Fractal-based image coding with fast decoder convergence

Abstract

In this paper, a new class of fractal image coders is described. As in previously published fractal coding algorithms, the encoder models each image to be coded as an attractor of a simple affine mapping, and finds the parameters in such a mapping by a blockwise image analysis. The image code consists of the parametric description of the mapping, which is selected to provide the best affine fit to the image in the l 2 sense. The decoder uses the parametric description it receives to synthesize the attractor of the mapping through a simple iterative procedure. Although the resulting coders are strongly related to previously published fractal coders, they are modified in a way that gives exact decoder convergence towards the attractor in the lowest possible number of iterations — typically three or less. In contrast to what has been the case with previous fractal coding algorithms, this number of iterations is image independent. The resulting decoder can be implemented in a computationally very efficient pyramid structure. Also, a coder offering non-iterative decoding is included as a special case. The paper describes the modifications of previously known fractal coders that are necessary to obtain the fast convergence. It is shown that the image quality remains unimpaired by these modifications. The computational complexity of the decoding algorithm in the new coder class is analyzed, and an efficient pyramid structure for the decoder is outlined. Finally, a coding example is given.