Image Processing Reference
amount of information shared between two variables by measuring their statistical
dependence. In the case of images, the MI describes the similarity in the distributions
of intensities of corresponding images. Qu et al. have proposed the use of mutual
information as the performance measure for image fusion . If images I 1 and
I 2 are fused to obtain the resultant image I F , then the MI-based measure M 1 F
obtained using Eq. ( 2.6 ).
M 1 F
I 1 ) +
I 2 )
are the amount of mutual information between the
fused image and corresponding input image. For the theoretical analysis of this
measure the readers may refer to .
The calculation of these objective and statistical measures is easy when only a few
images are to be fused. The expected behavior of these measures can be interpreted
well—theoretically as well as intuitively. However, the extension of such measures
for the assessment of hyperspectral image fusion is a non-trivial task. For example,
although the definition of mutual information (MI) for a large number of variables is
known, the computation and its physical interpretation is very difficult as the number
of variables increases. Sometimes, the assessment is solely based on the quality of
the output image itself. The correlation coefficient among the components of the
final RGB image has been used to analyze the fusion technique in [49, 176, 206].
The spectral angle has been suggested as the distance measure between two vec-
tors formed by two pixels in the hyperspectral data for evaluation of fusion in .
Wang et al. have proposed the correlation information entropy (CIE) to evaluate the
performance of the fusion technique . This measure quantifies the correlation
between the images before and after fusion to determine the amount of information
transferred from the source images to the fused image. Cui et al. have used preserva-
tion of spectral distance as a quality measure, which is evaluated over a sparse subset
of image pixels to reduce computational requirements .
I 1 )
I 2 )
2.4 Notations Related to Hyperspectral Image
We have covered the current state-of-the-art in the area of hyperspectral image fusion.
We have also familiarized our readers with several fusion methodologies for the
general case of images. The next chapter onwards, we shall explain some recent
techniques of hyperspectral image fusion in a detailed manner. Before we begin
with the discussion, we shall first introduce to the readers the notations used in this
monograph. These notations are consistent with most of the existing literature on
hyperspectral images and image processing. In this monograph, we shall work with
hyperspectral data which are 3 dimensional structures. These dimensions correspond
to the spatial and the spectral information, respectively. Consider a hyperspectral
image denoted by I of dimensions ( X
K ) where K indicates the number of
bands with a spatial dimension ( X
Y ) each.