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Mapping without the sun
Zhang, Jixian

Chao Mu a , Qin Yan b , Jie Yu a , Huiling Qin a
a School of Remote Sensing Information Engineering, Wuhan University, Wuhan 430079,CHINA- (otto0127,yuj_2004) @126.com,
qhlchch@ 163 .com
b Chinese Academy of Surveying and Mapping, Beijing 100039,CHINA-
KEY WORDS: Remote Sensing Image, Fractal Compression, Iterated Function System, Classification, Self-similarity
The high compression ratio and excellent quality of fractal image compression have restricted the applications, due to the consuming
encoding time. This paper discusses an improved method of the fractal remote-sensing image compression. The method is to divide
the images and searching the iterated function system between the range blocks and the domain blocks quickly through analyzing the
texture characters of the images. The goal is to identify the most similar range blocks and domain blocks among the blocks with same
characteristic features. The test results demonstrated the quality and the speed of the remote-sensing images coding were improved
with this method.
The spatial resolution of remote sensing images is of
unceasing enhancement; huge amount of data will require
much more storage space and transmission time. In order to
solve the problem of storage space and transmission time, the
remote sensing images compression becomes one of the hot
topics at present.
Recently, the main image compression methods are the JPEG
compression standard, the wavelet analysis compression and
so on (Hongmei Tang, 2004). But the characteristics of the
remote sensing images are different from the other general
images; its content is mostly about natural surface, such as the
water, vegetation, mountains, etc. These textures are often
clear, and the content generally has the characteristic of the
self-similarity. In this paper, a traditional fractal compression
method applied in the remote sensing images is introduced.
As the exhausted encoding time, an improved method base on
the classification is discussed. It could be proved to lower the
encoding time.
The most famous characteristic of Fractal is the self-similar. It
means no matter how changes of the scale of geometry, a
small part of any image is extremely similar with the larger
part ones. From the perspective of fractal image compression,
it is to the most efficiently use of the self-similarity between
the parts and blocks of image. The main point is to divide an
image into several parts (range blocks), which aren’t
overlapped; meanwhile, dividing the image into several
blocks (domain blocks) that could overlap each other. Then
for each range blocks R t , finding the most similar domain
block D\ to match with them. At last, establishing the
relationship between the range blocks and domain blocks: the
domain block may infinite approach to the range block
through the affine transformation, that is r * w. (z>.). For
each range blocks, finding the Iterated function w j , range
blocks are storied in the form of Iterated Function. The
Iterated Function often can be expressed by only a few
parameters, and according to the Collage Theorem, the
iterated image (decoded image) has nothing to do with the
original images. Therefore, the fractal compression can be
achieved at a high compression ratio. When decoding the
images, we need only iterate the Iterated Function parameters
of each range blocks; the original images can be restored.
Iterated Function System (listed IFS) is the important content
of fractal theory. The basic idea is to identify geometric
objects as a whole and partial, having the self-similar
structure in the meaning of affined change. The most
important theorem of fractal image compression is the
Collage Theorem (Welstead, 1999). This theorem proves that
for a range block we can always find the domain block, which
is closest to the range block with a low erroneous distortion. It
also manifested that the decoding image is nothing to do with
the original image. So only saving every Iterated function w t ,
it can achieve the aim of compression (Yudong Fang, 1996).
In this experiment, a 512 x 512 greyscale TM image, with 265
grey levels for each pixels has been taken for being compressed