Abstract: 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 $MUL N image in O(N$+2$/) 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. Performance of the algorithms is evaluated by applying them to both Gabor filters and the first derivative of Gaussian filters. A VLSI architecture for orientational filters using the separable approximation is presented. !4
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