Image Processing Reference

In-Depth Information

Q
2
also increases. Thus, increase in the value of
C
leads to more pixels contributing

towards the fusion output. One should, however, note that the value of the sensor

selectivity factor

does not change in the same manner as the
C
or
Q
2
due to explicit

normalization. The exact relation between
C
and the quality of the fused image is

dependent on the data statistic, and thus, it is difficult to obtain a simple expression

relating them. One can, however, say that the value of
C
is related to the total number

of pixels contributing towards the fusion result. We have heuristically selected
C
to

be equal to 1.0. The regularization parameter

β

λ
β

determines the relative weightage

given to the smoothness in

β

as compared to the product of quality measures. A too

high value of

, while a very small value of

the regularization parameter does not consider the effect of spatial correlation within

the constituent bands. As mentioned earlier, most of the hyperspectral images (or

remote sensing images) capture large areas on the earth from a high altitude. These

images depict a large agglomeration of very small objects. For a better visualization,

we expect these objects to be clearly identifiable in the fused image. A high value of

λ
β
can oversmooth small objects as smaller gradient values may get flattened. We

have chosen the values of

λ
β

brings in an excessive smoothness in

β

λ
β
around 50 to solve Eq. (
5.8
).

The final stage of the Bayesian fusion in Eq. (
5.16
) requires the choice of two

parameters- the step size

λ
F
. These parameters

govern the convergence and performance of the TV norm-based iterative procedure.

The step size

τ

, and the regularization parameter

decides the magnitude of the change in the output per iteration. A

process with very small values of the step size turn out to be quite slow as they

require a large number of iterations to converge. High values of the step size may

lead to instability in the iterative process. We have chosen the step size

τ

τ

to be small,

around 0.20 for the stability considerations. The choice of regularization parameter

λ
F
is critical as it decides the relative weightage of the total variation (TV) term, i.e.,

the prior, with respect to the weightage associated with the image formation model,

i.e., the data fitting term. High values of

λ
F
in Eq. (
5.15
) indicate a much higher

weightage of the TV term as compared the image model. This excessive domination

may result in flattening of the output by removal of the small textures/features. We

have chosen this value to be in the range of 10
−
2
to 10
−
3
which provides enough

weightage to the TV term to take into account the spatial correlation within the fused

image. One of the typically employed procedure to stop the iterations is based on the

change in the successive values of the minimization functional. We have employed

a similar stopping criteria in this work, that is comparing the relative difference in

the minimization functional per iteration. Results were typically obtained after 6-8

iterations as the process converged.

5.7 Experimental Results

In this monograph we have already explained a different solution for the problem

of fusion of hyperspectral images. In the next two chapter we present the readers

with two more methods for the hyperspectral image fusion. We believe that putting