A pyramid algorithm for fast fractal image compression

Abstract

We present a fast fractal image encoding algorithm which is based on a refinement of the fractal code from an initial coarse level of the pyramid. The pyramid search algorithm is quasi-optimal in terms of minimizing the mean square error. Assuming that the distribution of the matching error is described by an independent, identically distributed (i.i.d.) Laplacian random process, we derive the threshold sequence for the objective function in each pyramidal level. The computational efficiency depends on the depth of the pyramid and the search step size and could be improved up to two orders of magnitude compared with the full search of the original image.