Implicit Image Models in Fractal Image Compression

Why does fractal image compression work? What properties must an image have for fractal block coders to work well? What is the implicit image model underlying fractal image compression? The behaviour of fractal block coders is clear for deterministically self-similar structures. We examine the behaviour of these coders on statistically self-similar structures. Specifically, we examine their behaviour for fractional Brownian motion, a simple texture model. Our analysis suggests that the properties necessary for fractal block coders to work well are not so dissimilar from those required by DCT and wavelet transform-based coders. Fractal block coders work well for images consisting of ensembles of locally self-similar regions together with locally stationary regions with decaying power spectra, local statistical similarity, and local isotropy. Our analysis motivates a generalization of fractal block coders that leads to substantial improvements in coding performance and also illuminates some of the fundamental limitations of current fractal compression schemes.