Analysis of green noise error diffusion

Unlike blue-noise halftone patterns which are composed of isolated pixels, green noise patterns are composed of pixel-clusters. This makes green noise halftones robust to printer distortions due to the poor isolated pixel reproduction. Levien modified error diffusion by adding a hysteresis filter that feeds a filtered version of the past outputs into the quantizer input in classic error diffusion in order to promote dot-clustering. The patterns produced by the Levien algorithm were analyzed by Lau, Arce and Galagher who coined the term ¿green-noise¿ since the pattern power spectrum was mid-frequency rather than high-frequency (characteristic of ¿blue-noise¿ halftones). However no work has been done to study Leviens algorithm directly in the frequency domain and understand why it works as a green-noise generator. In this paper we will first analyze the Levien green noise error diffusion based on the gain model proposed by Kite et al.. We isolate the noise shaping behavior of the Levien algorithm in the frequency domain and show that it indeed shapes noise into the mid-frequency regions. We then develop two new green noise generators from frequency domain considerations by first by modifying how the error term is computed in conventional error diffusion and then by replacing the error filter in conventional error diffusion by an infinite impulse response (IIR) filter.