The mathematics of halftoning

This paper describes some mathematical aspects of halftoning in digital printing. Halftoning is the technique of rendering a continuous range of colors using only a few discrete ones. There are two major classes of methods: dithering and error diffusion. Some discussion is presented concerning the method of dithering, but the main emphasis is on error diffusion.

[1]  Kevin J. Parker,et al.  Modified approach to the construction of a blue noise mask , 1994, J. Electronic Imaging.

[2]  Risto Näsänen Visibility of halftone dot textures , 1984, IEEE Trans. Syst. Man Cybern..

[3]  R. E. Miller,et al.  Image halftoning using a visual model in error diffusion , 1993 .

[4]  Zhigang Fan,et al.  Error diffusion with a more symmetric error distribution , 1994, Electronic Imaging.

[5]  H. G Meijer On a distribution problem in finite sets , 1973 .

[6]  Robert Ulichney,et al.  Void-and-cluster method for dither array generation , 1993, Electronic Imaging.

[7]  Chai Wah Wu,et al.  Error bounds for error diffusion and related digital halftoning algorithms , 2001, ISCAS 2001. The 2001 IEEE International Symposium on Circuits and Systems (Cat. No.01CH37196).

[8]  Robert Tijdeman On a Distribution Problem in Finite and Countable Sets , 1973, J. Comb. Theory, Ser. A.

[9]  Robert Ulichney,et al.  Digital Halftoning , 1987 .

[10]  Luiz Velho,et al.  Digital halftoning with space filling curves , 1991, SIGGRAPH.

[11]  Isaac Amidror,et al.  The Theory of the Moiré Phenomenon , 2000, Computational Imaging and Vision.

[12]  Charles Tresser,et al.  A decoding problem in dynamics and in number theory. , 1992, Chaos.

[13]  John F. Jarvis,et al.  A survey of techniques for the display of continuous tone pictures on bilevel displays , 1976 .

[14]  Chai Wah Wu,et al.  Error bounds for error diffusion and other mathematical problems arising in digital halftoning , 1999, Electronic Imaging.

[15]  G. A. Hedlund,et al.  Unending chess, symbolic dynamics and a problem in semigroups , 1944 .

[16]  Joan L. Mitchell,et al.  Multilevel Color Halftoning , 2001, Color Imaging Conference.

[17]  K. F. Roth On irregularities of distribution , 1954 .

[18]  Harald Niederreiter,et al.  On the Existence of Uniformly Distributed Sequences in Compact Spaces , 1972 .

[19]  Robert Tijdeman The chairman assignment problem , 1980, Discret. Math..

[20]  David L. Neuhoff,et al.  Printer models and error diffusion , 1995, IEEE Trans. Image Process..

[21]  Harold Marston Morse Recurrent geodesics on a surface of negative curvature , 1921 .

[22]  J. Beck,et al.  Irregularities of distribution , 1987 .

[23]  Robert Ulichney,et al.  Dithering with blue noise , 1988, Proc. IEEE.

[24]  Henry R. Kang Color Technology for Electronic Imaging Devices , 1997 .

[25]  Rodney L. Miller,et al.  Design of minimum visual modulation halftone patterns , 1991, IEEE Trans. Syst. Man Cybern..

[26]  G. A. Hedlund,et al.  Symbolic Dynamics II. Sturmian Trajectories , 1940 .

[27]  Keith T. Knox Error diffusion: a theoretical view , 1993, Electronic Imaging.

[28]  Gunther Wyszecki,et al.  Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd Edition , 2000 .