Image Processing Reference
In-Depth Information
intermediate variables of the fusion process, define the fractional weight assigned
to each pixel for the combining purposes. Thus, for each of the input images, these
weights form what is known as the fusion matte. The variational fusion technique
does not explicitly compute the fusion weights, and hence the fusion mattes. This
solution models fusion weights as a data dependent term, and develops a weighting
function as a part of the fusion algorithm. The weighting function is based on two
terms—local contrast in the input data and adherence to the radiometric mean in
the fused image. The local contrast which can be measured via the local variance,
spatial gradient, etc., is an input-dependent (and hence a constant) term. The mean
correction, however, is a quantity to be measured for the present output i.e., the fused
image. We address this problem using the calculus of variations, and provide a solu-
tion using the Euler-Lagrange equation. The solution iteratively seeks to generate a
resultant image that balances the radiometric property in the scene with reference to
the input hyperspectral image. The variational technique penalizes the fused image
for its departure from smoothness. This leads to a certain amount of blurring of the
edges and boundaries in the fused image.
In the last solution we focus on certain properties of the fused image that are
desirable for a better visualization. As the primary objective of fusion is visualization,
the fusion process is expected to provide the best possible output image, independent
of the characteristics of the input hyperspectral image. Images with a high amount
of local contrast are visually appealing. However, the high contrast should not push
the pixels into over- or under-saturation which reduces the information content in
the image. This solution defines fusion as a multi-objective optimization problem
based on these desired characteristics of the output. Like in the previous method, the
final solution has been provided using the Euler-Lagrange equation. The novelty of
the solution lies in defining fusion weights based on the characteristics of the fused
image. This optimization-based solution has several interesting aspects as follows.
In order to consider the spatial correlation among the pixels of the fused image, a
commonly employed approach is to enforce a smoothness constraint over the fused
image as explained in the variational fusion technique. However, this constraint often
leads to over-smoothening of the output, blurring of edges and thereby degrading
the visual quality of the image. The optimization-based technique acknowledges the
spatial correlation within the scene by enforcing the smoothness constraint on the
fusion weights rather than the fused image. The fusion weights typically have two
additional constraints—the non-negativity and the normalization. We have explained
how to address these constraints without transforming the optimization problem into
a computationally expensive constrained optimization problem. The fused images
are able to represent the scene contents with clarity and a high contrast, as desired.
The optimization-based technique does not consider any of the input characteristics
for the fusion process. Therefore, the solution is generic, and can be implemented
for fusion of images with different modality.
While the topic of hyperspectral image fusion is being investigated, it is highly
necessary to develop appropriate performance measures for the quantitative assess-
ment of these fusion techniques. The existing measures for assessment of generalized
image fusion that involves only a very few images, may not be readily suitable for
