Convergence of fractal encoded images

Abstract

Fractal image compression, despite its great potential, suffers from some flaws that may prevent its adaptation from becoming more widespread. One such problem is the difficulty of guaranteeing convergence, let alone a specific error tolerance. To help surmount this problem, we have introduced the terms compound, cycle, and partial contractivity concepts indispensable for understanding convergence of fractal images. Most important, they connect the behavior of individual pixels to the image as a whole, and relate such behavior to the component affine transforms.