A FRACTAL APPROXIMATION OF CURVES

Abstract

This paper deals with the approximation of rough curves using a fractal model. The approximation criterion is based on a curve parametrization and the fractal model is a projected iterated function system (IFS) model. This model unifies the IFS model and a classical model used in computer graphics (free form representation with control points). To formulate the approximation problem, we introduce a family of curves based on our model. Then, the approximation problem has a nonlinear fitting formulation. We have tested this fractal approximation method on both smooth and rough synthetic curves. A shape extracted from a natural scene has also been approximated. The obtained results are very satisfying from both quantitative and visual point of view.