Proceedings PaperAffine transformations, Haar wavelets, and image representation
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An image representation based on a generalization of quad trees, related to the definition of Haar wavelets and the resulting multi-resolution decomposition of L2(Rn) is presented. The basic Haar theory is presented, and then generalized to the case of multiple dilation matrices, allowing for the definition of (almost) arbitrary tilings. The image representation is translation invariant with a computational complexity of O(NlogaN) where a is determined by the mixing of the individual dilation matrices. The technique has been applied to the unsupervised clustering of magnetic resonance imagery and is being studied for the lossless coding of imagery.