Image Processing Reference
how the edge-preserving property of a bilateral filter enables us to extract the minor
features in the data, and obtain a visually sharp yet artifact free fused image.
Fusion of hyperspectral data often demands resources in terms of memory and
time due to its huge volume. We demonstrate a hierarchical implementation of the
bilateral filtering-based solution which overcomes the aforementioned issues. This
scheme operates over smaller subsets of hyperspectral bands to provide the final
resultant image without any degradation in the quality.
To begin with, we provide an overview of edge-preserving filters in Sect. 3.2 ,
followed by a brief overview of bilateral filter in Sect. 3.3 which has been used to
develop the edge-preserving fusion solution. The actual fusion solution has been
explained in Sect. 3.4 . The hierarchical scheme for an efficient implementation has
been described in Sect. 3.5 . In Sects. 3.6 and 3.7 we have provided the implementation
details of the above solution, and the experimental results, respectively. Summary is
discussed in Sect. 3.8 .
3.2 Edge-Preserving Filters
Filtering is one of themost fundamental operations in image processing and computer
vision. The term filtering refers to manipulating the value of the image intensity at a
given location through a functionwhich uses a set of values in its small neighborhood.
When the images are assumed to be varying slowly over space, the adjacent pixels
are likely to have similar values. As the noisy pixels are less correlated than the signal
ones, the weighted averaging can minimize the effect of noise. However, the images
are not smooth at the boundaries and edges. Therefore, the conventional smoothing
or low pass filters produce undesirable effects at edges by blurring them.
The class of edge-preserving filters provides an answer to this problem by averag-
ing within the smooth regions, and preventing this operation at the edges. Anisotropic
diffusion implements the scale-space to generate a parameterized family of succes-
sively blurred images based on the diffusion equation . Each of these images
is a result of convolution of the image with a 2-D Gaussian filter where the width of
the filter is governed by the diffusion parameter. This anisotropic diffusion process
facilitates the detection of locations having strong edge information, and prevents
them while smoothing. This technique is also referred to as the Perona-Malik diffu-
sion. Black and Sapiro used the local statistics for calculation of a parameter related
to the termination criteria of the Perona-Malik diffusion . The use of a local
noise estimate to control the diffusion process which is piecewise linear in nature for
selective smoothing has been proposed in .
An adaptive smoothing operation can also be used to accomplish the similar goal.
Adaptive smoothing involves repeated convolution of the image pixels with a very
small averaging filter modulated by a measure of signal discontinuity at that location
to produce smooth regions with preserved discontinuities . Adaptive smooth-
ing is a refinement of the Perona-Malik diffusion which is also related to the scale-
space representation. An adaptive smoothing approach based on the higher order