256 
times, it can restore the original images. (Wenqu Zeng, 2002; 
Wee Meng Woon 2000) 
types often have the characteristics of self-similar, it can 
quickly and accurately obtain the most similar blocks. 
The Figure 1 shows the decoding process of iterating IFS with 
1, 3, 7 times. 
Ipl 
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A) Original TM image 
B) Once a time 
of a city 
Iterated 
% 
jp 
C) Three times D) Seven times 
Iterated Iterated 
Figure 1. Remote sensing image compression using fractal 
theory 
The result of the image compression is presented in the Table 
1. The average of RMS for the 4096 range blocks to their 
closest domain blocks is 19.17; the compression ratio is 
4.02:1, the Peak Signal-to-Noise Ratio of seven times iterated 
decoding image to the original image is 21.5891. The biggest 
problem is the exhausted encoding time—about 27min. 
How to improve the fractal encoding speed is the main point 
that many scholars considered. The time-consuming of fractal 
compression mainly manifested in finding the most similar 
domain blocks to the range blocks. As the domain blocks 
could overlap each other, it brings a lot of computation. At 
present, the main solution is to reduce the search area and 
assure the most similar domain blocks in this area. Some of 
the improved ways has been described in [Shuguang W, 
2004]. 
For some improved methods based on the classification, 
considering to the characteristics of remote sensing image, it 
could classify the image with the types of features. To 
different types of range blocks, we only search the most 
similar domain blocks in the same types of area. It can reduce 
the searching time and area. As the features with the same 
On the base of above methods, first, the author makes the 
pre-processing of the original image: the image is classified 
into three types according to the pixel value. One is the water 
area, another is mountain and the other is residential area. The 
Fuzzy C-Means (FCM) clustering algorithm is taken to 
classify the image. Compared with crisp or hard segmentation 
methods, FCM is able to retain more information from the 
original image. (Yunsong Li, 2007). The Figure 2 shows the 
result of the classification using the FCM. 
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Figure 2. Result of the classification using FCM clustering 
algorithm 
After classification, setting: 
The attribution value of each pixel 
bfia IjsnogE 
Second, for each range blocks, the average of attribution 
values of 64 pixels is calculated, and the average of 
attribution values of 256 pixels in every domain blocks is also 
computed. To every range blocks, we find the closest domain 
blocks through the nearest average of attribution values. 
Third, after finding the closest domain blocks for each range 
blocks, we also choose the eight different basic 
rotary-reflection and stretching transformations for the closest 
domain blocks, then calculating the minimum RSM between 
them. That is easy to obtain the Iterated function w. for each 
range blocks. 
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The TM image is compressed by using the improved method; 
the result is showed in Table 1. 
Table 1. Comparison of the two methods 
METHOD 
AVG RMS 
PSNR 
ENCODEING 
TIME(min) 
Traditional 
method 
19.17 
21.5891 
27 
{ 
If it belongs to water 
If it belongs to mountain 
If it belongs to residential 
area