Editing Fractal compression (section)

==Features==
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.<ref name="Jenson">{{Citation
 |author      = John R. Jensen
 |title       = Remote Sensing Textbooks
 |url         = http://www.cas.sc.edu/geog/rslab/Rscc/mod2/2-4/2-4.html
 |publisher   = [[University of South Carolina]]
 |work        = Image Compression Alternatives and Media Storage Considerations (reference to compression/decompression time)
 |url-status     = dead
 |archive-url  = https://web.archive.org/web/20080303154903/http://www.cas.sc.edu/geog/rslab/Rscc/mod2/2-4/2-4.html
 |archive-date = 2008-03-03
}}</ref><ref name="Heath1999">{{cite book|author=Steve Heath|title=Multimedia and communications technology|url=https://books.google.com/books?id=S4tQAAAAMAAJ&q=fractal|date=23 August 1999|publisher=Focal Press|isbn=978-0-240-51529-8|pages=120–123
}} [http://www.focalpress.com/books/details/9780240515298/ Focal Press link]</ref>

At common compression ratios, up to about 50:1, fractal compression provides similar results to [[Discrete cosine transform|DCT-based]] algorithms such as [[JPEG]].<ref>{{cite book |last1=Sayood |first1=Khalid |title=Introduction to Data Compression |date=2006 |publisher=Elsevier |isbn=978-0-12-620862-7 |pages=560–569 }}</ref> At high compression ratios fractal compression may offer superior quality. For satellite imagery, ratios of over 170:1<ref name = "ieee_2000">{{cite book |doi=10.1109/IGARSS.2000.861646 |chapter=Achieving high data compression of self-similar satellite images using fractal |title=IGARSS 2000. IEEE 2000 International Geoscience and Remote Sensing Symposium. Taking the Pulse of the Planet: The Role of Remote Sensing in Managing the Environment. Proceedings (Cat. No.00CH37120) |year=2000 |last1=Wee Meng Woon |last2=Anthony Tung Shuen Ho |last3=Tao Yu |last4=Siu Chung Tam |last5=Siong Chai Tan |last6=Lian Teck Yap |volume=2 |pages=609–611 |isbn=0-7803-6359-0 |s2cid=14516581 |url=https://openresearch.surrey.ac.uk/view/delivery/44SUR_INST/12139532970002346/13140433940002346 }}</ref> 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).<ref>{{cite conference |id={{INIST|1572685}} |last1=Fisher |first1=Y. |title=Fractal encoding of video sequences |conference=Fractal image encoding and analysis |location=Trondheim |date=July 1995 }}</ref>

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<ref>[http://www.byte.com/art/9701/sec12/art1.htm Walking, Talking Web] {{webarchive|url=https://web.archive.org/web/20080106202236/http://www.byte.com/art/9701/sec12/art1.htm |date=2008-01-06 }} Byte Magazine article on fractal compression/resolution independence</ref> 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]].<ref>{{cite journal |last1=He |first1=Chuan-jiang |last2=Li |first2=Gao-ping |last3=Shen |first3=Xiao-na |title=Interpolation decoding method with variable parameters for fractal image compression |journal=Chaos, Solitons & Fractals |date=May 2007 |volume=32 |issue=4 |pages=1429–1439 |doi=10.1016/j.chaos.2005.11.058 |bibcode=2007CSF....32.1429H }}</ref>
Fractal interpolation maintains geometric detail very well compared to traditional interpolation methods like [[bilinear interpolation]] and [[bicubic interpolation]].<ref>{{cite journal |last1=Navascués |first1=M. A. |last2=Sebastián |first2=M. V. |title=Smooth fractal interpolation |journal=Journal of Inequalities and Applications |date=2006 |volume=2006 |pages=1–20 |doi=10.1155/JIA/2006/78734 |s2cid=20352406 |doi-access=free }}</ref><ref>{{cite journal |last1=Uemura |first1=Satoshi |last2=Haseyama |first2=Miki |last3=Kitajima |first3=Hideo |title=EFIFを用いた自己アフィンフラクタル図形の拡大処理に関する考察 |trans-title=A Note on Expansion Technique for Self-Affine Fractal Objects Using Extended Fractal Interpolation Functions |language=ja |journal=IEICE Technical Report |volume=102 |issue=630 |date=28 January 2003 |pages=95–100 |id={{NAID|110003171506}} |doi=10.11485/itetr.27.9.0_95 }}</ref><ref>{{cite journal |id={{NAID|110003170896}} |last1=Kuroda |first1=Hideo |last2=Hu |first2=Xiaotong |last3=Fujimura |first3=Makoto |title=フラクタル画像符号化におけるスケーリングファクタに関する考察 |trans-title=Studies on Scaling Factor for Fractal Image Coding |language=ja |journal=The Transactions of the Institute of Electronics, Information and Communication Engineers |volume=86 |issue=2 |pages=359–363 |date=1 February 2003 }}</ref> Since the interpolation cannot reverse Shannon entropy however, it ends up sharpening the image by adding random instead of meaningful detail. 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.