Image Processing Reference

In-Depth Information

or reverse direction, but the correlations among the successive bands still exist, which

facilitate the application of the performance measures in exactly the same manner.

Furthermore, the above argument also holds true for any random permutation of

the given set of image bands during fusion. The band-to-band strong correlation no

longer persists. In such cases, a large amount of disparate information is contained

by the first few randomly permuted bands. Thus, the plots for asymptotic measures

tend to saturate quickly as compared to the sequential case.

In the following subsections, we describe each performance measure and its sig-

nificance in hyperspectral image fusion.

9.3.1 No Reference Quality Measures

The set of no reference measures includes the statistical and other parameters typ-

ically used for the evaluation of general image fusion techniques. These measures

are evaluated directly over the fused image and no extra information is required.

Generally, these measures have a simple physical interpretation which makes them

quite popular. For a small number of input images, say 2 or 3, these measures are

computed for the resultant image, and the numerical values obtained by applying

different techniques are compared. In the case of hyperspectral image fusion, the

number of image bands is in the range of hundreds and therefore, it is advisable to

study the behavior of these measures over the increasing number of images being

fused. Although the relation between the no-reference measures and the quality of

the image has been well studied in the literature, here our focus lies in analyzing how

these measures reflect the performance of the corresponding fusion technique as the

number of constituent input images increases. A brief description of some of these

measures and their expected behavior in the context of a set of incrementally fused

images is presented below.

2

1.
Variance:
The variance of an image,

, is directly related to the image

contrast. Variance measures the deviation of gray values of the pixels from the

image mean. Images with higher variances have a better contrast, which makes

visualization simple and appealing. A smaller variance indicates that gray values

of most of the pixels are close to the image mean, and thus, the image mainly

consists of a less number of gray value with pixels mostly centered around its

mean. The variance

σ

=

var

(

I

)

2

σ

k
of the
k
-th incrementally fused image is given by Eq. (
9.2
).

var
F
I
1
,

I
k
.

2

k

2

σ

≡
σ

(

F
k
)
=

I
2
,...,

(9.2)

The variance tends to be higher with addition of noise. Therefore, a high value

of

2

k
need not necessarily imply a better quality. One needs to be careful while

relying completely on the variance measure alone. Notwithstanding above, when

calculated over each of the incrementally fused images, the image variance

σ

2

k

σ

should ideally increase as the number of constituent images increases.