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.
A three-dimensional (3-D) spatiotemporal prediction-error filter (PEF) is used to enhance foreground/background contrast in (real and simulated) sensor image sequences. Relative velocity is utilized to extract point targets that would otherwise be indistinguishable with spatial frequency alone. An optical-flow field is generated using local estimates of the 3-D autocorrelation function via the application of the fast Fourier transform (FFT) and inverse FFT. Velocity estimates are then used to tune in a background-whitening PEF that is matched to the motion and texture of the local background. Finite impulse response (FIR) filters are designed and implemented in the frequency domain. An analytical expression for the frequency response of velocity-tuned FIR filters, of odd or even dimension with an arbitrary delay in each dimension, is derived.