Threshold modulation in error diffusion

A theoretical analysis of threshold modulation in error diffusion is given. It is shown that spatial modulation of the threshold is mathematically identical to processing an equivalent input image with the standard error diffusion algorithm. The equivalent input is the sum of the original image with a high-pass-filtered version of the threshold spatial modulation. The filter is a function only of the weights used to distribute the errors. This result can be used to explain the several published observed effects of threshold modulation, such as edge enhancement and the effects of adding noise to the threshold.