Symmetry and wavelet transforms for image data compression

This paper describes work in the application of wavelet transforms to the data compression of both still images and image sequences. The main principle underlying the work is the representation of the natural symmetries of image data, which form a subgroup of the 2-d affine group, itself an approximation in 2-d of the motions resulting from perspective projection of the rigid motions in 3-d. It will be shown how the use of a suitable wavelet transform can simplify the representation of these motions, to good effect in two data compression applications. The first is a recasting of fractal compression into a more conventional predictive framework, using an orthonormal wavelet basis. The second makes use of an overcomplete wavelet transform in estimating motions for video coding.