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1. All approaches

.SURES

always unknown,

signing objective

; would produce is

a very difficult task but such metrics are highly desired. Among

the limited number of methods that have been proposed in the

literature for image fusion quality assessment without an ideal

image, most of them are not very suitable [15, 16]. Some

researchers assess the results by using subjective tests [17].

However, although subjective tests can sometimes be accurate

if performed correctly, they are inconvenient, expensive, and

time consuming. Further, it is impossible to use them to

continually adjust system parameters in a real time manner.

There are a few objective metrics which do not require the

availability of an ideal image in the literature.

In the article, we present representational and some new

quality metrics for the experiments. Some useful conclusion can

draw out through comparing. One type of metrics is Standard

Deviation (SD), Entropy (EN); the other type is cross entropy

(CE), mutual information (MI), and universal index (UI) [18],

which utilizes the features of both the fused and source.

3.1 A Standard Deviation (SD)

As we know, SD can provide some contrast information. For

a fused image of size N X M, its standard deviation can be

estimated by

SD =

N M

/=1 jm 1

where C(i, j) is the (i, j)th pixel intensity value and lfl is the

sample mean of all pixel values of the image. It is known that

SD is composed of two parts, the signal part and the noise part.

This measurement will be more efficient in the absence of noise.

3.2 Entropy (EN)

l FA (/»«)=

PFA(f> a )

P F (f)P A ( a )

1 F B (f’ b )= Y.Pfb(/¿) log 2

f,b

p FB (f’ b )

PÁf)PÁ b )

Performance is measured by the value of

Mlf = l FA (f, a) + \ FB (f ,b)

3.5 Universal Index (UI)

Based on the SSIM measure [20] gives an indication of how

much of the salient information contained in each of the input

images has been transferred into the fused image. First calculate

SSIM (a, /|w) and SSIM (b, /|w) which are the structural

similarity measures between the input images and the fused

image in a local window w. Then a normalized local weight A.

(w) indicate the relative importance of the source images. The

index is calculated by the function

UI = ~X( k (oASSIM(a,f\ m )

\W\ aeW

+ (\-X((ù))SSIM(b,f\(ù))

where SSIM is the structural similarity measure of two

2

sequences, let fl x , G x ,and O xy be the mean of x, the

variance of x, and the covariance of x and y, respectively. Then

SSIM compute as

CT

SSIM = —2L

G y ct

2 M x M y 2a x a y

2 2 2 2

Mx + My CT x + a y

An index to evaluate the information quantity contained in an

image. Entropy has often been used to measure the information

content of an image. Entropy is define as

L-1

£ = -Xft l0 §2 Pi

/=0

where L is the total of grey levels, p-{po, Pi, Pi-i} is the

probability distribution of each level.

3.3 Cross Entropy (CE)

The source images A, B and fused image F, the cross entropy

is defined as (p A is p for image A)

CE= CE(A, F) + CE(B, F)

2

where CE(A, F)(CE(B, F)) is the cross entropy of the source

image A(B) and fused image F

CE(A,F)= f>,(/)log 2 £ig

i=0 P F (l)

CE(B,F)= f> s (/)log 2 MJ

,=o P F ( 0

3.4 Mutual Information (MI)

A higher value of the index indicates that the fused image

contains fairly good quantity of information in both images.

Define the joint histogram of source image A (B) and the fused

image F as P FA (f, a) (P FB (f, b)). The mutual information

between source image and the fused image is [19]

4. EXPERIMENTS AND ANALYZING

We applied the above methodologies and assessment system

to fuse SAR and SPOT panchromatic images which has 5m

pixels (Figure 1). The experiments compared the different

alternatives for each procedure of the generic fusion framework

described in Figure 2. It is worth noticing AMO in method (b)

to search the Pareto optimal weights of the coefficients and

compared the results with popular method (a) in figure 2. The

abbreviations used in the paper are described in table l.The

performance of method (WA-WBA+NG+AMO+RBV) using

different decomposition levels are shown in the table 2. In the

table 2, the first column shows the combinations of alternatives

in figure 2 for the procedures, and the second column lists the

different alternatives MSD for the current procedure. Columns

3-7 show the performance using the criteria we introduced in

Section 3.

(a) SAR (b) SPOT

Figure 1. Source images