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