Error Diffusion for Color Halftoning Using Three-Dimensional Neural Interconnects

We have previously developed a two-dimensional monochromatic halftoning with error diffusion neural networks (EDNs). We showed that EDNs find local minima of frequency-weighted error between a binary halftone output and corresponding smoothly varying input, an ideal framework for solving halftone problems. The advantage of the neural algorithm is that all pixel quantization decisions are computed in parallel and therefore the error diffusion process becomes un-directional and symmetric. Thus eliminates the artifacts caused by the traditional error diffusion method. This paper casts color halftoning as four related sub-problems: the first three are to compute good binary halftones for each primary color and the fourth is to simultaneously minimize frequency-weighted error in the luminosity of the composite result. We show that an EDN with a three-dimensional interconnect scheme can solve all four problems in parallel with user-adjustable emphasis on the relative importance of weighted error in luminosity. Our results show that the three-dimensional EDN matrix not only shapes the error to frequencies that human visual system (HVS) is least sensitive but also shapes the error in colors to which the HVS is least sensitive - namely it satisfies the minimum brightness variation criterion.