Band Selection Through Redundancy Elimination - Hyperspectral Image Fusion - page 69

Fig. 4.8 Plots of PSNR of the fused images against the timing requirements for the urban and the
moffett 2 data for the bilateral filtering-based fusion technique. The resultant image from the fusion
of the entire dataset is used as a reference in each case for the evaluation of the PSNR (© ACM
2010, Ref: [87])

process. Therefore, the entropy-based subset selection scheme proves to be highly
effective for complex and computationally extensive techniques of fusion. The total
computation W , taken for the pixel-level fusion procedure as a function of threshold
κ , is of the form-

W (κ) = γ B(κ) + c E (4.12)

where , and

c E is the amount of computation for the evaluation of conditional entropies of the
image bands for the band selection procedure. This second term is a constant for a
given dataset. The

B(κ) represents the number of bands selected for a given threshold κ

factor is a proportionality factor to account for computational
requirements of a given fusion technique. If the time required for the computation
of the conditional entropy is negligible as compared to the timing requirements of
actual fusion, we can approximate Eq. ( 4.12 )as, W

γ

which indicates
that the order of computation is linear with respect to the number of bands selected.
It should be noted that as

(κ) ≈ γ B(κ)

decreases leading to a lesser amount
of computation, however this does not affect the linear nature of the computational
complexity.
For a qualitative analysis of the band selection scheme for the computational
requirements, we provide the plot of PSNR of fused images against the total time
taken by varying the threshold parameter

κ increases, B(κ)

. Figure 4.8 depicts the plots for the urban
and the moffett 2 datasets for fusion using the bilateral filtering-based technique.
A monotonically increasing nature of these plots indicate the improvement in the
quality of the fusion result at the expense of computational requirements when more
bands are fused. The reason that the computational requirements are nearly double

κ