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	Fractal compression - Wikipedia, the free encyclopedia
		Fractal compression is a lossy compression method used to compress images using fractals.
		Fractal compression appeared to be a promising technology in the late 1980s, when in some circumstances it appeared to compress much better than JPEG, its main competitor at that time.
		According to [1], fractal image compression is sardonically known as the "graduate student algorithm": lock a graduate student in a room with a computer until they solve your problem.
	en.wikipedia.org /wiki/Fractal_compression (412 words)

	Fractal Solution
		Each of these applications focuses on the fundamental property of fractals: they are generated by repeating a simple pattern over and over again.Take the most famous of all fractals the so-called Mandelbrot Set, named after IBM mathematician Benoit Mandelbrot.
		Better still, although working out the right fractals to compress a particular image might take a while, decompressing the image would be fast, as fractals are just mathematical formulae - bread-and-butter work to any computer.
		Meanwhile the Queen Mother Library of Aberdeen University recently used fractal compression to shrink a collection of 44,000 historic photographs down on to a single CD- ROM - a somewhat handier format than the five tonnes of magic lantern glass plates on which the images were originally stored.
	www.geocities.com /Omegaman_UK/fractal.html (2143 words)

	FRACTAL IMAGE COMPRESSION
		Hence, for image compression applications where the input files are usually measured in megabytes, and where the losses of very minor graphic details are not critical, lossy methods are mostly used.
		The result is either longer compression and decompression times, or, if one choose to fix the compression and decompression times by increasing the size of the blocks (so the 64 cosine functions will now represent more than 64 pixels), the output graphics will be very blocky due to pixel replication.
		For example, its lengthy compression step will preclude it from being used in applications where it is essential to be able to send out the compressed images with minimal delay, such as live broadcast of video over a network, tele-conferencing, and videophone.
	www.math.psu.edu /tseng/class/Fractals.html (2178 words)

	Fractal Compression
		A Brief History of Fractal Image Compression -------------------------------------------- The birth of fractal geometry (or rebirth, rather) is usually traced to IBM mathematician Benoit B. Mandelbrot and the 1977 publication of his seminal book The Fractal Geometry of Nature.
		Quality: Fractal vs. JPEG ------------------------- The greatest irony of the coding community is that great pains are taken to precisely measure and quantify the error present in a compressed image, and great effort is expended toward minimizing an error measure that most often is -- let us be gentle -- of dubious value.
		Proponents of fractal compression counter that signal-to-noise is not a good error measure and that the distortions present are much more 'natural looking' than the blockiness of JPEG, at both low and high bit rates.
	www.mcs.csuhayward.edu /~grewe/CS6825/Mat/Compression/Fract.htm (3068 words)

	1.05: My Main Squeeze: Fractal Compression
		Because fractal images are stored as mathematical formulas rather than as bit maps, they can be decompressed to resolutions that are higher or lower than those of the original.
		Fractal compression can also improve as you apply more processing power - that is, you can improve both the amount of compression as well as the quality of the image by just letting the system chew on the image longer.
		It may be possible to improve fractal compression technology even further by refining the formulas that recognize fractal patterns.
	www.wired.com /wired/archive/1.05/fractal_pr.html (1248 words)

	A Logical System for Multicriteria Decision Analysis
		Fractal compression is one of the most exotic procedures in image data compression known so far.
		The whole process of image compression minds the fact that images are nature- generated and that the human eye may not perceive the details possibly lost during this type of image codification process.
		Fractal image coding is an interesting approach to image compression, which concerns the data to be actually compressed as an image, not as a succession of bits, or as a signal.
	www.ici.ro /ici/revista/sic1999_4/art08.html (1576 words)

	Wired 1.05: My Main Squeeze: Fractal Compression
		Compression of graphic images, on the other hand, does not preserve all of a file's data.
		Invented in the 1980s by Michael Barnsley and Alan Sloan, two mathematicians at Georgia Tech, fractal compression is based on the discovery by Benoit Mandelbrot, an IBM scientist, that a hidden geometry exists in apparently random patterns of nature.
		Photographic images can be compressed from 20:1 and 50:1 with no noticeable loss in resolution, and the company also claims that it can compress images with a ratio of more than 200:1 and maintain acceptable resolution.
	www.wired.com /wired/archive/1.05/fractal.html (802 words)

	Video Compression Tutorial (Site not responding. Last check: 2007-10-13)
		Discrete cosine transform is a lossy compression algorithm that samples an image at regular intervals, analyzes the frequency components present in the sample, and discards those frequencies which do not affect the image as the human eye perceives it.
		Fractal compression is a form of VQ and is also a lossy compression.
		Compression is performed by locating self-similar sections of an image, then using a fractal algorithm to generate the sections.
	www.wave-report.com /tutorials/VC.htm (1024 words)

	Fractal Image Compression
		Further studies of fractals revealed that images, from mountains to clouds to snowflakes can be built from simple fractal patterns.
		Fractal compression can also improve as you apply more processing power, you can improve both the amount of compression as well as the quality of the image by just letting the system process the image longer.
		This underscores the fact that fractal compression is an asymmetric system, it takes ages to compress, but decompressing is quick.
	web.ukonline.co.uk /p.boughton/fractal.htm (881 words)

	Practical Fractal
		JPEG uses a well-understood mathematical procedure, the discrete cosine transform, to compress files by 90 to 95 percent-equivalent to compression ratios of 10:1 to 20:1.
		What is more, because fractal images are encoded by equations they have no inherent size-an attractive quality to publishers who want their products to work as well on a laptop screen as on a 21 -inch monitor.
		Fractals are beautiful and complex geometric structures that occur naturally around us - the fronds of a fern plant are a good example.
	www.fortunecity.com /emachines/e11/86/pracfrac.html (1438 words)

	Fractal Questions and Answers - Iterated function systems and compression (Site not responding. Last check: 2007-10-13)
		If a fractal can be described by a small number of mappings, the IFS is a very compact description of the fractal.
		A11b: Fractal compression is quite controversial, with some people claiming it doesn't work well, and others claiming it works wonderfully.
		Fractal compression is covered in detail in the comp.compression FAQ file (See compression-faq).
	www.softlab.ntua.gr /miscellaneous/faq/fractal/faq-doc-11.html (553 words)

	Fractal Image Compression
		Fractal Image Compression is based on the fact that any image can be aproximated by several fractals.
		Fractals are self-similar geometrical objects, or what often is heard: several parts of an fractal look similar as the entire image.
		Fractal Image Compression is based on the fact that parts of the image look alike other parts of the same image.
	homepages.cwi.nl /~bens/comp.html (531 words)

	DataCompression.info - Fractals (Site not responding. Last check: 2007-10-13)
		The key to a good fractal compression algorithm is the method by which it breaks down segments of an image into smaller pieces, called partitioning.
		Fractal image compression is a promising new technology that may successfully provide a codec for PC-to-PC video communications.
		A fractal compression patent held by Iterated Systems, Inc. This appears to be a very fundamental patent issued 13 September 1994.
	www.datacompression.info /Fractal.shtml (1538 words)

	Fractal Image Compression and the Self-Affinity Assumption: A Stochastic Signal Modelling Perspective
		Fractal image compression is a comparatively new technique which has gained considerable attention in the popular technical press, and more recently in the research literature.
		While many of the claims published in the popular technical press are clearly extravagant, it appears from the rapidly growing body of published research that fractal image compression is capable of performance comparable with that of other techniques enjoying the benefit of a considerably more robust theoretical foundation.
		So called because of the similarities between the form of image representation and a mechanism widely used in generating deterministic fractal images, fractal compression represents an image by the parameters of a set of affine transforms on image blocks under which the image is approximately invariant.
	math.lanl.gov /Research/Publications/wohlberg-1996-fractal.shtml (354 words)

	FractalSqueeze
		The compression method used is Yuval Fisher's quad-tree fractal compression algorithm.
		And this is the compressed data file generated.
		This compression is not necessarily as good as JPEG but as shown in the tests with Mars, we can get very good results using other fractal compression schemes.
	www.liquidninja.com /FractalSqueeze (652 words)

	Fractal Image Encoding
		Fractal Image Compression: Theory and Application to Digital Images, Yuval Fisher (Ed.), Springer Verlag, New York, 1995 is a collection of articles on Fractal Image Encoding.
		Fractal Image Encoding and Analysis, an NATO Advanced Study Institute, was held in Trondheim, Norway July 8-17, 1995.
		The Waterloo Fractal Compression Project is part of a general research programme dedicated to the study of fractal analysis and Iterated Function Systems/Fractal Transforms from both theoretical as well as practical perspectives.
	inls.ucsd.edu /~fisher/Fractals (4079 words)

	Dr. Dobb's \| Faster Fractal Compression \| July 22, 2001
		The wizardry of fractal compression is embodied in the regeneration of the image from pairs of similar squares.
		If you set up a fractal decompression program to output to the screen (showing you the image as it is decompressed), you initially see a patchwork of small, uniformly colored squares; eight pixels on an edge, for example.
		Table 1(a) shows how long it takes to compress the image on a Sun 4/75, as well as the relative quality of the compression as reflected in the root-mean-square (RMS) pixel-by-pixel difference between the original and the reconstructed images.
	www.ddj.com /184409802?pgno=9 (2961 words)

	Fractal Compression
		The basic idea behind fractal image compression is to express the image as an iterated function system (IFS).
		Barnsley, who invented fractal image compression, has a patent on fractal compression techniques (4,941,193).
		One of the best online references for Fractal Compress is Yuval Fisher's Fractal Image Encoding page (http://inls.ucsd.edu/y/Fractals/) at the Institute for Nonlinear Science, University for California, San Diego.
	fractals.iut.u-bordeaux1.fr /sci-faq/compression.html (426 words)

	Fractal Frequently Asked Questions and Answers FAQ (Site not responding. Last check: 2007-10-13)
		Roughly, fractal dimension can be calculated by taking the limit of the quo- tient of the log change in object size and the log change in measurement scale, as the measurement scale approaches zero.
		Fractal images including some recent alt.binaries.pictures.fractals images are archived at spanky.triumf.ca:/fractals [142.90.112.1].
		The aim of this first international journal on fractals is to bring together the most recent developments in the research of fractals so that a fruitful interaction of the various approaches and scientific views on the complex spatial and temporal behavior could take place.
	www.non.com /news.answers/fractal-faq.html (9552 words)

	Coproc. Paper
		Fractal image compression has recently been proposed as an alternative to JPEG and other compression techniques [1,2,3].
		Profile results gathered from running a fractal compression program on sample images on IBM RS6000/340 workstation show that the program spends more than 80% of total run time computing the absolute error between image blocks.
		Fractal Image Compression using Iterated Transforms, Image and Text Compression, J. Storer Editor, Kluwer Academic Publishers, 1992.
	www.faginfamily.net /barry/Papers/FPL94.htm (623 words)

	fractalus - PNG, JPEG, and Fractals
		LZW compression can often achieve 2:1 compression ratios for an image--meaning the uncompressed image is twice as large as the compressed file.
		The second image uses a compression setting of 10 (and is 18K), and the third uses a compression setting of 30 (it's 8K).
		A "compression 10" in one program doesn't get you the same thing as "compression 10" in another one--one might produce a bigger file, or the same file but with more loss.
	www.fractalus.com /info/png-jpeg.htm (2518 words)

	Dr Tim Ferguson
		This is a Windows application for compressing images through IFS to achieve "compression ratios of 24:1 in 6 minutes on a 320x200 true-color image".
		They have developed the fractal image format `.FIF' for which they supply a shareware encoder (Fractal Imager), a stand alone decoder and a Netscape plug-in decoder, and a development package for use under Windows.
		Fractal Frequently Asked Questions and Answers page updated by Ermel Stepp covers general FAQ's on fractals with a section on fractal image compression.
	www.csse.monash.edu.au /~timf/fractal.html (366 words)

	Femtosoft Technologies - Fractal Imaging Software
		When the algorithm finishes compressing the image, it will prompt you for a filename to save the resulting fractal image model (the set of fractal codes that design the image).
		The fractal compression scheme is based on self-similarity: the fractal code for a given image region tells which part of the image, when constracted, rotated, flipped, skewed, and contrast-modified, looks the most like the destination region.
		The storage mechanism for the Java and Delphi compressed images is different (in Java I used the built-in object serialization, in Delphi I wrote directly to a file).
	www.femtosoft.biz /fractals/fractal.html (923 words)

	Ben Schouten en het CWI
		Using present compression techniques is simply too slow and even after compression the standard techniques remain to be improved.
		Fractal Image Coding is a new technique for compact storing after which transmission takes less time.
		Fractals in Engineering will be held at Arcachon, France from June 25 th to 27 th.
	www.cwi.nl /archive/projects/fractals/index.html (414 words)

	Bibliography: Fractal compression
		Fractal image coding based on a theory of iterated contractive image transformations.
		Fractal compression of single images and image sequences using genetic algorithms.
		Fractal model of a one-dimensional discrete signal and its implementation.
	cnls.lanl.gov /~brendt/bibliographies/html/fractal_coding.html (4973 words)

	Algorithm for Fast Fractal Image Compression - Kominek (ResearchIndex)
		Abstract: Fractal image compression is a promising new technology that may successfully provide a codec for PC-to-PC video communications.
		Unfortunately, the large amount of computation needed for the compression stage is a major obstacle that needs to be overcome.
		On the Convergence of Fractal Transforms - Hürtgen, Hain (1994)
	citeseer.ist.psu.edu /kominek95algorithm.html (673 words)

	WebFractales - Report and software - FracTalCompressions (Image compression thanks to fractals !) (Site not responding. Last check: 2007-10-13)
		We actually choose three efficient methods: the Jacquin's compression, the Delaunay's compression and another one named Compression by successive subdivision of triangles.
		The complexity of the compression module stays high, but that's not a burning issue for the project.
		FracTal Compressions RapportBD rapport-cdrom rapport-codages Contours actifs rapport de stagerapport-images Rapport_MMC_BaumWelch Contours actifs rapport de stage L-systèmes modélisation arbre 3D et plante
	www.webfractales.com /rapport.php?see=16 (313 words)

	SS > NSC > Fractal image compression
		Notes for a talk I gave on fractal image compression, in August 1991.
		I'll talk about how an image is reconstructed from compression data, and how images are encoded, and the errors introduced.
		This is the reason behind the fantastic compression ratios possible with fractal compression.
	www-users.cs.york.ac.uk /~susan/complex/compress.htm (843 words)

	[No title]
		There is also an updated bibliography (December 1998) on Fractal Image Compression listing many more papers that are not available online here.
		An introduction and review of fractal image compression is available here: D. Saupe, R. Hamzaoui, H. Hartenstein, Fractal image compression - An introductory overview, in: Fractal Models for Image Synthesis, Compression, and Analysis, D. Saupe, J. Hart (eds.), ACM SIGGRAPH'96 Course Notes.
		Fractal image compression by the classification in the wavelet transform domain,
	www.compression.ru /download/fractal.html (1764 words)

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