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
(.)
