- 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 algorithmsconvert 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, GIFand MPEGsince 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 Barnsleyled development of fractal compression in 1987, and holds several patents on the technology. [ US patent|4941193 – Barnsley and Sloan's first iterated function systempatent, 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. [ [http://www.cse.buffalo.edu/tech-reports/95-05.ps 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 transformusing iterated function systems. Michael Barnsley and Alan Sloan formed Iterated Systems Inc. [Iterated Systems Inc. changed its name to [http://sec.edgar-online.com/2001/03/30/0000931763-01-000662/Section20.asp 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 [ [http://statusreports.atp.nist.gov/reports/91-01-0057TEXT.html 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 Fractals5 [ [http://www.pcpro.co.uk/macuser/reviews/15870/genuine-fractals.html?searchString=fractal Genuine Fractals Product Review] ] which is a Photoshopplugin capable of saving files in compressed FIF (Fractal Image Format). To date the most successful use of still fractal image compression is by Microsoftin its Encartamultimedia encyclopedia [ [http://www.mathaware.org/mam/98/articles/theme.essay.html 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 Holobytefor use in its CD-ROMgames including Falcon Gold and [ [http://www.startrekgames.cz/downloads/fu_manual_cz.pdf 1994 Manual] specifying on page 11 SoftVideo under license to Spectrum Holobyte] .
In 1996 Iterated Systems Inc. announced [ [http://findarticles.com/p/articles/mi_m0EIN/is_1996_Oct_29/ai_18810482 Mitsubishi Corporation ClearVideo press release] ] an alliance with the
MitsubishiCorporation to market ClearVideo to their Japanese customers. The original ClearVideo 1.2 decoder driver is still supported [ [http://support.microsoft.com/kb/291948/en-us Microsoft ClearVideo support] ] by Microsoft in Windows Media Playeralthough 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. [ [http://portal.acm.org/citation.cfm?id=261444 Advances in fractal compression for multimedia applications] ] [ [http://cat.inist.fr/?aModele=afficheN&cpsidt=1380599 Fast calculation of IFS parameters for fractal image coding] ] [ [http://ieeexplore.ieee.org/Xplore/login.jsp?url=/iel5/4289832/4289833/04289976.pdf?temp=x Fractal image compression performance synthesis through HV partitioning] ] [ [http://www.actapress.com/PaperInfo.aspx?PaperID=13701&reason=500 Simple and Fast Fractal Image Compression] Circuits, Signals, and Systems - 2003] [ [http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V2M-4M7VB17-1&_user=10&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=890409343ad7b639e855141c44d174fb Schema genetic algorithm for fractal image compression] Department of Electrical Engineering, National Sun Yet-Sen University, Kaohsiung, Taiwan] [ [http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V25-4H27BX7-3&_user=10&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=faf77464c176654cb1f27e29ef6e4077 A fast fractal image encoding method based on intelligent search of standard deviation] Department of Electrical and Computer Engineering, The University of Alabama] [ [http://spiedl.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=OPEGAR000044000010107002000001&idtype=cvips&gifs=yes 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] [ [http://adsabs.harvard.edu/abs/2000SPIE.4122..190T 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. [ [http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19980197313_1998220371.pdf NASA Technology Directions for the 21st Century] Section 2.3.2 reference to Iterated Systems Inc.'s patents.] [ [http://www.wired.com/wired/archive/1.05/fractal_pr.html Wired.com article] Reference to fractal compression patents.] [ [http://www.ercb.com/ddj/1993/ddj.9307.html Graphics Gems and Fractal Compression] Reference to license restrictions.] [ [http://www.tasi.ac.uk/advice/creating/fformat.html#ff1 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. [ [http://www.cas.sc.edu/geog/rslab/Rscc/mod2/2-4/2-4.html Image Compression Alternatives and Media Storage Considerations] Georgia Institute of Technology reference to compression/decompression time.] [cite book
last = Heath
first = Steve
title = Multimedia and Communications Technology
publisher = Focal Press
date = 1999
pages = pp 120 - 123
isbn = 0240515293 ]
At common compression ratios, up to about 50:1, Fractal compressionprovides similar results to DCT-based algorithms such as
last = Sayood
first = Khalid
title = Introduction to Data Compression, Third Edition
publisher = Morgan Kaufmann
date = 2005
pages = pp 560 - 569
isbn = 012620862X ] . At high compression ratios fractal compression may offer superior quality. For satellite imagery, ratios of over 170:1 [ [http://ieeexplore.ieee.org/Xplore/login.jsp?url=/iel5/6913/18661/00861646.pdf?arnumber=861646 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). [ [http://cat.inist.fr/?aModele=afficheN&cpsidt=1572685 Fractal encoding of video sequences] ]
Compression efficiency increases with higher image complexity and color depth, compared to simple
Resolution independence and fractal scaling
An inherent feature of fractal compression is that images become resolution independent [ [http://www.byte.com/art/9701/sec12/art1.htm 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".
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. [ [http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TJ4-4J4B95D-3&_user=10&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=2f639f75d0ef4078bac00cf994fbedfd 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. [ [http://www.hindawi.com/GetArticle.aspx?doi=10.1155/JIA/2006/78734 Smooth fractal interpolation] Departamento de Matemáticas, Universidad de Zaragoza, Campus Plaza de San Francisco, Zaragoza, Spain] [ [http://sciencelinks.jp/j-east/article/200310/000020031003A0228183.php A Note on Expantion Technique for Self-Affine Fractal Objects Using Extended Fractal Interpolation Functions] Hokkaido Univ., Graduate School of Engineering, JPN] [ [http://sciencelinks.jp/j-east/article/200214/000020021402A0392249.php 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. [ [http://www.dpreview.com/learn/?/key=interpolation Digital Photography Review] Interpolation method comparisons] [ [http://www.designpreference.com/reviews/software/genuinefractals5.html DesignPreference] Interpolation method comparisons] Other forms of up-scaling include
bilinear interpolationand bicubic interpolation.
Iterated function system
* [http://www.verrando.com/pulcini/gp-uw1.html Pulcini and Verrando's Compressor]
* [http://links.uwaterloo.ca/ Waterloo Fractal Coding Project] Formerly the "Waterloo Fractal Compression Project"
* Web Archive copy of [http://web.archive.org/web/*/http://inls.ucsd.edu/y/Fractals/ Fractal Image Encoding] website
* Keith Howell's 1993 M.Sc. dissertation [http://www.howell1964.freeserve.co.uk/MSc/FIC/FIC_00.htm Fractal Image Compression for Spaceborne Transputers]
* [http://www.wired.com/wired/archive/1.05/fractal.html My Main Squeeze: Fractal Compression] , Nov 1993, Wired.
* [http://www.fileformat.info/mirror/egff/ch09_09.htm Fractal Basics] description at FileFormat.Info
* [http://www.superfractals.com/ Superfractals] website devoted to fractals by the inventor of fractal compression
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