Image Processing Reference
In-Depth Information
output-based perspective. We would again like to select only a few specific bands
to accomplish an efficient fusion of hyperspectral images without much sacrificing
the quality of the fusion output. We discuss an information theoretic strategy for the
selection of specific image bands of the hyperspectral data cube using the correspond-
ing intermediate output of the fusion process. It should be noted that the input-based
band selection scheme is independent of the fusion technique. The present output-
based band selection, however, makes use of the intermediate outputs of the fusion
process, and thus, is very much dependent on the fusion technique employed.
The conditional entropy acts as a measure of the amount of additional information
contained in the band. The rationale and theory behind the use of conditional entropy
the possibility of having an output-based scheme of band selection. Section
8.3
con-
sists of some of the experimental results and the performance analysis of the output-
based band selection scheme. Section
8.4
presents the summary.
8.2 Output-Based Band Selection
We have discussed an input-based scheme of band selection, and its special case for a
in the input prior to the actual fusion. This scheme is independent of the fusion
technique, and hence, does not consider how the fused image gets generated from the
selected image bands. Different fusion techniques have varying capabilities in terms
of combining information from two different sources into a single representation.
Thus, as more and more images are fused, one cannot prove that an increase in
the information content in the fused image is always either equal or proportional to
the conditional entropy of the additional image being fused with. As one is mainly
interested in the final result of fusion for visualization purposes, one may expect to
choose a specific subset of image bands which produce a fused image of a higher
quality for the given fusion technique.
Let us consider a hyperspectral image
I
containing
K
bands. As usual, we can
represent this image as a set of
K
bands,
,...
be the resultant fused image from the fusion of
p
selected bands using a pixel-based
fusion rule
{
I
k
;
k
=
1
,
2
,...,
K
}
.Let
F
p
,
p
=
1
,
2
should possess a
significant amount of additional information compared to the existing fusion output,
i.e.,
F
p
, for the fusion to be statistically efficient. We explain an output-based scheme
for the selection of bands which evaluates the redundancy of the successive input
image bands as compared to the corresponding intermediate output image using the
conditional entropy, and selects only the less redundant bands for fusion.
Initially, the first band is selected trivially for fusion, and it is considered to be
equivalent to the first intermediate fused image
F
1
. The conditional entropy of the
successive input bands with respect to this intermediate resultant image is evaluated.
The next band is selected when the corresponding conditional entropy exceeds a
pre-determined threshold, i.e., when the corresponding band possesses a sufficiently
F
. The next band to be selected for fusion using
F
