Optimal digital design of steerable differentiators with the flatness of polynomial filters and the isotropy of Gaussian filters
Hugh L. Kennedy · Journal of Electronic Imaging · 2018
Digital filters with separable realizations and steerable responses are ideal for processing multidimensional signals, e.g., two-dimensional (2-D) images, in high-throughput sensor systems. Banks of band-pass differentiators with perfectly shaped frequency responses at the dc limit, for impulse responses with vanishing moments—e.g., Savitzky–Golay, Butterworth derivatives, and other maximally flat filters—are appealing because they support a bivariate polynomial interpretation (in Cartesian coordinates) of the input signal; however, for nonpolynomial inputs, the behavior of these directional filters changes with steering angle (i.e., they are anisotropic). Filter banks designed from Gaussian derivatives have almost perfect isotropy; however, they have nonvanishing moments. A procedure for the design of highly isotropic separable filters with steerable responses, vanishing moments, and configurable scale is described in this paper. It may be used to develop both finite-impulse response and low-complexity infinite-impulse response designs with linear-phase noncasual realizations.