International Journal of Computer and Organization Trends, 3, Journal of Information Systems and Communication, 3, Computer Graphics World, 10, Byte, 13, Academic Press, New York. Springer-Verlag, New York. Thesis, University of Technology, Sydney. International Journal of Bifurcation and Chaos, 16, Information Technology Journal, 7, In: Crilly A.

Biological Cybernetics, 43, Amesterdam Univerisity, Amesterdam. Freeman Press, New York. Springer-Verlag, London. Sc Thesis, Taiz University, Yemen.

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In: Saupe, D. According to these mapping functions, the IFS describes a two-dimensional set S as the fixed point of the Hutchinson operator. The idea is to construct the IFS such that this set S is the input binary image. A simple approach [1] for doing so is the following partitioned iterated function system PIFS :.

In the second step, it is important to find a similar block so that the IFS accurately represents the input image, so a sufficient number of candidate blocks for D i need to be considered. On the other hand, a large search considering many blocks is computationally costly. This bottleneck of searching for similar blocks is why PIFS fractal encoding is much slower than for example DCT and wavelet based image representation.

The initial square partitioning and brute-force search algorithm presented by Jacquin provides a starting point for further research and extensions in many possible directions -- different ways of partitioning the image into range blocks of various sizes and shapes; fast techniques for quickly finding a close-enough matching domain block for each range block rather than brute-force searching, such as fast motion estimation algorithms; different ways of encoding the mapping from the domain block to the range block; etc.

Other researchers attempt to find algorithms to automatically encode an arbitrary image as RIFS recurrent iterated function systems or global IFS, rather than PIFS; and algorithms for fractal video compression including motion compensation and three dimensional iterated function systems. Fractal image compression has many similarities to vector quantization image compression.

With fractal compression, encoding is extremely computationally expensive because of the search used to find the self-similarities. Decoding, however, is quite fast.

## Fractal image compression theory and application download

While this asymmetry has so far made it impractical for real time applications, when video is archived for distribution from disk storage or file downloads fractal compression becomes more competitive. For satellite imagery, ratios of over [9] have been achieved with acceptable results. Fractal video compression ratios of — have been achieved in reasonable compression times 2. Compression efficiency increases with higher image complexity and color depth, compared to simple grayscale images.

An inherent feature of fractal compression is that images become resolution independent [11] after being converted to fractal code.

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This is because the iterated function systems in the compressed file scale indefinitely. This indefinite scaling property of a fractal is known as "fractal scaling". The resolution independence of a fractal-encoded image can be used to increase the display resolution of an image. This process is also known as "fractal interpolation". In fractal interpolation, an image is encoded into fractal codes via fractal compression, and subsequently decompressed at a higher resolution. The result is an up-sampled image in which iterated function systems have been used as the interpolant.

One cannot, for example, enlarge an image of a crowd where each person's face is one or two pixels and hope to identify them. Michael Barnsley led development of fractal compression in , and was granted several patents on the technology.

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Barnsley's graduate student Arnaud Jacquin implemented the first automatic algorithm in software in A major breakthrough for Iterated Systems Inc. In , Iterated Systems Inc.

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Fractal image compression has been used in a number of commercial applications: onOne Software , developed under license from Iterated Systems Inc. To date the most successful use of still fractal image compression is by Microsoft in its Encarta multimedia encyclopedia, [22] also under license. Iterated Systems Inc. As wavelet-based methods of image compression improved and were more easily licensed by commercial software vendors the adoption of the Fractal Image Format failed to evolve. During the s Iterated Systems Inc. While compression results were promising, computer hardware of that time lacked the processing power for fractal video compression to be practical beyond a few select usages.

Up to 15 hours were required to compress a single minute of video. ClearFusion was Iterated's freely distributed streaming video plugin for web browsers. The original ClearVideo 1. Two firms, Total Multimedia Inc. The technology basis appears to be Dimension's U. Numerous research papers have been published during the past few years discussing possible solutions to improve fractal algorithms and encoding hardware.