On the limitations of fractal image texture coding

Fractal-based image coders suuer from perceptually annoying distortion in textured areas. This paper discusses possible reasons for this limitation. A texture may be modelled as a stochastic process with place-independent autocorrelation properties. Two image areas should have similar correlation (spectral) properties to be perceived as belonging to the same texture. We show that stationary textures in the general case do not possess the self-similarity property on which current block-based fractal coding methods are based. A fractal collage approximation of such a texture may possess quite diierent spectral properties than is the case for the texture itself. We derive a formula for the transformed correlation function introduced by the decima-tion in the collage modelling process for the one-dimensional case, and provide coding examples and comparisons to JPEG for practical texture images. Areas with diierent spectral content, elsewhere in the same image, are needed in order to obtain an approximation with the desired spectral properties for a given texture area. The probability for this speciic kind of image nonstationarity to be present may be rather small, which may explain why fractal texture coding often yields perceptually unsatisfying results, even with extensive domain searching.