Image Processing Reference
In-Depth Information
The homogeneous regions in the image remain unaltered after filtering. The
fusion weight in such areas is effectively zero. If any image region appears to be
homogeneous over all the bands in a hyperspectral image, the denominator in the
Equation of fusion weights (Eq. ( 3.5 )) turns out to be zero in the absence of a
constant C . This causes numerical instability in the formulation of fusion process.
Incorporation of the numerical constant ensures that the denominator is always
a non-zero, positive number, and thus, the fusion weights are generated within a
proper range. The constant, thus, prevents numerical instability in the homoge-
neous regions.
The denominator of Eq. ( 3.5 ) guarantees that the sum of all weights at any spatial
location equals unity, i.e., normalized weights.
K
w i (
x
,
y
) =
1
(
x
,
y
).
k
=
1
The final fused image of the hyperspectral data is given by Eq. ( 3.6 )as,
K
F
(
x
,
y
) =
w k (
x
,
y
)
I k (
x
,
y
).
(3.6)
k
=
1
3.5 Hierarchical Implementation
We are dealing with the problem of combining a few hundred bands into a single
image, either a grayscale or an RGB. The process may involve reading all the bands
in the input hyperspectral image at once, computing the weights, and generating a
resultant fused image as the linear combination of all the input bands. This one time
reading and combining all the image bands have the following shortcomings.
1. This results in assigning very small fractional weights to the locations in each
of the image bands. Some of the weights are even comparable to the truncation
errors which might lead to washing out some of the minor details.
2. It requires the entire data along the spectral dimension to be read. Therefore,
the entire hyperspectral data cube has to be read into memory. Due to the huge
size of a hyperspectral data, the memory requirement is over a few hundreds of
megabytes.
We describe a hierarchical scheme for fusion in order to overcome these issues.
Instead of employing the bilateral filter-based scheme to the entire set of bands, this
scheme creates partitions of the data into subsets of hyperspectral bands. For a given
image of dimensions
(
×
×
)
X
Y
K
, containing K bands, one forms P subsets of
(
×
×
)
dimensions
X
Y
M
from contiguous bands of the data, where P is given
K
by P
=
M
. Then, the bilateral filter-based fusion scheme may be employed to

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