Image Processing Reference
advocated the goal of preservation of spectral distances in . This work has used
the same measures as used in , albeit in the L
b which is
known to be perceptually uniform. It has been suggested that each of the objective
functions to be minimized corresponding to one each in L , a , and b channels, can
be defined as a Gibbs energy field related to a non-stationary Markov random field
(MRF) defined on a complete graph formed with pairwise interactions of pixels.
Having formulated the problem in a Markovian framework, it is possible to employ
efficient optimization methods to obtain a minimum in the perceptual L
b color space L
space. In , the images are decomposed into a 4-level multi-resolution pyramid,
and the optimization is accomplished by coarse-to-fine conjugate gradient method.
In the previous section we have already explained the application of the matrix
fundamental form (MFF) for image fusion [158, 159]. This scheme has been extended
for the visualization of hyperspectral images in . They perform denoising and
contrast enhancement during the fusion of hyperspectral bands. This enhancement
is achieved by combining the gradient information from the wavelet-decomposed
hyperspectral bands. The low-resolution subbands, however, are combined using the
color matching functions (CMFs) described in . We have also explained in the
previous section the Bayesian approach for hyperspectral image fusion proposed by
Xu et al. [192, 193]. They have employed the statistical model of image formation
where they have assumed the parameters to follow a Markov random field (MRF).
They have also suggested modeling of the fused image using an MRF.
Cai et al. have proposed an interesting visualization technique for hyperspectral
data with a different application—to display the results of mixed-pixel classifica-
tion . A single pixel in the hyperspectral data is a resultant of mixture of a
number of materials present in the corresponding location on the earth. In the remote
sensing literature, these materials are known as the endmembers, and their propor-
tion into the pixel composition is known as the abundance . The purpose of the
methodology proposed in  is to provide a single image which displays—( i ) over-
all material composition of the scene, and ( ii ) material composition at the particular
location. The endmembers and their abundances are estimated using a linear mixture
analysis which provides their spatial distributions. Each of the endmembers is then
assigned to a different color, so that all of them can be visualized in a single color
(RGB) image. The final color image has been composed of two layers. The first
layer depicts the general distribution of the materials. The second layer provides the
detailed composition for each pixel. The final image is composed by overlaying the
detail-layer image onto the first one.
2.3 Quantitative Evaluation of Fusion Techniques
As the research in the field of image fusion began to develop, the problem of evalua-
tion and assessment of fusion techniques has gained a lot of importance. Evaluation
and assessment of fusion techniques are essential to compare different techniques,
and to determine the benefits of each.