Image Processing Reference

In-Depth Information

Fig. 8.5
Plots of Bhattacharyya coefficient between the resultant image from the fusion of entire

data and the resultant images for various values of

κ

for the urban and the moffett
2
data using

the bilateral filtering-based fusion technique over the subsets selected using the output-based band

selection scheme

for the output-based band selection scheme

can be provided by Eq. (
8.3
) which is quite similar to the requirement for the input-

The computational requirement
W

(κ)

W

(κ)
=
γ B(κ)
+

c
E
,

(8.3)

where

, and
c
E
denotes

the amount of computation for the evaluation of conditional entropies of the succes-

sive image bands. The

B(κ)

is the number of bands selected for a given threshold

κ

factor represents the proportionality factor to account for

computational requirements of a chosen fusion technique. The only difference lies in

the fact that an intermediate fusion has been carried out first before the computation

of the conditional entropies, unlike in the input-based scheme wherein fusion fol-

lows the entropy computation. This inherently assumes that one uses an incremental

fusion technique for the output-based scheme. The incremental fusion makes use

of the resultant of the previous intermediate fusion for carrying out the next fusion

process. Thus, if
F

γ

is the intermediate fused image from fusion of upto

(

k

−

1

)

(

k

−

1

)

bands from the data using the fusion technique

F

(the actual number of bands being

fused might be much less than

), and
I
k
be

the next input band to be selected for fusion, then the output of the fusion, i.e.,
F
k
,is

obtained as
F
k
≡
F(

(

k

−

1

)

depending upon the values of

κ

. Unfortunately, the incremental fusion methods may

suffer from numerical inaccuracies, and one may have to recompute the fusion of all

selected bands after every additional selection of a band. In this scenario, the compu-

tation increases after every selected band and one may not have any computational

advantage over the normal scheme of fusion of all bands.

F
k
−
1
,

I
k
)