Modeling and quality assessment of halftoning by error diffusion

Digital halftoning quantizes a graylevel image to one bit per pixel. Halftoning by error diffusion reduces local quantization error by filtering the quantization error in a feedback loop. In this paper, we linearize error diffusion algorithms by modeling the quantizer as a linear gain plus additive noise. We confirm the accuracy of the linear model in three independent ways. Using the linear model, we quantify the two primary effects of error diffusion: edge sharpening and noise shaping. For each effect, we develop an objective measure of its impact on the subjective quality of the halftone. Edge sharpening is proportional to the linear gain, and we give a formula to estimate the gain from a given error filter. In quantifying the noise, we modify the input image to compensate for the sharpening distortion and apply a perceptually weighted signal-to-noise ratio to the residual of the halftone and modified input image. We compute the correlation between the residual and the original image to show when the residual can be considered signal independent. We also compute a tonality measure similar to total harmonic distortion. We use the proposed measures for edge sharpening, noise shaping, and tonality to evaluate the quality of error diffusion algorithms.