Digital filters with vanishing moments for shape analysis

Abstract: Shape- and scale-selective digital-filters, with steerable finite/infinite impulse responses (FIR/IIRs) and non-recursive/recursive realizations, that are separable in both spatial dimensions and adequately isotropic, are derived. The filters are conveniently designed in the frequency domain via derivative constraints at dc, which guarantees orthogonality and monomial selectivity in the pixel domain (i.e. vanishing moments), unlike more commonly used FIR filters derived from Gaussian functions. A two-stage low-pass/high-pass architecture, for blur/derivative operations, is recommended. Expressions for the coefficients of a low-order IIR blur filter with repeated poles are provided, as a function of scale; discrete Butterworth (IIR), and colored Savitzky-Golay (FIR), blurs are also examined. Parallel software implementations on central processing units (CPUs) and graphics processing units (GPUs), for scale-selective blob-detection in aerial surveillance imagery, are analyzed. It is shown that recursive IIR filters are significantly faster than non-recursive FIR filters when detecting large objects at coarse scales, i.e. using filters with long impulse responses; however, the margin of outperformance decreases as the degree of parallelization increases.