Good fractal compression methods rely on iterative function systems (IFS), which have been designed by Barnsley [1] and Jacquin [2]. The main principle is that an image can be built by combining parts which are similar to the other parts. When encoding an image, the image is partitioned into possibly overlapping square blocks called domain blocks. Subsequently a new partition is made into smaller range blocks [2]. For each range block the closest domain block is searched among all domain blocks by applying a set of transformations on the domain blocks. Compression is obtained by storing only the information about these transformations. The information stored includes domain number, scaling constant, offset etc. This method of compressing images is called Partitioned Iterated Function System (PIFS). This paper explores the use of difference between range and domain elements to find the scaling constants and offset. This paper also explores the implications of mapping IFS blocks on a non-linear basis between range and domain blocks. Further, difference based non-linear mapping is also looked upon. The results show comparable ratios of compression and RMS error with PIFS based fractal compression.

Fractal Image Compression IFS