Image Processing Reference
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pan-sharpening technique using hyperspectral images [118]. Their technique consists
of a variational scheme that integrates objectives related to the image geometry,
fidelity with respect to the pan image, and preservation of the spectral correlation.
2.2 Hyperspectral Image Fusion
We have discussed various techniques for pixel-based image fusion in the previous
section, most of which have been proposed for fusion of a very few images (say
2-4). The extension of these techniques for fusion of hyperspectral data which con-
tain 200-250 bands is a non-trivial task. While the fusion of hyperspectral images
has been performed for various objectives such as quick visualization, resolution
enhancement [72], spectral unmixing [208], etc., we restrict the scope of this section
to the fusion techniques specifically developed for the scene visualization—which
is the primary objective of this monograph.
The simplest way to fuse the hyperspectral data is to compute an average of all the
bands. However, as mentioned earlier, this technique may provide satisfactory output
when the input contents are highly correlated, but it results in the loss of contrast when
the contents of the input are dissimilar. In the case of hyperspectral bands, the amount
of independent information is quite high as one proceeds along the bands, and thus,
mere averaging of the bands across spectral dimension lacks quality, although this
technique is computationally most efficient. The distribution of information across
hyperspectral bands is highly uneven [71]. Guo et al. have developed spectrally
weighted kernels for fusion of hyperspectral bands for classification purposes [71].
The kernels which have been estimated using mutual information between image
bands and the reference map of the same region, are in the form of Gaussian radial
basis functions (RBFs). The fusion, however, is meant for classification purposes.
Although, our primary objective is visualization of hyperspectral data, we believe
that it is worth mentioning various attempts in the literature related to fusion of
hyperspectral data.
Wilson et al. have extended a multi-resolution based technique for hyperspectral
image fusion where contrast sensitivity defines the fusion rule [189]. Initially every
band of the hyperspectral image is decomposed using a Gaussian pyramid. They have
used a 5
3 Gaussian
kernels to filter the input image as proposed in [20]. The size of the kernel indicates
the spatial extent of the filtering operation. As the size increases, we are able to obtain
a better filtering, but it increases the cost of computation. The filtered image is then
downsampled by the factor of 2 at every stage to form a multi-resolution pyramid.
Each level of this pyramid for each of the image bands is then subjected to the set of
gradient filters to extract directional details (except for the topmost level which refers
to the gross approximation). If
5 Gaussian kernel formed through a convolution of two 3
G k represents the pyramid at the decomposition level
k , and
3 Gaussian kernel, then the directional decomposition for orientation
l is given as d l ∗[ G k + ω G k ]
is a 3
4, in order to represent the gradient
filters for detecting edges at 0 ,
45 ,
90 ,
and 135 , respectively [189]. The saliency
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