Reducing frequency-domain artifacts of binary image due to coarse sampling by repeated interpolation and smoothing of Radon projections

Abstract

We develop a method to calculate 2D spectrum of a binary image with better quality than that obtained via direct 2D-FFT. With FFT, jagged edges of objects due to coarse sampling introduce artifacts into the frequency domain, especially in the high-frequency area. With the proposed method, Radon projections of the binary image along lines at different viewing angles are calculated. Each projection is extended by interpolation, then smoothed and decimated. The interpolation–smoothing–decimation operation is repeated several times to reduce ruggedness and improve quality of the Radon projections considerably. One-dimensional FFT of each refined Radon projection is calculated, resulting in a set of frequency-domain samples distributed on a polar coordinate system. These samples are interpolated onto a Cartesian grid to give the required 2D spectrum of the sampled binary image. Numerical computations on several objects show that the method can provide significant improvement to the spectrum as compared with direct 2D-FFT.