Efficient filtering of images using binomial sequences

The authors introduce a class of nonrecursive multidimensional filters for frequency-selective image processing without multiply operations. These binomial filters constitute a family of orthogonal filters. The magnitude responses are narrowband and approximately Gaussian-shaped, with center frequencies that can be positioned to yield low-pass, bandpass, or high-pass filtering. It is shown that the binomial algorithms provide a fast, easily implemented, noise-free family of filters for image processing in the spatial domain. A software implementation of the low-pass and high-pass filtering operators is useful for seismic data. A hardware implementation can be realized with only adders and delay elements. Since no coefficient multipliers are needed, reliability is improved, there are no attendant accuracy or roundoff errors, and a substantial savings in cost is achieved