Fractal Image Compression Using Modified Operator (IFS)

Abstract

Image data Compression based on fractal theory is fundamentally dierent from conventional compression methods, its idea is to generate a contraction operator whose fixed point approximates the original image in a complete metric space of images. The specication of such operator can be stored as the fractal code for the original image. The contraction mapping principle implies that the iteration of the stored operator starting from arbitrary initial image will recover its xed point which is an approximation for the original image. This Contraction mapping is usually constructed using the partitioned IFS(PIFS) technique which relies on the assertion that parts of the image resemble other parts of the same image. It then, nds the fractal code for each part by searching for another larger similar part. This high costly search makes fractal image compression dicult to be implemented in practice, even it has the advantages of a high compression ratio, a low loss ratio, and the resolution independence of the compression rate. In this paper, we investigate fractal image compression(FIC) using Iterated Function Systems(IFS). After reviewing the standard scheme, we state a mathematical formulation for the practical aspect. We then propose a modied IFS that relies on the fact  that, there are very smooth parts in certain images. From the view point of mathematics, we present the modied operator, proving its properties that make it not only a fractal operator but also more eective than the standard one. The experimental results are presented and the performance of the proposed algorithm is discussed.