Band Selection Through Redundancy Elimination - Hyperspectral Image Fusion - page 64

Fig. 4.3 Performance evaluation of the input-based band selection scheme as a function of the
number of bands required for effective fusion of the urban data for different values of

κ

using the
bilateral filtering-based fusion and entropy as the performance measure (© ACM 2010, Ref: [87])

that Fig. 4.2 a retains most of the image features, and provides a visually comparable
image quality.
We shall introduce the readers to some of the commonly used statistical para-
meters used for the performance evaluation of fusion results. Chapter 9 is dedicated
to the performance evaluation of the hyperspectral image fusion techniques which
describes various measures in detail. In this chapter, we brief readers with a few sim-
ple parameters in order to provide the performance evaluation of the entropy-based
band selection scheme. Figure 4.3 represents the entropies of the fused images as
more and more bands are fused progressively, for various values of

κ

, where the plot

for 0 corresponds to the fusion of the entire data. For the fusion of selected 27

image bands, corresponding to

κ =

50, the entropy of the resultant fused image
rises very rapidly, as compared to the fusion of the entire dataset. Thus, one can
obtain fusion results with a very little sacrifice in the quality when compared against
the resultant image from fusion of entire dataset. Also, as only a small fraction of
the entire dataset is undergoing actual fusion, the fused images can be obtained in a
very short time. The number of bands selected determines the savings in processing
time and computation. This number is related to the value of threshold parameter

κ = 0 .

κ ,

and thus, as increases there is further reduction in the computation. Therefore, we

may relate Fig. 4.3 to the savings in computation. It may be noted here that as these
data are spectrally ordered, we assume the time to compute H

κ

is negligible
compared to the fusion process, which is often true due to the common assumption of
spatial memorylessness of individual bands while computing the entropy. Figure 4.4 a
shows the entropies of the fused images for different values of the threshold para-
meter

( I r | I k )

. It can be seen that for both test data, the performance drops very slowly
beyond a value of 0.30 for

κ

. This indicates presence of a large amount of redundant
data. Therefore, there exists an opportunity to speed up the fusion process. Another
performance measure based on the sharpness of the fused image F of size ( X

κ

, Y )is

defined as: