Image Processing Reference
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unavailability of the ground truth in most cases,
large data volume, and
ambiguity in the quantification of useful data which is largely dependent on the
context and application.
Several attempts to quantify the useful information from the point of visualization
have been made, yet there is no standardization in this process. Furthermore, most
of these measures have been developed for generalized image fusion where only a
few images are to be fused. In such cases, mathematical formulation of performance
measures may be easy and intuitive. One can easily interpret the physical meaning of
quantities and terms involved. However, this may not be the case when the number
of constituent images increases.
In this chapter, we extend some of these measures for an objective assessment of
fusion of hyperspectral images. We also explain several modifications in the defini-
tions of some of the existing measures in order to facilitate a better evaluation. The
field of hyperspectral image fusion is not as mature as the field of generalized fusion,
where the later is enriched with a large number of different methodologies. Hence,
one may wish to experiment with extensions of these techniques toward the fusion
of hyperspectral data. We also explain a notion of consistency of a fusion technique
to understand the behavior of a given technique when it is applied over a progres-
sively increasing sets of images. We believe that the consistency analysis will help
in deciding the suitability of a particular technique toward fusion of a large number
of images. Illustrations of the usage of these measures and the consistency analysis
over some of the datasets and fusion techniques used in the previous chapters have
also been provided.
We begin with a definition of the fusion consistency in Sect. 9.2 . We then present
the analysis of different quantitative measures and discuss several modifications in
Sect. 9.3 . The performance assessment of some of the recent techniques of hyperspec-
tral image fusion, including the ones discussed in the monograph, using these mod-
ified measures has been provided in Sect. 9.4 . Section 9.5 summarizes the chapter.
9.2 Consistency of a Fusion Technique
Let us consider fusion as a mathematical technique that determines how the pixels
across multiple bands (or observations in the case of generalized image fusion) are
combined. We would like to study the behavior of a fusion technique as a function
of the number of images being fused. The focus is to understand how the fusion
technique (a fusion rule, to be precise) reacts to the varying number of images being
fused. Does the performance of a technique degrade with an increasing number of
input images? Is the technique able to perform better with different implementation
schemes?We shall try to answer these questions by developing a notion of consistency
of a fusion technique.
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