IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 9, NO. 5, MAY 2000 923 Digital Color Halftoning with Generalized Error Diffusion and Multichannel Green-Noise Masks Daniel L. Lau, Gonzalo R. Arce, Senior Member, IEEE, and Neal C. Gallagher, Fellow, IEEE Abstract—In this paper, we introduce two novel techniques for digital color halftoning with green-noise—stochastic dither pat- terns generated by homogeneously distributing minority pixel clus- ters. The first technique employs error diffusion with output-de- pendent feedback where, unlike monochrome image halftoning, an interference term is added such that the overlapping of pixels of different colors can be regulated for increased color control. The second technique uses a green-noise mask, a dither array designed to create green-noise halftone patterns, which has been constructed to also regulate the overlapping of different colored pixels. As is the case with monochrome image halftoning, both techniques are tun- able, allowing for large clusters in printers with high dot-gain char- acteristics, and small clusters in printers with low dot-gain charac- teristics. Index Terms—AM, color, dither techniques, FM, green-noise, halftoning. I. INTRODUCTION D IGITAL halftoning is a technique used by binary display devices to create, within the human eye, the illusion of continuous tone. Designed to mimic analog techniques, dot-clustered ordered dithering or amplitude modulated (AM) halftoning produces this illusion by varying the size of round printed dots which are arranged along an ordered grid. When using AM halftoning, the parameters of particular importance are the lines-per-inch (lpi) or the number of rows/columns of the regular grid 1 and the screen angle or the orientation of the regular grid relative to the horizontal axis. Typically, monochrome screens have an angle of as the human visual system is least sensitive to diagonal artifacts [1]. In color printers, the illusion of continuous shades of color is produced by superimposing the binary halftones of cyan, ma- genta, yellow, and black (CMYK) inks. As the dots of an AM halftone form a regular grid, clustered-dot dithering suffers from moiré—the secondary interference patterns created by superim- posing two or more regular patterns. In order to minimize the appearance of moiré, the screens of cyan, magenta, yellow, and black are typically oriented at the angles of , , , and to create a pleasant rosette pattern. Manuscript received February 5, 1999; revised September 17, 1999. This re- search was supported in part by the National Science Foundation under Grant CDA-9703088 and by Lexmark International. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Jan P. Allebach. The authors are with the Department of Electrical and Computer Engineering, University of Delaware, Newark, DE 19716 USA (e-mail: lau@ece.udel.edu; arce@ece.udel.edu; gallaghe@ece.udel.edu). Publisher Item Identifier S 1057-7149(00)03564-8. 1 The highest quality AM halftones will have 150 lpi or more. The problems of moiré and screen angles are avoided in frequency modulated halftoning where continuous tone is produced by varying the distance between printed dots and not varying the size. Typically, FM halftones are produced by the process of error diffusion which creates a stochastic arrangement of dots. Besides avoiding moiré, FM halftoning, by isolating minority pixels, maximizes the spatial resolution of the printed image relative to the printer [2], but this distri- bution also maximizes the perimeter-to-area ratio of printed dots [3]—making FM halftones more susceptible to printer distortions such as dot-gain, the increase in size of a printed dot. Whether a function of the printing process (mechanical dot-gain) or of the optical properties of the paper (optical dot-gain), dot-gain causes the printed halftone to appear darker than the original ratio of white-to-black pixels [4]. In printers with high dot-gain characteristics, AM halftoning, with its lower spatial resolution and moiré, may be the preferred tech- nique, as its clustered-dots have the lower perimeter-to-area ratio. An alternative to AM and FM halftoning, Levien’s [5] error diffusion with output-dependent feedback is an AM-FM hybrid which creates the illusion of continuous tone by producing a sto- chastic patterning of dot clusters which vary in both their size and in their separation distance. The major advantage, of this new technique over prior error diffusion schemes, is that by ad- justing a single parameter, the output is tunable—capable of cre- ating halftones with large clusters in printers with high dot-gain characteristics and small clusters in printers with low dot-gain characteristics. Error diffusion with output-dependent feedback, therefore, can trade halftone visibility for printer robustness. Studied by Lau et al. [2], Levien’s technique creates patterns described in terms of their spectral content as green-noise—con- taining no low or high frequency spectral components. This green-noise model is presented in accordance with Ulichney’s [6] blue-noise model which describes the spectral characteris- tics of the ideal error-diffused halftone patterns as having no low-frequency content. Furthermore, as Mitsa and Parker [7] used the spectral characteristics of blue-noise to generate the blue-noise mask, a binary dither array which greatly reduces the computational complexity associated with FM halftoning, Lau et al. [8], using the spatial and spectral characteristics of green-noise, have introduced the green-noise mask. The problem yet to be addressed in the evolution of green- noise halftoning is its application to color. FM halftoning has been studied in great detail with respect to color printing. The techniques introduced range from simply halftoning each color independently to more complex model-based techniques which transform the CMYK color space to alternate spaces such as the 1057–7149/00$10.00 © 2000 IEEE