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.
