Image Processing Reference
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which a large number of statistical tools are available. Thus, one may experiment
with a variety of estimators, priors, and implementations.
First two fusion techniques discussed in this monograph explicitly compute the
fusion weights from the input data. These weights are also known as fusion matte,
or more commonly
-matte in the graphics literature. However, an explicit pres-
ence of a matte is not required if the fusion model is well-specified. In this tech-
nique, we model the weighting function as an input data-dependent term, and
provide an iterative solution that generates the fused image without explicit com-
putation of the fusion weights (or mattes). The weighting function has been derived
from two important aspects of fusion—first, we want fusion weights to be propor-
tional to the local contrast of the pixel which we calculate as the local variance.
We also expect the intensity of the fused pixel at any location to remain close
to the intensities of all the constituent pixels from input bands at the given loca-
tion. This second aspect tries to minimize the radiometric distortion in the fused
image. Another important requirement for visualization-oriented fusion is the nat-
ural appearance of the fused image with no visible artifacts. As most of the nat-
ural images are spatially smooth, several smoothness-based constraints are often
employed in various problems of image processing. We incorporate the smooth-
ness constraint on the fused image that penalizes the discontinuities in the image,
and formulate the problem in the framework of variational calculus. The solution
is provided using the Euler-Lagrange equation which iteratively refines the fused
image for the above mentioned objectives. The final fused image is formed by an
appropriate combination of pixels with higher local variance, and at the same time
it minimizes the radiometric distortion in the fused image with respect to the input
hyperspectral data. As there is no explicit computation of fusion mattes, one may
refer to this as a matte-less approach to hyperspectral image fusion.
Most of the fusion techniques including these discussed above define the fusion
weights from certain properties of the data. Therefore, the properties of the input
define how the data should be combined, and thus drive the fusion process. The
goal of fusion is related to an efficient visualization of the scene by a human
observer. The fused image is, thus, expected to have certain properties that are
considered to be desirable for a better visualization. For example, well-exposed
and high local contrast in the fused image. Given the input data, the existing fusion
techniques do not guarantee to what extent such properties will be satisfied in the
resultant image. Interestingly, one can think of the fusion problem from a com-
pletely different perspective. One may aim at the generation of a fused image
with such desired properties, irrespective of the characteristics of the data con-
tents. We formulate a multi-objective cost function based on these properties and
transform fusion into an optimization problem. Likewise in the earlier technique,
we consider the well-exposedness and contrast on a per pixel basis. In order to
obtain a regularized solution, one may enforce a smoothness constraint on the out-
put image. However, this constraint often leads to over-smoothening of the fused
image, blurring of edges, and reduction in the contrast. In order to acknowledge the
spatial correlationwithout degrading the contrast in the resultant image, we enforce
the smoothness constraint over the fusion weights, rather than the fused image.
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