Editing Fractal compression (section)

===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.