Fractal Image Compression

Abstract

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