Patent US 7,664,339

Provided is a method for digital image representation based upon Discrete Projective Fourier Transform (DPFT) constructed in the noncompact (DNPFT) and compact (DCPFT) realizations of geometric Fourier analysis on SL(2,C) groups. Novel characteristics are that the model is well adapted to perspective image transformations and well adapted to the retinotopic (conformal) mapping of the biological visual system. To compute the DPFT of a digital image by Fast Fourier transform (FFT), an image is re-sampled with a non-uniform log-polar sampling geometry. A “deconformalization” procedure corrects the “conformal lens optics” of the conformal camera to render image perspective transformations. DNPFT computes the convolution in the noncompact realization defined over 2-dimensional rotations in the image plane and dilations while the DCPFT computes the convolution in the compact realization (which is defines over all 3-dimensional rotations) and therefore provides basis for developing projectively invariant under all rotations object matching.