Fractal coding of shapes based on a projected IFS model

Abstract

This paper addresses the problem of approximation of natural complex shapes. Using MPEG-7 terminology, this problem can be considered as the search of a descriptor for a shape feature. This shape can be defined either as a frontier between image regions or a natural curve. For this purpose, an original descriptor which combines iterated function system (IFS) model and the notion of free form curves is proposed. A set of control points allows one to define the IFS model in a barycentric space. This generalization adds a real flexibility to fractal approximation techniques enriching the set of contractive operators which are candidate to model the self-similarity. This new descriptor named projected IFS model allows the reconstruction of a shape using a projection via the control points. It is adapted to the representation of both smooth shapes (man-made objects, body,..) and fractal shapes (mountain, cloud, tree,..). Results on synthetic shapes and a real mountain shape are presented.