Fractal Methods for Greyscale Image Data Compression

Abstract: In this thesis fractal methods for image coding of still images are discussed. A specific class of encoding algorithms is introduced, where the algorithms are based on dividing image data into two components. One component is the part of the data which can be represented by a parametric model. The other component, the remaining part of the data, is the residual, or the difference between the original data and the data represented by the model. The model data is represented by its model parameters, and the residual is approximated by using a simplified fractal technique.Two examples of model-residual algorithms are proposed, differing only by the model used.A model-residual algorithm defines a contractive transformation, which is used as the representation of the original image. Decoding is done by finding the fixed point, the invariant image, of the transformation. A numerical method for calculating the contractivity properties of the transformation is presented.The output code from model-residual algorithms is shown to be robust to transmission over noisy channels.