Design and implementation of orientational filters using separable approximation methods

Two separable approximation methods, Chebyshev approximation and SVD approximation, are described as ways of implementing an orientational filtering operation on a 2D image. They are both suitable for parallel implementation and enable the orientational filter to be performed on an N×N image in O(N²) time with a small amount of hardware. It is shown that these algorithms can be combined with Shensa´s algorithm so that a multi-resolution pyramid can be efficiently constructed from orientational filter wavelets. The performance of the algorithms are evaluated by applying the algorithms to both Gabor filters and the first derivative of Gaussian filters. Implementation schemes for orientational filters using the separable approximation are presented