Abstract
Digital halftoning is a technique to convert a continuoustone image into a binary image consisting of black and white dots. It is an important technique for printing machines and printers to output an image with few intensity levels or colors which looks similar to an input image. The purposes of this paper are to reveal that there are a number of problems related to combinatorial and computational geometry and to present some solutions or clues to those problems.
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References
T. Asano: “Digital Halftoning Algorithm Based on Random Space-Filling Curve,” IEICE Trans. on Fundamentals, Vol.E82-A, No.3, pp.553–556, Medgeh 1999.
T. Asano, K. Obokata, N. Katoh, and T. Tokuyama: “Matrix rounding under the L p-discrepancy measure and its application to digital halftoning,” Proc. ACMSIAM Symposium on Discrete Algorithms, pp.896–904, San Francisco, 2002.
T. Asano, T. Matsui, and T. Tokuyama: “Optimal Roundings of Sequences and Matrices,” Nordic Journal of Computing, Vol.7, No.3, pp.241–256, Fall 2000.
T. Asano and T. Tokuyama: “How to Color a Checkerboard with a Given Distribution — Matrix Rounding Achieving Low 2 X 2-Discrepancy,” Proc. ISAAC01, pp. 636–648, Christchurch, 2001.
T. Asano, D. Ranjan and T. Roos: “Digital halftoning algorithms based on optimization criteria and their experimental evaluation,” IEICE Trans. Fundamentals, Vol. E79-A, No. 4, pp.524–532, April 1996.
B. E. Bayer: “An optimum method for two-level rendition of continuous-tone pictures,” Conference Record, IEEE International Conference on Communications, 1, pp.(26–11)-(26-15), 1973.
B. Chazelle: “The Discrepancy Method: Randomness and Complexity,” Cambridge University Press, 2000.
R. W. Floyd and L. Steinberg: “An adaptive algorithm for spatial gray scale,” SID 75 Digest, Society for Information Display, pp.36–37, 1975.
D. E. Knuth: “Digital halftones by dot diffusion,” ACM Trans. Graphics, 6–4, pp.245–273, 1987.
D. L. Lau and G. R. Arce: “Modern Digital Halftoning,” Marcel Dekker, Inc., New York, 2001.
J. Matoušek: “Geometric Discrepancy,” Springer, 1991. 62
T. Mitsa and K. J. Parker: “Digital halftoning technique using a blue-noise mask,” J. Opt. Soc. Am., A/Vol.9, No.11, pp.1920–1929, 1992.
R. Morelli: “Pick’s theorem and Todd class of a toric variety,” Adv. Math., 100, pp.183–231, 1993.
R. Motwani and P. Raghavan: “Randomized Algorithms,” Cambridge University Press, 1995.
V. Ostromoukhov, R. D. Hersh, and I. Amidror: “Rotated Dispersed Dither: a New Technique for Digital Halftoning,” Proc. of SIGGRAPH’ 94, pp.123–130, 1994.
P. Raghavan and C. D. Thompson: “Randomized rounding,” Combinatorica, 7, pp.365–374, 1987.
R. Ulichney: Digital halftoning, MIT Press, 1987.
R. A. Ulichney: “Dithering with blue noise,” Proc. IEEE, 76, 1, pp.56–79, 1988.
R. Ulichney: “The void-and-cluster method for dither array generation,” IS&T/SPIE Symposium on Electronic Imaging Science and Technology, Proceedings of Conf. Human Vision, Visual Processing and Digital Display IV, (Eds. Allebach, John Wiley), SPIE vol.1913, pp.332–343, 1993.
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Asano, T., Katoh, N., Obokata, K., Tokuyama, T. (2003). Combinatorial and Geometric Problems Related to Digital Halftoning. In: Asano, T., Klette, R., Ronse, C. (eds) Geometry, Morphology, and Computational Imaging. Lecture Notes in Computer Science, vol 2616. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36586-9_4
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DOI: https://doi.org/10.1007/3-540-36586-9_4
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