Approximation of natural objects (curves, surfaces, or images) with fractal models is an important center of interest for research. The general inverse problem paradigm concerns many application fields and a large variety of studies have been proposed to address it. The most known of them is the fractal image compression method introduced by Jacquin. Generally speaking, these techniques lack of flexibility in term of control over the approximated shape. Furthermore, iteration space used is the visualisation space, R². Previous work achieved a general framework for fractal modeling: fractal free forms. This model allows user to define self-similar objects in a space of a higher dimension. We propose a resolution of the inverse problem based on this model and a non-linear regression algorithm. A hierachical extension of this model is introduced for modeling heterogeneous objects, for which characteristics are varying in space. A complete coding scheme has been performed on such a model showing good performances for low bitrate compression.