| Fractal
Image Compression |
Introduction
The subject of this work is image compression with fractals. Today JPEG has become
an industrial standard in image compression. Further researches are held in two
areas, wavelet based compression and fractal image compression. The fractal scheme
was introduced by Michael F Barnsley in the year 1945.His idea was that images
could be compactly stored as iterated functions which led to the development of
the IFS scheme which forms the basis of fractal image compression. Further work
in this area was conducted by A.Jacquin, a student of Barnsley who published several
papers on this subject. He was the first to publish an efficient algorithm based
on local fractal system.
Fractal
image compression has the following features: "
Compression has high complexity.
" Fast image decoding
" High
compression ratios can be achieved.
These features enable applications such
as computer encyclopedias, like the Microsoft Atlas that came with this technology.
The technology is relatively new.
Overview
Of Image Compression Images are stored
as pixels or picture forming elements. Each pixel requires a certain amount of
computer memory to be stored on. Suppose we had to store a family album with say
a hundred photos. To store this on a computer memory would require say a few thousands
of dollars. This problem can be solved by
image compression. The number of pixels involved in the picture can be drastically
reduced by employing image compression techniques. The human eye is insensitive
to a wide variety of information loss. The redundancies in images cannot be easily
detected and certain minute details in pictures can also be eliminated while storing
so as to reduce the number of pixels. These can be further incorporated while
reconstructing the image for minimum error. This is the basic idea behind image
compression. Most of the image compression techniques are said to be lossy as
they reduce the information being stored.
The present method being employed consists of storing the image by eliminating
the high frequency Fourier co-efficients and storing only the low frequency coefficients.
This is the principle behind the DCT transformation which forms the basis of the
JPEG scheme of image compression. Barnsley
suggested that storing of images as iterated functions of parts of itself leads
to efficient image compression.
In the middle of the 80's this concept of IFS became
popular. Barnsley and his colleagues in the Georgia University first observed
the use of IFS in computerized graphics applications. They found that IFS was
able to cress colour images upto 10000 times. The compression contained two phases.
First the image was partitioned to segments that were self-similar as possible.
Then each part was described as IFS with probabilities
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