Image Processing Reference

In-Depth Information

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

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.