Image Processing Reference

In-Depth Information

where

2

D
(
m
)

k

D
(
m
)

k

C
)(

F
(
m
)
(

2

k

≡

(

x

,

y

)
=

(σ

(

x

,

y

)
+

x

,

y

)
−

I
k
(

x

,

y

))

,

(6.11)

B
(
m
)

k

B
(
m
)

k

2

C
)(

F
(
m
)
(

2

≡

(

x

,

y

)
=
(σ

k
(

x

,

y

)
+

x

,

y

)
−

I
k
(

x

,

y

))

,

(6.12)

K

A
(
m
)
≡

A
(
m
)
(

B
(
m
)

k

x

,

y

)
=

,

(6.13)

k

=

1

K

D
(
m
)

k

E
(
m
)
≡

E
(
m
)
(

x

,

y

)
=

,

(6.14)

k

=

1

where (
m
) indicates the iteration index, and
F
denotes the average value of
F
over its

nearest 4-connected neighborhood. The variables
A, B, D
, and
E
are computed at each

iteration. It may be noted that
B
is same as the un-normalized fusion weights, and
A

refers to the summation of the fusion weights for the process of normalization. As the

resultant image
F
changes at every iteration, these variables also need recomputation

at the end of every iteration. This slows down the whole fusion process.

6.4 Implementation

The variational technique described in this chapter is conceptually very simple. Addi-

tionally, it requires only two input parameters from the user- the constant
C
(used in

conjunction with variance

2

σ

k
(

x

,

y

)

to define fusion weights), and the regularization

λ
var
. We have heuristically chosen the value of
C
to be 50 which was

found to provide good visual results by appropriately balancing the weightage of

the local variance at the pixel. As most of the natural images are smooth, one may

assume the final fused image also to be smooth. In case of noisy hyperspectral bands,

a higher value of

parameter,

λ
var
can be used to generate a smoother final resultant image. For

the illustrations in this monograph, we have assigned the value of

λ
var
to be of the

order of 1-10. Higher values of

λ
var
tend to smooth out fine textural details which

are important to preserve the overall contrast. For most test datasets, the algorithm

was found to converge within 10-12 iterations, when the stopping criteria employed

was to observe the relative change in the cost function over successive iterations.

6.5 Experimental Results

Like in the previous two chapters, we provide a couple of illustrative results of

fusion using the variational technique. We have provided the results over the same

hyperspectral datasets used in the previous chapter in order to maintain uniformity.