Affine transformations, Haar wavelets, and image representation

Joel A. Rosiene

doi:10.1117/12.205386

6 April 1995 Affine transformations, Haar wavelets, and image representation

Joel A. Rosiene

Proceedings Volume 2491, Wavelet Applications II; (1995) https://doi.org/10.1117/12.205386
Event: SPIE's 1995 Symposium on OE/Aerospace Sensing and Dual Use Photonics, 1995, Orlando, FL, United States

Abstract

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(Nlog_aN) 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.

Citation Download Citation

Joel A. Rosiene "Affine transformations, Haar wavelets, and image representation", Proc. SPIE 2491, Wavelet Applications II, (6 April 1995); https://doi.org/10.1117/12.205386

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