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