A hybrid fractal transform

A generalization of fractal coding of images is presented in which image blocks are represented by mappings derived from least squares approximations using fractal functions. Previously known matching techniques used in fractal transforms are subjects of this generalized method, which is called the Bath fractal transform (BFT). By introducing searching for the best image region for application of the BFT, a hybrid of known methods is achieved. Their fidelity is evaluated by a root-mean-square error measure for a number of polynomial instances of the BFT, over a range of searching levels using a standard test image. It is shown that the fidelity of the fractal transform increases with both search level and order of the polynomial approximation. The method readily extends to data of higher or lower dimensions, including time as an image sequences.<>