Hierarchical Interpretation of Fractal Image Coding and Its Applications

Many interesting features associated with iterated function systems and standard fractals seem to fade away as the fractal coding of images evolves. For example, the property of self- similarity at different resolutions, inherent to fractals, does not show up in a simple form in the image coding problem. In this chapter we will demonstrate a hierarchical model for the fractal encoding of images, and we will use it to show that the properties of self-similarity at different resolutions, and the related notion of fractal dimension, exist in fractal coding of images. Moreover, applications of these properties will be given.