Variations on error diffusion: Retrospectives and future trends

Grayscale error diffusion introduces nonlinear distortion (directional artifacts and false textures), linear distortion (sharpening), and additive noise. Since error diffusion is 2-D sigma-delta modulation (Anastassiou, 1989), Kite et al. linearize error diffusion by replacing the thresholding quantizer with a scalar gain plus additive noise. Sharpening is proportional to the scalar gain. Kite et al derive the sharpness control parameter value in threshold modulation (Eschbach and Knox, 1991) to compensate linear distortion. These unsharpened halftones are particularly useful in perceptually weighted SNR measures. False textures at mid-gray (Fan and Eschbach, 1994) are due to limit cycles, which can be broken up by using a deterministic bit flipping quantizer (Damera-Venkata and Evans, 2001). We review other variations on grayscale error diffusion to reduce false textures in shadow and highlight regions, including green noise halftoning (Levien, 1993) and tone-dependent error diffusion (Li and Allebach, 2002). We then discuss color error diffusion in several forms: color plane separable (Kolpatzik and Bouman, 1992); vector quantization (Shaked et al. 1996); green noise extensions (Lau et al. 2000); and matrix-valued error filters (Damera-Venkata and Evans, 2001). We conclude with open research problems.