The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B7. Beijing 2008 
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distance from p to P x as d x from the curve, if 
d x2 <d x considering P 4 as step ® until the last point of the 
spectral curve. @ summarize the step number 77, under the 
step measurement unit d x . Then the length of spectral curve 
under d x is, 
L{d x ) = n x d x (17) 
© Change step measurement unit to obtain spectral curve 
length as equation (18). 
L(d 2 ) = n 2 d 2 , ,L(d m ) = n m d m (18) 
Thus we can calculate the fractal dimension value of spectral 
curve as equation (15). 
3.3 Dimensionality reduction with fractal feature image 
With the fractal dimension calculation of spectral curve for 
each pixel, it can be taken as the feature of spectral curve. This 
feature value is the result of dimensionality reductions of 
spectral curve. The fractal feature of spectral curve cab be used 
for hyper spectral image segment and classification for it can 
transform the hyper spectral information into one dimension 
fractal feature image. Thus the fractal feature image analysis 
can realize dimensionality reduction and increase the efficiency 
of data processing for it can full use the image analysis 
algorithm in spatial domain. 
The fractal dimension value is taken as the feature of spectral 
curve and the fractal dimension feature image is proposed to 
represent the dimensionality reduction result of hyper spectral 
image. The dimensionality reduction procedure based on the 
fractal analysis has been described as figure 3. Figure 5 gives 
the dimensionality reduction feature image of MAIS image. 
Figure 5(a) is one of band images. Figure 5(b) is the fractal 
feature image. 
Figure 5(a) Original band image of MAIS 
Figure5 (b) Spectral fractal dimension feature image of MAIS 
Figure 5 Dimensionality reduction result based on spectral 
fractal analysis 
As figure 5, the fractal feature can combine the spectral 
information and spatial information together and realize the 
dimensionality reduction through the spectral feature 
transformation. The fractal feature image can represent the 
spectral information of hyper spectral image and obtain better 
detail representation and it is a new method of spectral feature 
analysis of hyper spectral image. 
4. EXPERIMENTS AND CONCLUSIONS 
Hyper spectral texture code is taken as the important hyper 
spectral image analysis technique[12]. In order to verify the 
dimensionality reduction algorithm based on fractal analysis, 
the author select different object texture unit to calculate the 
fractal dimension value of spectral curve of each pixel together 
with the correlation of the centre pixel. The texture unit is 3 X3. 
The result is shown as table 3. 
resident area 
tree 
water 
Fractal 
dimension 
correlation 
Fractal 
dimension 
correlano 
n 
Fractal 
dimension 
correlatici 
n 
1 
1. 0237 
0. 8869 
1.0210 
0. 9786 
1. 0128 
0. 9652 
2 
1. 0271 
0. 8771 
1.0169 
0. 9919 
1. 0152 
0. 9851 
3 
1.0262 
0. 8204 
1.0197 
0. 9951 
1. 0146 
0. 9891 
4 
1. 0243 
0. 9835 
1. 0152 
0. 9929 
1.0105 
0. 9830 
5 
1.0239 
1. 0000 
1. 0200 
1. 0000 
1.0145 
1. 0000 
6 
1.0202 
0. 8325 
1. 0161 
0. 9967 
1. 0176 
0. 9974 
7 
1. 0244 
0. 9621 
1.0179 
0. 9886 
1. 0111 
0. 9623 
8 
1. 0237 
0. 9644 
1. 0198 
0. 9942 
1.0138 
0. 9806 
9 
1. 0199 
0.8377 
1. 0175 
0. 9924 
1.0153 
0. 9743 
max 
1. 0271 
1. 0000 
1. 0210 
1. 0000 
1. 0176 
1. 0000 
min 
1. 0199 
0. 8204 
1. 0152 
0. 9786 
1. 0105 
0. 9623 
deviation 
0. 0024 
0. 0707 
0. 0020 
0. 0060 
0. 0022 
0. 0130 
range 
0. 0072 
0. 1796 
0. 0058 
0. 0214 
0. 0071 
0. 0377 
Table 3 Fractal dimension and correlation of spectral curve in 
texture unit