Image Processing Reference

In-Depth Information

Table 10.7
Performance measures for various techniques for visualization of the urban data

Fusion technique

Variance Entropy Avg gradient Relative Fusion

Fusion

bias
b

σ

2

H

g

¯

factor
FF
symmetry
FS

Bilateral filtering technique

619.50

6.28

6.68

0.17

1.49

0.11

Bayesian technique

855.56

6.34

7.16

0.21

2.04

0.16

Variational technique

558.26

6.14

6.57

0.13

1.58

0.26

Optimization-based technique 665.11

6.43

7.46

0.24

1.47

0.14

Three band selection

477.04

6.41

6.13

0.25

1.33

0.12

Piecewise linear function

282.54

5.80

4.55

0.31

1.34

0.22

Color matching function

260.90

5.78

4.59

0.22

1.20

0.23

fusion process involves significant computation at every iteration, it is possible to

speed up the computation to some extent by pre-computing the data-dependent terms

that remain unchanged throughout the fusion procedure. The average time for a single

iteration for the AVIRIS data was 72 s, while the time required for the single iteration

of the Hyperion images was found to be 28 s. Nearly 9-10 iterations were required

for the solutions to converge.

The optimization-based solution too, is an iterative solution where the fusion

weights are re-computed at every iteration. This solution, thus, turns out to be compu-

tationally expensive. Additionally, each iteration involves several terms that require

a dot product and an element-wise product. On average a single iteration took 92 s

for the AVIRIS datasets of dimensions

(

614

×

512

×

224

)

pixels, while the Hyperion

datasets with dimensions

pixels produced the result of a single

iteration in 35 s. It took nearly 6-8 iterations for all the datasets till the solutions

converge. This algorithm, however, has a vector operation defined over the spec-

tral arrays (
s

(

512

×

256

×

242

)

). Each dataset contains
XY
spectral arrays which are processed

independently to generate the pixels of the fused image. We believe that these inde-

pendent operations can be parallelized to a large extent so that the computation time

can be drastically reduced.

The band selection technique chooses the three bands through several filtering

operations, and thus turns out to be quite fast. The PLF and the CMF techniques assign

a fixed weight to each of the spectral bands, and thus the process of fusion reduces to

merely a weighted linear addition where weights have already been predefined. On

average, these techniques generated fused images from each of the AVIRIS datasets

in 29, 12, and 11 s, respectively. For the Hyperion datasets, the average computation

times required to generate the fused images for these techniques were 12, 7, and

7 s, respectively. The details of the computation time for these techniques have been

summarized in Table
10.8
.

(

x

,

y

)