Image Processing Reference

In-Depth Information

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 [144]. If images
I
1
and

I
2
are fused to obtain the resultant image
I
F
, then the MI-based measure
M
1
F

is

obtained using Eq. (
2.6
).

M
1
F

=

MI

(

F

,

I
1
)
+

MI

(

F

,

I
2
)

(2.6)

where
MI

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 [37].

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 [78].

Wang et al. have proposed the correlation information entropy (CIE) to evaluate the

performance of the fusion technique [182]. 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 [44].

(

F

,

I
1
)

and
MI

(

F

,

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

×

Y

×

K
) where
K
indicates the number of

×

bands with a spatial dimension (
X

Y
) each.