Image Processing Reference
In-Depth Information
radiometric fidelity of the data as a quality measure while increasing the spatial
resolution in the case of pan-sharpening [207].
2.
Fusion Factor:
The fusion factor quantifies the amount of mutual information
between each of the input bands (or images) and the fused image. It indicates the
extent of similarity of each of the bands with the final fused image, and hence,
the contribution of each band towards the final result. The fusion factor FF while
fusing two images
I
1
and
I
2
is defined as [144, 147]:
FF
(
I
1
,
I
2
)
=
MI
(
I
1
,
F
)
+
MI
(
I
2
,
F
),
(9.11)
where the MI is the amount of mutual information between the fused image
F
. Chen et al. presented a detailed theoretical
analysis of this mutual information-based measure in [37]. A higher fusion factor
implies a higher similarity between the final image and the input bands- a necessity
for any good fusion technique. However, this definition does not take into account
the variation in information contents of individual bands of the hyperspectral data.
It is reasonable to expect a smaller value of mutual information for the bands with
lesser information content, and vice-versa. To circumvent this problem, we use
a modified expression by considering the entropies of the individual bands that
indicate the intrinsic amount of information in the corresponding bands [92]. It
suggests a weighted addition of the mutual information between the constituent
bands and the final image where the weights have been set to the entropy of the
corresponding input band. The fusion factor FF is calculated as the normalized
weighted sum of the mutual information between input bands and the resultant
image. The modified fusion factor assesses the participation of the input bands
I
k
,
∀
=
F(
I
1
,
I
2
)
using technique
F
k
towards the fused image
F
by appropriately weighing them with respect
to their intrinsic information content measured in terms of entropy, i.e.,
H
.
Through a normalizing denominator, it also makes the term independent of the
number of constituent image bands. The modified FF for fusion of hyperspectral
data set with
K
bands is given by Eq. (
9.12
).
(
I
k
)
k
=
1
MI
(
I
k
,
F
)
H
(
I
k
)
FF
=
.
(9.12)
k
=
1
H
(
I
k
)
A higher value of FF, which implies a higher amount of information in
F
from
its constituent bands, is desirable.
3.
Fusion Symmetry:
The measure fusion factor does not provide any idea about
the uniformity of the technique in combining the information from all of the
constituent images (or hyperspectral bands). A good fusion technique should
avoid uneven participation from input bands. In such cases, fused images often
highlight features only from a particular subset of hyperspectral bands, while
several other features get lost in the process of combining. A higher fusion factor
FF does not necessarily indicate a uniform participation or contribution from all
