Modeling and quality assessment of halftoning by error diffusion

Digital halftoning quantizes a graylevel image to one bit per pixel, Halfto ning by error diffusion reduces local quantization error by filtering the q uantization error in a feedback loop. In this paper, we linearize error dif fusion algorithms by modeling the quantizer as a linear gain plus additive noise. We confirm the accuracy of the linear model in three independent way s. Using the linear model, we quantify the two primary effects of error dif fusion: edge sharpening and noise shaping. For each effect, we develop an o bjective measure of its impact on the subjective quality of the halftone. E dge 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 appl y a perceptually weighted signal-to-noise ratio to the residual of the half tone and modified input image. We compute the correlation between the resid ual and the original image to show when the residual can be considered sign al independent. We also compute a tonality measure similar to total harmoni c distortion, We use the proposed measures for edge sharpening, noise shapi ng, and tonality to evaluate the quality of error diffusion algorithms.