel-wise relationship between the two images.
9.3.3 Participatory Performance Measures
Evaluation of fusion quality is an interesting and useful topic. However, the scope
of the traditional aspect of quality evaluation is limited to the fused image, and little
attention has been paid to how each of the input images (or bands) contribute towards
the final result of fusion. This aspect of contribution can be visually judged from the
input images and the fused image in case of generalized fusion of a very few images.
However, this task is difficult and cumbersome when the number of input images
grows to a few hundreds. For efficient fusion, it is necessary that all the input images
(or bands) participate towards the fusion process. A good fusion technique should
extract the
useful
information content from each of the bands, and combine it to
form the resultant image. Understanding the participation from constituent bands
is an important aspect of fusion, especially in case of hyperspectral data. If some
input bands do not participate towards fusion, one may lose the specific information
contained by those bands, and essentially the corresponding details and features will
be absent in the final fused image. It is also possible, that such a loss of information
might remain unnoticed unless one specifically compares the fused image against all
the input bands. Hence, one needs to consider developing certain specific measures
that can quantify the relative participation of all constituent bands.
