Incorporating Orientation Selectivity in Wavelet Transforms: For Multi--Resolution Fourier Analysis of Images

The problem of incorporating orientation selectivity into transforms which provide local frequency representation of image regions over a range of spatial scales is investigated. It is shown that this can be achieved if the local spectra are defined on a log-polar coordinate lattice and that by appropriate choice of window functions, the spectra can be designed to be steerable in arbitrary orientations. In addition, the resulting class of transforms can be defined to be invertible, be based on window functions having good localization in both the spatial and spatial frequency domains, and be efficiently implemented using FFT techniques. Results of using one such transform for linear feature extraction demonstrate its effectiveness when dealing with oriented features