A fractal based approach to image compression

We introduce a new approach to the issue of lossy data compression. The basic concept has been inspired by the theory of fractal geometry. The idea is to traverse the entire data string utilizing a fixed length "yardstick". The coding is achieved by transmitting, only, the sign bit (to distinguish between the ascent and the descent) and the horizontal distance covered by the "yardstick". All data values are estimated, at the receiver's site, based on this information. We have applied this approach in the context of image compression, and the preliminary results seem to be very promising. Indeed, the proposed approach is very simple (both conceptually and from the point of view computational complexity), and it seems to be well suited to the psycho-visual characteristics of human eye. The paper includes a brief description of the coding concept. Next a number of possible modifications and extensions are discussed. Finally a number of simulations are included in order to support the theoretical derivations. Good quality images are achieved with as low as .5 bit/pel.