Image Processing Reference

In-Depth Information

Fig. 4.1
Correlation coeffi-

cient (CC) over the adjacent

bands in the hyperspectral

data. The
black line
represents

the CC for the urban data

from the Hyperion, and the

blue line
represents the CC

for the moffett
2
data from the

AVIRIS

of hyperspectral bands that contain a higher amount of independent information, and

fusing this subset of bands instead of processing the entire set of hyperspectral bands.

Fusion of such a subset would generate an output image without much loss in the

quality when compared with the output image obtained from fusion of the entire data

using the same fusion technique. We explore this possibility of selection of subset

of bands where each band possesses a certain amount of additional information with

respect to other bands, and thus, together they capture of the information content in

the hyperspectral image cube. We describe a conditional entropy-based scheme for

the selection of a fewer number of image bands which are mutually less correlated

in order to facilitate a faster visualization. This scheme turns out to be quite faster

and memory efficient as one can achieve the required quality of fusion using only a

much smaller subset of the hyperspectral data.

4.2.1 Redundancy Elimination

An image band undergoing fusion should possess a significant amount of addi-

tional information for the fusion process to be efficient. We shall now explain

an algorithm to select a subset of image bands based on conditional entropy. Let

I

={

I
k
;

=

,

,...,

}

be the hyperspectral image consisting of
K
bands. We

seek to identify only a subset of bands that will actually undergo fusion. We denote

this subset of cardinality

k

1

2

K

K
as
I
, such that
I

K

K
. The first band is

trivially selected for fusion, which forms the first element of the subset of bands

to be fused, i.e.,
I

⊂

I
, and

. The conditional entropies of the successive bands with

respect to this band are evaluated. The next band is selected when the corresponding

conditional entropy exceeds a pre-determined threshold, i.e., when the additional

information content in the given band is sufficiently high. This threshold has been

selected as an appropriate fraction of the entropy of the band under consideration.

The newly selected band becomes a member of
I
subset. Subsequently, for every

image band, the conditional entropy with respect to each of the previously selected

bands

={

I
1
}

I
k
is calculated. The motivation lies in the fact that a newly available image