A method of fractal coding for measure-valued images

Fractal image coding generally seeks to express an image as a union of spatially contracted and greyscale modified copies of subsets of itself. Generally, images are represented as functions u(x) and the fractal coding method is conducted in the framework of L2 or L1. Here we formulate a method of fractal image coding on measure-valued images: At each point x, u(x) is a probability measure over the range of allowed greyscale values. It is natural to consider the possibility of more than one domain subblock mapping onto a given range block Rj. We consider in particular the case in which all subblocks from a common domain pool D can contribute to the image supported on each range block. Using an appropriate weighting of these subblocks, in invariant measure that reflects the local self-similarity properties of the image can be constructed.