THE APPLICATION OF IFS [Iterated Function Systems] TO IMAGE ANALYSIS

Following their early success in the utilisation of IFS to describe fractals, Barnsley and Demko mounted an investigation of the applicability of the IFS scheme for the description of arbitrary shapes. Central to the (general) IFS has became what they refer to as the collage theorem: the notion that if a figure can be "lazy tiled" with sufficient accuracy by smaller copies of itself at various orientations (contraction mappings) then the figure can be generated to satisfactory accuracy by the IFS scheme. In a series of recent papers Barnsley, Demko and their co-workers have proposed a method for the description of arbitrary images through an encoding of image segments by means of sets of contraction mappings and associated probabilities, which they term the IFS (Iterated Functions System) description. From an IFS description, each segment can be reconstructed by a stochastic process by applying each mapping at its associated probability. This reconstruction process (image synthesis from IFS parameter description) lends itself to parallel implementation on processor networks, so that the decoding process is computationally tractable. By encoding manually real-world scenes, Barnsley, Demko, et al have shown that compressions from 2000 to 10,000 can be realised with acceptable accuracy. Barnsley and Demko have reported that work is proceeding on the development of an automated system for IFS encoding. With the promised availability of such highly compressed IFS images, the need to examine the practicality and difficulties of the use of IFS encoded images for computer vision and image processing becomes urgent. It is worth noting that one of the motivations that Barnsley and Demko offer for the development of the IFS encoding is that highly compressed images will be more suitable for computer vision. In this paper problems and issues related to the use of IFS encoded images for 2-D recognition purposes are discussed