Image Processing Reference
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of high dynamic range-like photographs with variable exposures as discussed in
[146]. Our focus, however, is to handle the problem of fusing remote sensing images
with variable reflectance of different regions contained in the scene spread over a
wide spectrum.
Like any other pixel-based fusion technique, the output image is generated as
a normalized weighted sum of the pixels from the input bands at the correspond-
ing location. The critical part of the algorithm is computing appropriate weights to
represent the subtle information at each location along the spatial and the spectral
dimension. We define the weight of the particular pixel from its relative importance
with respect to its spatial neighborhood. Hyperspectral images are generated as the
reflectance response of the scene, which mainly depends on the composition of the
materials in the scene. Certain materials exhibit a stronger response over a given
wavelength range, and give rise to strong and sharp features. On the other hand,
some materials exhibit their peak response over a very narrow spectral range. Thus,
the data contain several weak features such as edges, which are prominent over only
a set of few bands, while the strong features appear in a large number of bands in
the data. When the final image is a linear weighted combination of the input images,
the strong features get preserved due to their significant, non-zero weights almost
in every band. The weak features, however, may get lost due to their local presence
across the spectral dimension. We want to specifically focus on preservation of these
weak features. Therefore, we assign higher weightage to those regions in the band
where the weak features are strong so that these will be well perceived in the output.
The first step in this regard is to identify the features in the formof weak edges, fine
textures, and objects apparent over only a few bands. Such slowly varying features of
hyperspectral band can be removed by a smoothing 2-D filter, which when subtracted
from the original image give the important local details of the band. However, a
conventional Gaussian low pass filter tends to blur the edges, and the difference
image so formed contains artifacts in the neighborhood of the edge pixels. This leads
to visible artifacts in the fused image. Therefore, we need a smoothing filter that
removes minor variations in the image, but does not smooth out the strong edges.
Bilateral filter, discussed in the previous section, satisfies our requirements for the
design of mattes, which in turn generate the fused image.
Having explained why the weak features should be given an adequate importance
while defining the matting/weighing function, let us now illustrate how bilateral filter
serves this purpose of extracting weak features through Fig. 3.2 .Asmallregionofan
urban area in Palo Alto has been depicted in Fig. 3.2 a. This is a part of the 50-th band
of the hyperspectral image captured by the Hyperion imaging sensor. Fig. 3.2 bshows
the output of bilateral filtering over the original data. As it can be easily observed,
this has retained the strong edges, however it has removed weak features, and it
appears slightly blurred. The difference image (between the original and the filtered)
in Fig. 3.2 c, thus displays these weaker parts in the original band more prominently.
The difference image in Fig. 3.2 c depicts the detail layer or the component of the
image which has been removed by the filtering operation. We formulate our weights
as the function of the difference image. Our weights are, thus, directly proportional
to the finer details in the given hyperspectral band. Let I 1 ,
I 2 ,...
I K be the set of
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