Determining and controlling convergence in fractal image coding

Fractal image coding, which has been used successfully for image compression, has previously found applications in other areas of image processing, such as object recognition, segmentation and contour extraction. The parameters of a fractal code determine whether or not it converges to a stable image. Methods have been proposed that predict the convergence of a fractal coding process, but to a significant degree they were dependent on the type of fractal encoding scheme used. In this paper we describe how the factors relating to convergence can be calculated for a general class of codes consisting of affine transformations. We demonstrate how it can be implemented and exploited during encoding. Consequently, this new understanding allows us to calculate and control the two factors that reflect convergence, the contractivity and eventual contractivity factors. The main theorems, and the experiments carried out to illustrate their implementation are presented here.