Performance Assessment of Fusion Techniques - Hyperspectral Image Fusion - page 138

The present chapter primarily focuses on the consistency analysis of the fusion
techniques, and illustrates the same over only two hyperspectral datasets for the pur-
pose of brevity. We use the moffett 2 dataset from the AVIRIS hyperspectral imager,
and the geological dataset from the Hyperion imager. The detailed description of
these two datasets can be found in Chap. 10 .
Consider the plot of variance as more and more bands are sequentially added
towards fusion of the moffett 2 data for various techniques as shown in Fig. 9.1 a. As
expected, the variance increases as the information from more numbers of image
bands is being combined. Figures 9.1 b, c depict the plots for entropy and for average
gradient, respectively for the same dataset, moffett 2 . One can observe a similar nature
of these performance measures from these plots. A larger fluctuation in these plots
for the incremental fusion violates the consistency property defined in Sect. 9.3.2 .
Therefore, one would ideally expect higher values of these no-reference performance
measures, but with lesser and smaller fluctuations. Also, we can observe a nearly
monotonically increasing nature of these plots, which confirm the consistency of
these techniques for the given performance parameter. However, it may be noted that
the technique based on the selection of three bands is not consistent as there are large
variations in the corresponding plots. As more bands are added, it selects totally
different subsets of bands for visualization, and these bands are not well correlated
to the results at the previous step. As a matter of fact, one may observe a similar
behavior for PCA-based techniques, signifying that the subspace-based techniques
are not consistent. We do not discuss PCA-based techniques, as they turn out to be
computationally very demanding. Further, Fig. 9.1 c suggests that average gradient
being a derivative-based measure is quite susceptible to the presence of noise in data,
and is not a good performance measure. The measure tends to saturate too quickly
and, hence, is not discriminatory enough.
Figure 9.2 a shows the variation in the Bhattacharyya distance for the incrementally
fused images of the moffett 2 dataset. As explained earlier, the final result obtained
through fusion of the entire data using the same fusion technique has been considered
as the reference for the corresponding technique. The plots of the Bhattacharyya
distance for different techniques show a gradual decrease in the value of the measure
asmore images are used. Asymptotically, the value of Bhattacharyya distance reaches
zero. It can be observed that most of the plots of the Bhattacharyya distance have
fluctuations till initial 40-50 bands get fused. Thus, the initial bands have larger
contributions towards the final fused image. The contribution from subsequent bands
gradually reduces, and the corresponding incrementally fused images do not change
much as k increases. An analysis of the Jensen-Shannon distances [Fig. 9.2 b] of
these images from the final output reveals a similar insight into the convergence
rate of the process. As expected, the JS distance asymptotically approaches zero.
The asymptotic behavior of the measure of correlation coefficient between the set
of corresponding incrementally fused images and the final image can be seen in
Fig. 9.2 c. The fairly non-decreasing nature of these plots again confirms, prima facie,
the suitability of these techniques, except the one based on band selection, for the
hyperspectral data.