Optimal digital design of steerable differentiators with the flatness of polynomial filters and the isotropy of Gaussian filters

Hugh L. Kennedy

doi:10.1117/1.JEI.27.5.051219

12 May 2018 Optimal digital design of steerable differentiators with the flatness of polynomial filters and the isotropy of Gaussian filters

Hugh L. Kennedy

Author Affiliations +

Journal of Electronic Imaging, Vol. 27, Issue 5, 051219 (May 2018). https://doi.org/10.1117/1.JEI.27.5.051219

Abstract

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.

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Hugh L. Kennedy "Optimal digital design of steerable differentiators with the flatness of polynomial filters and the isotropy of Gaussian filters," Journal of Electronic Imaging 27(5), 051219 (12 May 2018). https://doi.org/10.1117/1.JEI.27.5.051219

Received: 20 October 2017; Accepted: 11 April 2018; Published: 12 May 2018

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