Image Processing Reference
in detail how the additional information in the band can be utilized for developing
band selection schemes. Due to this redundant nature of the hyperspectral data, a
particular band provides only a small amount of additional information towards the
final result. One would want a fusion technique to exploit this intrinsic relationship
among bands while extracting the information from them. A good fusion technique
should be capable of extracting and combining information across different bands in
such a manner, that the sequence g
for the corresponding performance measure is
monotonic in nature. That is, a good fusion technique should satisfy Property (9.1).
In order to check the consistency one first needs to fix a performance measure.
The set of incrementally fused images
, that involve fusion of a progressively
increasing number of image bands using a technique
F k }
, needs to be generated.
The exact definition of
depends on the specific technique used and we provide
some illustrations with some existing fusion techniques later in this chapter. During
subsequent discussions, let us refer to the k th incrementally fused image as F k , and
the final fused image resulting from fusion of the entire data will be referred to as
F K , such that,
F k | k = K
I 1 ,
I 2 ,...,
I K }=
Notwithstanding the incremental behavior, we refer to the final fused image as F
instead of F k for notational ease.
9.3 Performance and Consistency Analysis
Now let us analyze the behavior of some of the commonly used performancemeasures
over the sets of incrementally fused images using fusion technique
. We group the
performance measures into three categories-
No reference quality measures,
Quality measures with an asymptotic reference, and
Participatory performance measures.
As the name suggests, the performance measures in the first category can be
employed directly over the corresponding fused images which could be either incre-
mental or final, as they do not require any reference image to evaluate the quality.
These are stand alone measures that are generally easy to calculate, intuitive, and
computationally inexpensive. These measures include entropy, variance, etc., which
have been traditionally employed for evaluation of fusion quality. As more and more
bands are used, One would like these measures to improve until they saturate as per
The second category refers to the performance measures with an asymptotic
reference that study the progressive behavior of a technique with reference to the
final fused image for a given hyperspectral data. These measures help us under-
stand the progression of the fusion technique with reference to the particular