Function Representation with Circle Inversion Map Systems.

The fractals literature develops the now well-known concept of local iterated function systems (using affine maps) with grey-level maps (LIFSM) as an approach to function representation in terms of the associated fixed point of the so-called fractal transform. While originally explored as a method to achieve signal (and 2-D image) compression, more recent work has explored various aspects of signal and image processing using this machinery. In this paper, we develop a similar framework for function representation using circle inversion map systems. Given a circle C with centre õ and radius r, inversion with respect to C transforms the point p to the point p′ such that p and p′ lie on the same radial half-line from õ and d(õ,p)d(õ; p′) = r², where d is Euclidean distance. We demonstrate the results with an example. [ABSTRACT FROM AUTHOR]