الفهرس 
General IntroductionOnly 14 pages are availabe for public view
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Abstract
The aim of this thesis is to study a special type of modem analysis,
Fractal Geometry, which has many applications. We emphasize on fractal
application in image processing caUed fractal image compression. Image
compression is needed in computers and modem technology for efficient
storage and speed of transmission. We study a new feature offractal image
compression, image enhancement. This feature is to be added to the known
benefit of fractal image compression, the high compression ratio.
To study fractal image compression, we introduce a fractal metric
space. Using modem set theory of Georg Cantor, a complete metric space
called Fractal Space or Hausdorff Space was established. The Contraction
Mapping Theory assures the existence of fixed points for contractive affine
transformation. Those fixed points were called the attractor of
transformation. They show amazing images when drawn using computer
program. But, it was not part of om work to study such images.
We address the reverse problem, if we have an image, how can we
find a transformation whose attractor is the given image. This is called
fractal image encoding. This problem was first addressed and solved by
Michael Bamsley. We use Yuval Fisher proposed quad-tree partitioning
algorithm. We give a detailed discussion of quad-tree algorithm
Emphasis is made on the advantages of applying fractal image
compression method to enhance the image properties. We did not examine
coding or decoding time, obtained compression ratio or complexity of
technique since these areas are well covered in other searches