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Mapping without the sun
Zhang, Jixian

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.
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A) Original TM image
B) Once a time
of a city
C) Three times D) Seven times
Iterated Iterated
Figure 1. Remote sensing image compression using fractal
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,
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
After classification, setting:
The attribution value of each pixel
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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
If it belongs to water
If it belongs to mountain
If it belongs to residential