Radially balanced error diffusion

The paper is concerned with digital halftoning by error diffusion. It discusses error diffusion where the error distribution from a pixel to the next scanline, resulting from the complete processing of the current scanline, approximates a standard Cauchy distribution, having the form (1/π)1/(1+x²). Such error diffusion is capable of generating sparse halftone patterns, which are free of worm artifacts, no matter how sparse the halftone patterns. It is argued that the well spread sparse halftone patterns are due to the remarkable properties of this particular distribution: the distribution is radially balanced, being equal within equiangular radial slices; and further, the distribution maintains this radial balance under self-convolution, spreading in proportion to the degree of self-convolution. Approximating this error distribution is an effective tool for designing error diffusion masks.