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IFS-based image geometry transform

In this paper, a method of IFS-based image geometry transform is proposed. Suppose the original image can be approximated with the attractor (denoted by A) of an Iterated Function System (IFS) consisting of N contractive mappings of wn (n=1, 2, ..., N), whose coefficients have been determined by fractal encoding. G(A) is used to denote the geometry transform on the attractor A. The result is equivalent to make a corresponding geometry transform on the original image. It is demonstrated in the paper that G(A) is the attractor of a new iterated function system (denoted by IFS') derived from the mappings of wn (n = 1, 2, ...N). In another word, we can modify the coefficients of wn (n=1, ..., N) to construct the IFS', and the result by decoding IFS' is A' = G(A), which is the approximation of the expected geometry transform of the original image. In order to translate, rotate and dilate images in the domain of IFS coefficients, formulas to construct the IFS' from wn are deduced in this paper. The experimental results have validated the proposed method.