Progressive decoding method for fractal image compression

Abstract

Fractal image compression is an efficient technique for compactly coding images, in which an image is encoded by a contractive transformation whose fixed point is close to the original image, and then is decoded by using an iteration procedure stemmed from the well known Banach fixed-point theorem. A new fixed-point iteration theorem with a control parameter is presented, which provides a novel iteration procedure that progressively approaches the fixed point of a contractive transformation and particularly reverts back to the conventional iteration procedure when the control parameter is set as one. Based on the new iteration procedure, a progressive decoding algorithm is proposed for fractal image compression, which does not need any specific fractal encoder and is useful for low bandwidth transmission. The experimental results demonstrate that the progressive fractal decoding is capable of controlling the decoding iteration procedure by varying the control parameter values and displaying progressively how the original image is obtained from a black image or another image at each step of the increasing iterations.