Fractal compression

Fractal compression

Fractal compression is a lossy image compression method using fractals to achieve high levels of compression. The method is best suited for photographs of natural scenes (trees, mountains, ferns, clouds). The fractal compression technique relies on the fact that in certain images, parts of the image resemble other parts of the same image. Fractal algorithms convert these parts, or more precisely, geometric shapes into mathematical data called "fractal codes" which are used to recreate the encoded image. Fractal compression differs from pixel-based compression schemes such as JPEG, GIF and MPEG since no pixels are saved. Once an image has been converted into fractal code its relationship to a specific resolution has been lost; it becomes resolution independent. The image can be recreated to fill any screen size without the introduction of image artifacts or loss of sharpness that occurs in pixel-based compression schemes.


Michael Barnsley led development of fractal compression in 1987, and holds several patents on the technology. [ US patent|4941193 – Barnsley and Sloan's first iterated function system patent, filed in October 1987] The most widely known practical fractal compression algorithm was invented by Barnsley and Alan Sloan. Barnsley's graduate student Arnaud Jacquin implemented the first automatic algorithm in software in 1992. [ [ Using Fractal Coding to Index Image Content for a Digital Library] Tech report] [Arnaud E. Jacquin. Image Coding Based on a Fractal Theory of Iterated Contractive Image Transformations. IEEE Transactions on Image Processing, 1(1), 1992.] All methods are based on the fractal transform using iterated function systems. Michael Barnsley and Alan Sloan formed Iterated Systems Inc. [Iterated Systems Inc. changed its name to [ MediaBin Inc. Inc.] in 2001 and in turn was bought out by Interwoven, Inc. in 2003)] in 1987 which was granted over 20 additional patents related to fractal compression.

A major breakthrough for Iterated Systems Inc. was the automatic fractal transform process which eliminated the need for human intervention during compression as was the case in early experimentation with fractal compression technology. In 1992 Iterated Systems Inc. received a $2.1 million government grant [ [ government grant] ] to develop a prototype digital image storage and decompression chip using fractal transform image compression technology.

Fractal image compression has been used in a number of commercial applications: onOne Software, developed under license from Iterated Systems Inc., Genuine Fractals 5 [ [ Genuine Fractals Product Review] ] which is a Photoshop plugin capable of saving files in compressed FIF (Fractal Image Format). To date the most successful use of still fractal image compression is by Microsoft in its Encarta multimedia encyclopedia [ [ Mathematics Awareness Week - April 1998 reference to Microsoft's Encarta fractal image compression] ] , also under license.

Iterated Systems Inc. supplied a shareware encoder (Fractal Imager), a stand alone decoder, a Netscape plug-in decoder and a development package for use under Windows. 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. Fact|date=March 2008

During the 1990s Iterated Systems Inc. and it partners expended considerable resources to bring fractal compression to video. 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.

ClearVideo also known as RealVideo (Fractal) and SoftVideo were early fractal video compression products. ClearFusion, was Iterated's freely distributed streaming video plugin for web browsers. In 1994 SoftVideo was licensed to Spectrum Holobyte for use in its CD-ROM games including Falcon Gold and [ [ 1994 Manual] specifying on page 11 SoftVideo under license to Spectrum Holobyte] .

In 1996 Iterated Systems Inc. announced [ [ Mitsubishi Corporation ClearVideo press release] ] an alliance with the Mitsubishi Corporation to market ClearVideo to their Japanese customers. The original ClearVideo 1.2 decoder driver is still supported [ [ Microsoft ClearVideo support] ] by Microsoft in Windows Media Player although the encoder is no longer supported.

Numerous research papers have been published during the past few years discussing possible solutions to improve fractal algorithms and encoding hardware. [ [ Advances in fractal compression for multimedia applications] ] [ [ Fast calculation of IFS parameters for fractal image coding] ] [ [ Fractal image compression performance synthesis through HV partitioning] ] [ [ Simple and Fast Fractal Image Compression] Circuits, Signals, and Systems - 2003] [ [ Schema genetic algorithm for fractal image compression] Department of Electrical Engineering, National Sun Yet-Sen University, Kaohsiung, Taiwan] [ [ A fast fractal image encoding method based on intelligent search of standard deviation] Department of Electrical and Computer Engineering, The University of Alabama] [ [ Novel fractal image-encoding algorithm based on a full-binary-tree searchless iterated function system] Department of Electrical and Computer Engineering, The University of Alabama] [ [ Fast classification method for fractal image compression] Proc. SPIE Vol. 4122, p. 190-193, Mathematics and Applications of Data/Image Coding, Compression, and Encryption III, Mark S. Schmalz; Ed]


The primary patents (These include U.S. Patents 4,941,193, 5,065,447, 5,384,867, 5,416,856, and 5,430,812.) are now held by Interwoven, from their purchase of MediaBin formerly known as Iterated Systems Inc. Patent restrictions have hindered widespread adoption of fractal compression. [ [ NASA Technology Directions for the 21st Century] Section 2.3.2 reference to Iterated Systems Inc.'s patents.] [ [ article] Reference to fractal compression patents.] [ [ Graphics Gems and Fractal Compression] Reference to license restrictions.] [ [ File Formats and Compression] Fractal compression subject to numerous patent applications.] [Encyclopedia of computer science and technology, authors Allen Keny/James G. Williams, Image Compression for Multimedia Publishing, page 196, reference to fractal compression patents.]


With fractal compression, encoding is extremely computationally expensive because of the search used to find the self-similarities. Decoding, however is quite fast. 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. [ [ Image Compression Alternatives and Media Storage Considerations] Georgia Institute of Technology reference to compression/decompression time.] [cite book
last = Heath
first = Steve
authorlink =
coauthors =
title = Multimedia and Communications Technology
publisher = Focal Press
date = 1999
location =
pages = pp 120 - 123
url =
doi =
id =
isbn = 0240515293

At common compression ratios, up to about 50:1, Fractal compressionprovides similar results to DCT-based algorithms such as JPEG [cite book
last = Sayood
first = Khalid
authorlink =
coauthors =
title = Introduction to Data Compression, Third Edition
publisher = Morgan Kaufmann
date = 2005
location =
pages = pp 560 - 569
url =
doi =
id =
isbn = 012620862X
] . At high compression ratios fractal compression may offer superior quality. For satellite imagery, ratios of over 170:1 [ [ Geoscience and Remote Sensing Symposium paper] Achieving high data compression of self-similar satellite images using fractal.] have been achieved with acceptable results. Fractal video compression ratios of 25:1-244:1 have been achieved in reasonable compression times (2.4 to 66 sec/frame). [ [ Fractal encoding of video sequences] ]

Compression efficiency increases with higher image complexity and color depth, compared to simple grayscale images.

Resolution independence and fractal scaling

An inherent feature of fractal compression is that images become resolution independent [ [ Walking, Talking Web] Byte Magazine article on fractal compression/resolution independence] after being converted to fractal code. 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".

Fractal interpolation

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. [ [ Interpolation decoding method with variable parameters for fractal image compression] College of Mathematics and Physics, Chongqing University, China ]

Because fractal interpolation operates on geometric information in the image, rather than pixel information, it maintains geometric detail very well compared to other interpolation methods. [ [ Smooth fractal interpolation] Departamento de Matemáticas, Universidad de Zaragoza, Campus Plaza de San Francisco, Zaragoza, Spain] [ [ A Note on Expantion Technique for Self-Affine Fractal Objects Using Extended Fractal Interpolation Functions] Hokkaido Univ., Graduate School of Engineering, JPN] [ [ Studies on Scaling Factor for Fractal Image Coding] Nagasaki University, Faculty of Engineering] Fractal interpolation is currently used in Genuine Fractals 5 and is best suited for extreme enlargements. [ [ Digital Photography Review] Interpolation method comparisons] [ [ DesignPreference] Interpolation method comparisons] Other forms of up-scaling include bilinear interpolation and bicubic interpolation.

ee also

*Iterated function system
*Image compression


External links

* [ Pulcini and Verrando's Compressor]
* [ Waterloo Fractal Coding Project] Formerly the "Waterloo Fractal Compression Project"
* Web Archive copy of [*/ Fractal Image Encoding] website
* Keith Howell's 1993 M.Sc. dissertation [ Fractal Image Compression for Spaceborne Transputers]
* [ My Main Squeeze: Fractal Compression] , Nov 1993, Wired.
* [ Fractal Basics] description at FileFormat.Info
* [ Superfractals] website devoted to fractals by the inventor of fractal compression

Wikimedia Foundation. 2010.

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