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

termsâ€”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 constraintsâ€”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