Orthonormal Fractal Image Encoding Using Overlapping Blocks

Abstract

This paper presents a novel approach to partitioned fractal image encoding. In this we seek to address a number of problems with earlier fractal encodings. These are: the artefacts associated with the block based approaches at high compression ratios; accuracy limitations imposed by the constraint that only one domain block is used to construct each range block; convergence problems which have required that constraints be imposed on the scaling coefficients to ensure that the mapping functions are contractive. These problems are addressed with a technique based on an orthonormal basis expansion using overlapping blocks, where the basis is partly fixed and partly derived from the image in such a way as to take advantage of local interscale self similarity. A fractal image codec based on this technique, which we call the Lapped Orthogonal Fractal Transform (LOFT), is described and tested, and the results are compared to those of other codecs.