Band Selection: Revisited - Hyperspectral Image Fusion - page 118

Fig. 8.1 Results of fusion of
the Hyperion data applied
over a subset of bands
selected using the output-
based scheme. a shows the
results of fusion of only 27
selected bands when

(a) (b)

was
set to 0.70. b shows the cor-
responding result of fusion of
the entire data

κ

the fusion output. However, it can be observed from the plots that the performance
remains almost the same till the value of becomes smaller than 0.60, and it drops

marginally beyond the value of 0.60 signifying that one may discard a large chunk
of bands in order to make fusion process computationally efficient, and yet not lose
on the information content in the fused image.
The average gradient

κ

g of an image evaluates the quality in terms of the spatial
gradient of the image at all pixels. Figure 8.2 b represents the relation between the
average gradient (

¯

g ) with respect to the variation in the threshold parameter ¯ κ .For

the values of nearly up to 0.40, the band selection scheme does not discard any of

the bands from both of the hyperspectral data. This suggests that for any candidate
band, the conditional entropy with respect to the fused image is at least greater than
40 % of its own entropy. Therefore, the corresponding plots of the average gradient
are constant for

κ

40. A gradual decrease in the values of the gradient
can be observed for higher values of

κ = 0to0 .

as fewer bands get selected resulting in a
slight degradation in the quality of the fused image. This reduction in the entropy
and gradient values is very minimal. For example, for

κ

κ = 0 . 80, the output-based

scheme selects less than 1 / 10 -th of the hyperspectral data, and yet the reduction in

the values of the evaluation measures is less than 10 %. The nature of entropy and
average gradient plots from Figs. 8.2 a, b is similar to that of the plots of these measures
for the input-based band selection scheme as one can observe from Figs. ( 4.4 a , b),
respectively. It may be understood that both these schemes suggest that one may carry
out efficient fusion using only a fraction of bands from the hyperspectral image.
While maintaining the consistency with the performance evaluation procedure for
the input-based band selection discussed in Chap. 4 , we shall proceed with the same