Fractal image compression
Fractal image compression is a method for lossy compression of digital images , in which the self-similarity in the images is used.
1988 put Michael F. Barnsley and Alan D. Sloan the theoretical foundations of fractal image compression, the first implementation , however, was from Barnsley doctoral Arnaud Jacquin 1992 .
principle
The idea is based on a certain kind of fractals, the attractors of iterated function systems (IFS). Here, complex maps are created with a set of affine maps of the image in itself.
Simple examples are ferns or clouds . If you look for a certain feature of the cloud, you will always be able to find a place that is very similar to it and is only a bit larger, rotated, lighter or compressed.
In order to be able to construct an arbitrary picture, a set of surfaces ( ) has to be sought which, when they are united, cover the entire picture, but must not overlap in pairs. For each of these areas , a different area must be found in the image that looks as similar as possible to this area. Transformations such as contrast and brightness adjustments, rotation, scaling, ... can be carried out.
It should be noted that the content of the areas is greater than the content of the areas .
The search for the smallest possible set of such surfaces with the associated parameters for mapping is extremely time-consuming.
An image is reconstructed in loops. It starts with any image of the target size. Then all mapping is done. The result is an image that looks a little more similar to the image you are looking for. These calculations are repeated until no further improvement is possible.
Fractal Image Format (FIF)
Fractal Image Format is a graphic format developed by Iterated Systems , which is based on fractal image compression and was aligned against JPEG. Despite some advantages, such as considerably better scalability and slightly higher quality with the same file size, the format has failed despite some minor successes. Some of the reasons for this were that neither Netscape nor Microsoft were willing to implement the format in their browser, plug-ins outside of the Win32 platform were not available (outside of Windows, it was initially not possible to display them) and files in this format initially could only be processed with a relatively expensive tool from Iterated. Nevertheless, many graphics programs today are able to at least decode FIF graphics. The plug-in for viewing with Netscape or Internet Explorer is no longer officially available today. The last version 1.6 of the Fractal Viewer plug-in can still be found on the FTP servers of some universities and also works correctly with the latest versions of Netscape, Opera and Internet Explorer. It is able to display FIF graphics as full screen or to scale them within the website.
See also
literature
- Michael F. Barnsley, Lyman P. Hurd, Louisa F. Anson: Fractal image compression. AK Peters / CRC Press 1993, ISBN 1568810008 .
- Yuval Fisher: Fractal image compression: theory and application. Springer 1995, ISBN 0387942114 .
- Michael F. Barnsley, Lyman P. Hurd: Image Compression with Fractals. Vieweg + Teubner 1996, ISBN 3528054646 .
- Yuval Fisher (Ed.): Fractal image encoding and analysis (NATO ASI Series F: Computer and Systems Sciences, Vol. 159) . Springer 1998, ISBN 3540631968 , ISBN 3642083242 .