Image Processing Reference
In-Depth Information
performance measure as more and more bands are added to the process of fusion.
This is particularly useful when one wants to extend a generalized fusion technique
towards fusion of a large number of images, e.g., hyperspectral data. As mentioned
earlier, image fusion literature is quite rich as this area is being actively researched for
nearly last two decades. However, research in hyperspectral image fusion has begun
recently. Naturally, one would like to extend the techniques of generalized image
fusion for the combining of bands of the hyperspectral data. However, one needs to
verify whether the technique under investigation is suitable for hyperspectral image
fusion. The performance measures from this category can provide some information
on the suitability and adaptability of generalized fusion techniques for fusion of a
large number of images. These measures include several distance measures between
a given fused image and another reference image. We use
F
K
(ideally,
F
k
as
k
)
as the reference image, but denote it by
F
for the ease and consistency of notations
used in this monograph. The evolution of these measures for progressive increase in
the number of bands being fused provides a useful information about the consistency
of the technique. It should, however, be noted that the consistency analysis in this
case refers to the behavior of the fusion technique with respect to a given performance
measure only.
The participatory performance measures are evaluated only over the final fused
image, and they do not enable us to study the progression of the fusion process. As the
name suggests, these measures are used to analyze the degree of
participation
from
the bands of input data. A good fusion technique
→∞
is expected to extract useful
contents from each of the hyperspectral bands, and combine them appropriately.
In this process, the contribution of each of the bands is expected to be similar for
fusion process to be robust and accurate. The participatory performance measures
indicate the uniformity and symmetry of the fusion technique
F
with respect to its
constituent images, i.e., whether all the input bands contribute well toward the fusion
process, an important aspect often overlooked in the existing literature. A well fused
image should have appropriate contributions from all the constituent bands, that is,
the fusion technique should be capable of extracting unique information from the
bands. This aspect becomes more important with an increasing number of bands,
as in hyperspectral images. These measures try to answer questions such as- how
the bands are
participating
into fusion? Do all bands participate in fusion? Is the
participation uniform across the bands or it is uneven?
In the discussion, we have so far assumed that the hyperspectral data is spectrally
ordered in increasing order of wavelengths, which one may refer to as the forward
order. The Eq. (
9.1
) and the subsequent discussions also refer to the incremental
fusion in the forward direction. However, the analysis of the technique for the image
quality and the consistency also holds true for the incremental fusion of bands in
the reverse order. Throughout our discussions, we have not explicitly considered
any specific ordering of bands. The spectral ordering is associated with the spatial
correlation among successive bands, but does not depend on the forward or reverse
ordering. The interpretation and the final result ideally remain exactly the same,
and it is largely governed by the spectral signature of a particular pixel. During
incremental fusion, the spectral signature of a pixel gets traversed either in forward
F
