Rate-Distortion Based Fractal Image Compression

In fractal image compression a contractive affine mapping whose fixed point is an approximation to the original image has to be determined. Usually, this mapping is found in a heuristic way. In this paper, we discuss rate-distortion based fractal image coding where the code corresponding to the mapping is optimal in the sense that it guarantees the lowest collage error (distortion between the original image and its first iterate) over a large set of admissible codes subject to a rate constraint. We show how optimal codes can efficiently be obtained. We begin with a fine scale partition of the image which gives a fractal encoding with many bits and a low collage error. The partition is hierarchical, thus, corresponds to a tree. We use a pruning strategy based on the generalized BFOS algorithm where we extract subtrees corresponding to partitions and fractal encodings which are optimal. We give results for fractal image compression with rectangular partitions. We also provide a comparison with heuristic techniques and review other rate-distortion based approaches.