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As we approach the new millenium, error diffusion is ap- proaching the 25th anniversary of its invention. Because of its ex- ceptionally high image quality, it continues to be a popular choice among digital halftoning algorithms. Over the last 24 years, many attempts have been made to modify and improve the algorithm—to eliminate unwanted textures and to extend it to printing media and color. Some of these modifications have been very successful and are in use today. This paper will review the history of the algorithm and its modifications. Three watershed events in the development of error diffusion will be described, together with the lessons learned along the way. © 1999 SPIE and IS&T. (S1017-9909(99)00104-X)

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.