Threshold modulation and stability in error diffusion

Many modifications to error diffusion have been proposed to improve the algorithm and to extend its application to print media and to color. In this article, we describe some of the lessons that have been learned in two areas of error-diffusion research: threshold modulation and error stability. Both of these areas are important in understanding how to improve and extend the algorithm. Many suggested modifications have been made over the years to eliminate these unwanted textures. One method to improve the algorithm involves different ways of calculating and distributing the errors. Some of the modified algorithms have even proposed amplifying or suppressing the errors. Strange effects can occur, however, when the errors are amplified or if negative components are introduced. The stability analysis presented in this article will illustrate these instabilities and explain their relationship to changes in the error distribution.