Image representation based on the affine symmetry group

The representation of 2-D signals which are symmetric under the affine group of transformations is considered. An extension of the multiresolution Fourier transform (MFT) is presented and shown to have a predictable redistribution of energy as a result of affine transformations of the input signal. An approximation based on the discrete MFT then forms the basis of a computationally efficient algorithm for estimating local affine coordinate transformations between pairs of image regions. Results of applying the technique to an image registration problem illustrate its potential