INVERSE AND APPROXIMATION PROBLEM FOR 2-DIMENSIONAL FRACTAL SETS

The geometry of fractals is rich enough that they have extensively bee n used to model natural phenomena and images, Iterated function system s (IFS) theory provides a convenient way to describe and classify dete rministic fractals in the form of a recursive definition. As a result, it is conceivable to develop image representation schemes based on th e IFS parameters that correspond to a given fractal image, In this pap er, we consider two distinct problems: an inverse problem and an appro ximation problem. The inverse problem involves finding the IFS paramet ers of a signal that is exactly generated via an IFS. We make use of t he wavelet transform and of the image moments to solve the inverse pro blem. The approximation problem involves finding a fractal IFS-generat ed image whose moments match, either exactly or in a mean squared erro r sense, a range of moments of the original image, The approximating m easures are generated by an IFS model of a special form and provide a general basis for the approximation of arbitrary images. Experimental results verifying our approach will be presented.