Optimization-Based Fusion

Abstract

We have discussed three hyperspectral image fusion techniques in the earlier chapters of the book. We have also reviewed several other hyperspectral image fusion techniques along with a brief overview of a number of generalized image fusion schemes. The common feature of most of the existing fusion methodologies is that the fusion rule operates over spatial characteristics of the input images (or hyperspectral bands) to define the fusion weights. Fusion weights which have been calculated from some kind of saliency measure of the pixel, determine the effective contribution of the corresponding pixel toward the final result. Thus, the characteristics of the input data control the process of fusion, and hence, the resultant-fused image. As mentioned earlier, in this monograph, we are focused on obtaining the fused image for the purpose of visualization of the scene contents. In such a case, would it not be highly desirable that the fused image should possess certain characteristics to facilitate a better visualization and interpretation of the scene? In other words, it is beneficial to have a fusion scheme that takes into consideration the characteristics of the output, rather than focusing on the input characteristics. In this chapter, we explain some of the desired elements of the image quality. Then we explain the formulation of a multi-objective cost function based on some of these elements. This cost function has been developed into the variational framework which has already been explained in the previous chapter. Finally, we discuss how an iterative solution can be formed using the Euler-Lagrange equation.