Image Processing Reference

In-Depth Information

In this chapter, we shall discuss a method for selection of a few specific bands

to accomplish a faster fusion of hyperspectral images, without much sacrificing

the quality of the result of fusion. We present an information theoretic strategy

for choosing specific image bands of the hyperspectral data cube using only the

input hyperspectral image. The selected subset of bands can then be fused using any

existing pixel-based fusion technique as the band selection process is independent

of the method of fusion. The objective of this chapter lies in providing a much faster

scheme for hyperspectral image visualization with a minimal degradation in the

fusion quality through selection of specific bands. The band selection process should

be computationally inexpensive, and yet, should be able to generate comparable

quality fusion results for the given fusion technique.

The next section describes a possible scheme of entropy-based band selection.

This is a generic scheme for the data containing a large number of bands. The hyper-

spectral data consist of a spectrally ordered set of contiguous bands. We exploit this

order
-based characteristic, and develop a model for measurement of the similarity

across bands. Section
4.3
provides details of the model, and develops the special

case for spectrally ordered hyperspectral data—which is usually the case. We also

provide a couple of theorems for the savings in computation for this special case of

band selection. Section
4.4
consists of the experimental results and the performance

analysis of the band selection scheme. Summary is presented in Sect.
4.5
.

4.2 Entropy-Based Band Selection

In case of hyperspectral imaging sensors, these images are acquired over a narrow

but contiguous spectral bands. Therefore, several image bands exhibit a very high

degree of spectral correlation among them, typically highest degree of correlation is

found within two successive bands as they depict the reflectance response of these

scene over contiguous, adjacent wavelength bands. For instance, consider the urban

hyperspectral image acquired by the Hyperion, and the moffett
2
hyperspectral image

acquired by the AVIRIS sensors. We may measure the correlation among the adjacent

bands of the respective datasets using the correlation coefficient CC, which is defined

by Eq. (
4.1
).

x
=
1
y
=
1
(
I
k
(
x
,
y
)
−
m
(
I
k
)) (
I
k
+
1
(
x
,
y
)
−
m
(
I
k
+
1
))

x
y
(
I
k
(
x
,
y
)
−
m
(
I
k
))

CC
(
k
)
=

1
≤
k
<
K
,

2
x
y
(
I
k
+
1
(
x
,
y
)
−
m
(
I
k
+
1
))

2

(4.1)

where
I
k
,

oper-

ator indicates mean of the corresponding argument. Figure
4.1
shows the correlation

coefficient among the adjacent bands of the urban and the moffett
2
datasets. Noisy

bands have been already discarded. The average value of the correlation coefficient

for both the datasets is higher than 0.97. When a fusion algorithm operates over the

similar bands, a very little amount of additional information is contributed towards

the fusion result. Therefore, one may think of selecting a subset of a fewer number

k

=

1to
K
represents the bands of the hyperspectral data. The
m

(.)