The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B7. Beijing 2008 
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2. Entropy: 
The entropy of the image is an important index to weigh the 
information capacity, according to the Shannon’s 
information theory principle, the definition of entropy is: 
where, M(i,j) , F(i,j) are the pixel value of original 
image and fused image in certain component, respectively. 
Correspondingly, M(i,j) and F(i,j) are the means. M 
and N are the weight and height of the image. 
4. Average Gradient (A. G.) 
(8) Average gradient is able to accurately reflect the fine 
contrast of the image. Generally, the larger the average 
gradient is, the clearer the image is. 
where, P is the ratio of the i pixel number to the total 
pixel number in the image, m is the number of grades. 
Since the entropy represents the information capacity, the 
larger the entropy is, the more the image contains 
information. Seen from formula (8), we know that the 
maximum value of H occurs if and only if each P is equal. 
It means that the information capacity tends to be the 
maximum if each gray grade has almost the same account 
pixels. By comparison of the entropies of different images, 
we can judge the ability of expressing detail information. 
3. Correlation Coefficient (C. C.) 
The correlation coefficient between the original image and 
the fused image shows the similarity in small size structures 
between the original and the fused images. It should be as 
close as possible to 1 (Luclen, 1997). The correlation 
coefficient p is: 
VG = ^J]yA/ 2 (x,y) + A)/ 2 (x,y) (10) 
MV Jm , 
where, Axf(x,y) and Ayf (jc, y) are the difference of 
f(x,y) at x and y direction in certain component, 
respectively. 
5. Average Spectral Distortion (A. D.) 
The definition of the spectral distortion in the Mi 
component is: 
p = 
Z Z (Af a, j) - M(i, j))(F(i, j) - F{i, j)) 
I M /V IYJ 
III (■m,j)-M{i,j))' TX (F(i, j) - F(i, j)) 
(9) 
where, V* and V' k are, respectively, the gray values of 
multispectral image and fused image in the Mi component 
at position (ij). As the spectral effect is expressed by the 
synthesized of the multiple bands, we employed the 
average spectral distortion, noted as D, to illustrate it. The 
greater the D is, the larger the distortion is. 
C.C with 
Image 
band 
Mean 
S.D. 
Entropy 
multi 
spectral 
SAR 
A.G. 
A. D. 
Multispec 
tral 
1 
89.3915 
2699.9938 
7.2407 
1.0000 
— 
16.1554 
— 
2 
100.7079 
2370.8928 
7.2342 
1.0000 
— 
16.1896 
— 
3 
76.6344 
2438.7121 
7.0459 
1.0000 
— 
15.9443 
— 
SAR 
- 
57.7986 
2438.6782 
7.0837 
— 
1.0000 
11.8878 
— 
1 
36.2861 
3745.5817 
6.0136 
0.1195 
0.7344 
20.4025 
Brovey 
2 
43.7587 
4371.4152 
6.3431 
0.1315 
0.6349 
28.0559 
212.7874 
3 
39.4694 
4757.6124 
5.9325 
0.1931 
0.5908 
29.3560 
Triangle 
IHS 
1 
55.3576 
2411.2494 
7.0468 
0.1136 
0.9457 
13.4192 
2 
66.3127 
2635.3794 
7.3110 
-0.0064 
0.9334 
15.6292 
165.2970 
3 
47.5083 
2397.7407 
6.7985 
0.1503 
0.8508 
14.3046 
1 
30.6315 
106.7828 
4.8998 
0.0962 
0.6671 
2.0525 
PCA 
2 
29.9306 
175.8581 
5.5172 
0.2041 
0.5935 
2.1249 
180.1813 
3 
29.6898 
110.6867 
4.9486 
0.1016 
0.6612 
2.1421 
Gram- 
Schmidt 
1 
20.7771 
172.5953 
5.4618 
0.1937 
0.8778 
3.0947 
2 
40.2084 
361.7482 
6.2062 
0.1502 
0.8136 
3.8246 
195.1719 
3 
10.9059 
146.2115 
4.8158 
0.1034 
0.9003 
2.8324 
Normal 
1 
40.0525 
482.7768 
6.3879 
0.9572 
0.2869 
6.7017 
wavelet 
2 
54.6524 
649.9612 
6.6190 
0.9684 
0.2852 
8.3276 
127.3534 
transform 
3 
42.6195 
663.5351 
6.5742 
0.9690 
0.2548 
8.2042 
The novel 
1 
83.3250 
1859.9954 
7.3748 
0.8014 
0.3683 
12.1231 
65.1349 
method 
2 
92.1778 
1652.6537 
7.3236 
0.7828 
0.4196 
11.7862