Fractal Compression Using Ifs Operators on Transforms

Standard fractal image compression techniques rely on using an IFS operator directly on the image function. However, sometimes it is more convenient to work on some transformed version of the image. For example, an MRI image is scanned in as frequency data. Thus, it is more natural to work on the Fourier Transform of the image rather than on the image itself. Furthermore, if your image quality metric involves a transform, then again it is more natural to work in the transform domain than in the spatial domain. After giving a brief introduction to IFS fractals and classical fractal image compression, we go on to discuss some generalities of IFS operators on transform spaces. Then we give the examples of the Fourier Transform (DCT), the Wavelet Transform and the Lebesgue Transform. We emphasize that the operations can be done completely in the transform domain. In some applications, we never need to return to the spatial domain.