The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B7. Beijing 2008 
3.1.2 Correlation Coefficient: CC measures the correlation 
between the original and the fused images. The higher the 
correlation between the fused and the original images, the better 
the estimation of the spectral values. The ideal value of 
correlation coefficient is 1. 
^MS U F, 
(6) 
''JEIfMS,. . MS . F 
V v mean) y v '»7 n 
g =^ (a/ ' +a/ ' )/2 
(9) 
Where a j is the difference of pixel in the direction of X , 
and a T is the difference of pixel in the direction of V • 
V 
4. EXPERIMENTTEST AND ANALYSIS OF FUSION 
RESULTS 
Where CC is the Correlation Coefficient, F is the fused image and 
i and j are pixels, MS is the multi-spectral data. 
3.2 High Spatial Frequency Information Absorption 
The high spatial frequency information absorption is that the 
enhancement of resolution and increasing of information of the 
fused image relative to the original MS image. The common 
assessing index is Entropy. Entropy is a measure of information 
and its concept has been employed in many scientific fields 
(Lau,2001). Sun et al. (1997) introduced. 
Entropy as a measure to directly conclude the performance of 
image fusion. The Entropy can show the average information 
included in the image and reflect the detail information of the 
fused image. Commonly, the greater the Entropy of the fused 
image is, the more abundant information included in it, and the 
greater the quality of the fusion is. According to the information 
theory of Shannon, The Entropy of image is: 
255 
E = ~ZP}og 2 P, 
/=0 
Where E is the Entropy of image, and p is the probability of i 
in the image. 
4.1 Experiment Data 
For evaluation, many QuickBird images of different regions 
have been tested, a small scene of a QuickBird image is used 
for demonstration of this paper, which has four 2.4-m 
resolution multi-spectral bands and a 0.6-m resolution Pan 
band. Band 3, 2, 1 are selected. The land use of the region is 
complex and it includes farm, vegetation, water, highway and 
so on. Therefore, if the region is tested, we can compare the 
fusion result at different DNs with diversified algorithms and 
assess the algorithms from many aspects. No rectification is 
needed for the fusion of QuickBird MS and Pan images as 
they are from same sensor system. As Liu (2000b) 
recommended (Liu., 2000b), a linear model is employed to 
resample the 2.4-m resolution multi-spectral bands to a 0.6-m 
pixel size before fusion can be taken. The resampled multi- 
spectral and Pan bands are then fused using the above 
algorithms, respectively. The fusion results are showed in 
figure 1. 
4.2 Analysis of Fusion Results 
Initial qualitative visual inspections reveal that all the fused 
images have better qualifications than original non-fused 
images. The sharpness of the fused images has been 
significantly enhanced. The further quantitative evaluation 
can be done with above criteria. The values of the evaluation 
have been showed in three tables. 
3.3 Definition of Image 
The definition of image is the contrast of hue between pixels 
border upon, it can be weighted using the following indexes: 
3.3.1 Standard Deviation: SD is an important index to weight 
the information of image, it reflects the deviation degree of values 
relative to the mean of the image. The greater SD is, the more 
dispersible the distributing of the gray grade is. In the statistical 
theory, the SD is defined as follows: 
Image 
BM 
SD 
AG 
MS 
0.0000 
38.2405 
2.8801 
MLT 
0.0447 
45.3288 
6.1909 
MB 
0.0167 
39.9507 
8.4097 
HPF 
0.0552 
43.4763 
8.2676 
SFIM 
0.0155 
45.8497 
13.8672 
Table 1. Bias of Mean, Standard Deviation, Average Grade 
of MS and various fused images 
° = \~±(MSiJ-MS m ean) 
Where <7 is the SD, MS is the multi-spectral data, n is the bands 
of MS. 
3.3.2 Average Grads: The AG can reflect the contrast of 
detail in the image, so it can be used to assess the definition of 
image. Commonly, the average grads is greater, the image is more 
legible. 
Image 
Entropy 
of 
Bandl 
Entropy 
of 
Band2 
Entropy 
of 
Band3 
Average 
Entropy 
MS 
7.5373 
7.5710 
7.4625 
7.5236 
MLT 
7.3377 
7.2514 
7.3555 
7.3148 
MB 
7.3292 
7.3774 
7.3331 
7.3466 
HPF 
7.4572 
7.4416 
7.4650 
7.4546 
SFIM 
7.5454 
7.4225 
7.5132 
7.4937 
Table 2. Entropy of MS and various fused images