Enhanced fractal image coding by combining IFS and VQ

Since the landmark paper in 1992 by A. Jacquin [1] on image coding with iterated function systems (IFS), many authors have studied IFS (or "fractal") and proposed many improvements to Jacquin’s algorithm [2]. While IFS has been viewed as a promising technique that might overtake more established coding methods, generally it has not so far lived up to these expectations. One fundamental problem of IFS coding methods is the lack of direct control over the reconstruction error (between original and decoded images) since the encoder attempts only to minimize the collage error (between the original and the self-similar transformation of the original generated in the encoder). Although the well-known Collage Theorem gives an upper bound on the reconstruction error as a function of the collage error, minimizing collage error does not minimize the reconstruction error. In practice, the reconstruction error is larger and often much larger than the collage error. This paper introduces a technique based on vector quantization (VQ) to reduce the collage error in such a way that the difference between the collage and reconstruction errors will also be substantially reduced. This is done in a selective manner without significantly increasing the bit rate.