Image Processing Reference

In-Depth Information

•

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.