|Speciale, modelbygger-variant, 3. modul, 2002, id:276|
|Vejleder:||Carsten Lunde Pedersen (Matematik) Keld Helsgaun (Datalogi)|
|Findes på RUb:||Ja|
This Master Thesis deals with Fractal Image Compression, a lossy method for compressing digital images. Fractal Image Compression is based on image modelling with fractal structures known as iterated function systems (IFS). Compression of an image is done by constructing a iterated function system having the image as its fixed point. The system is composed of contractive affine mappings between self similar regions of the image. The parameters describing the function system serves as the compressed representation of the image. Decompression is done by iterating the function system from a random image, thus generating the fixed point of the system i.e. the original image. This thesis deals with three aspects of fractal compression, including mathematical foundation, implementation and useability of the method. The underlying mathematics is explored, covering traditional IFS, IFS with Probabilities and Recurrent IFS. Based on the mathematical theory, a prototype for fractal compression is implemented and then compared to both JPEG and an existing fractal compression application. We conclude that the most important mathematical results that makes fractal compression possible are the collage theorem for compression and the fixed point theorem for decompression. For the implementation of fractal compression methods, partitioned iterated function systems (PIFS) are used. These systems are not as mathematically well founded as the traditional IFS, but solves a number of problems that hinder implementation of traditional IFS in applications for image compression. Even though the prototype proves fractal compression to be a working method for lossy image compression, our tests show the quality vs. Compression ratio to be poor and not comparable to standard JPEG compression. Thus, fractal compression as implemented in the prototype is a poor substitute for common lossy image compression methods.