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Alexandru Bogdan. Multiscale Fractal Image Coding and the Two-scale Difference Equation. CU/CTR Technical Report 358-94-05 Columbia University, 1994.

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Decoding a fractal compressed image can be seen as solving an affine two-scale functional equation. If the affine term is zero, the dilation equation becomes linear and the solution is similar to the scaling functions from wavelet theory. In both cases a linear operator, parameterized with a few variables, determines a complicate looking function. We present two classes of algorithms for gray image coding, based on the solutions of the affine and of the linear equation. The affine algorithm is used to build a multiscale pyramid coding scheme. It has been applied to the coding of gray images and also to color image compression and interframe video coding

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   Author = {Bogdan, Alexandru},
   Title = {Multiscale Fractal Image Coding and the Two-scale Difference Equation},
   Institution = {Columbia University},
   Year = {1994}

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