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A New Halftoning Method Based on Error Diffusion with Rough Set Filtering

  • Huanglin Zeng
  • R. Swiniarski
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 19)

Abstract

A new technique is proposed for converting a continuous tone image into a halftone image using the combined error diffusion with rough set (Pawlak, 1991; Skowron, Stepaniuk, 1994; Polkowski, Skowron, Zytkow, 1995; Swiniarski, 1993; Lin, 1997) filtering. The rough set filtering uses the concepts of tolerance relation and (Skowron, Stepaniuk, 1994, 1996; Polkowski, Skowron, Zytkow, 1995) and approximation spaces to define a tolerance class of neighboring pixels in a processing mask, then utilizes the statistical mean of the tolerance classes to replace the gray levels of the central pixel in a processing mask. The error diffusion uses the correction factor which is composed with the weighted errors for pixels (prior to addition of the pixel to be processed to diffuse error over the neighboring pixels in a continuous tone image). A system implementation as well as an algorithm of halftoning on error diffusion with rough sets are introduced in the paper. A specific example of halftoning is conducted to evaluate the efficient performances of the new halftoning system proposed in comparison with that of an adaptive error diffusion strategy.

Keywords

Gray Level Neighboring Pixel Central Pixel Approximation Space Halftone Image 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Javvis, J. F., et al. (1976a). “A new technique for displaying continuous tone images on a bilevel display”, IEEE Trans on Comm., Vol. Com-24, 891–89.Google Scholar
  2. 2.
    Javvis, J. F. et al. (1976b). “A survey of techniques for the display of continuous tone images on a bilevel display”, Comput. Graphics, Image Processing, Vol. 5, 13–40.Google Scholar
  3. 3.
    Mohamed, S. A. (1995). “Binary image compression using efficient partitioning into rectangular regions”, IEEE Trans on Comm. Vol. 43, 1888–1893.Google Scholar
  4. 4.
    Lin, T. Y. (1997). “Neighborhood systems–information granulation”. In: P.P. Wang (ed.), Joint Conference of Information Sciences, March 1–5, Duke University, Vol. 3 (1997) 161–164Google Scholar
  5. 5.
    Ochi, H.et al., (1987). “A new halftone reproduction and transmission method using standard black and white facsimile code, IEEE Trans on Comm., Vol. COM35, 466–470.Google Scholar
  6. 6.
    Pawlak, Z. (1991). Rough Sets. Kluwer Academic Publishers.Google Scholar
  7. 7.
    Polkowski, L., Skowron, A., and Zytkow, J., (1995), “Tolerance based rough sets”, in: T.Y. Lin and A. Wildberger (eds.), Soft Computing: Rough Sets, Fuzzy Logic Neural Networks, Uncertainty Management, Knowledge Discovery, Simulation Councils, Inc. San Diego CA, 55–58.Google Scholar
  8. 8.
    Shu, J. (1995). “Adaptive Filtering for Error Diffusion Quality Improvement”, SID’95 DIGEST, 833–836.Google Scholar
  9. 9.
    Skowron, A., and Stepaniuk, J., (1994), “Generalized approximation spaces”, in: T.Y. Lin and A.M. Wildberger (eds.), The Third International Workshop on Rough Sets and Soft Computing Proceeding (RSSC’94), San Jose State University, San Jose, California, USA, November 1–12, 156–163.Google Scholar
  10. 10.
    Skowron, A., and Stepaniuk, J., (1996), “Tolerance approximation spaces”, Fundamenta Informaticae, 27, 245–253.Google Scholar
  11. 11.
    Skowron, A., (1994), “Data filtration: a rough set approach”, in: W. Ziarko (ed.), Rough Sets, Fuzzy Sets and Knowledge Discovery, Workshops in Computing, Springer-Verlag Si British Computer Society, London, Berlin, 18–118.Google Scholar
  12. 12.
    Skowron, A., (1995), “Synthesis of adaptive decision systems from experimental data”, in: A. Aamadt and J. Komorowski (eds.), Proc. of the Fifth Scandinavian Conference on Artificial Intelligence SCAI-95, Fundamenta Informaticae, Amsterdam, 220–238.Google Scholar
  13. 13.
    Stevenson R. L., and G. R. Arce. (1985). “Binary display of hexagonally sampled continuous tone images”, J. Opt. Soc. Am. A. Vol. 2, 1009–1013.Google Scholar
  14. 14.
    P. Stuck, P. et al. (1981). “A multiple error correcting computation algorithm for bilevel image hardcopy reproduction”, RZ1060, IBM Research Lab. Switzerland.Google Scholar
  15. 15.
    Swiniarski, R. (1993). Introduction to Rough Sets“. Materials of The International Short Course Neural Networks. Fuzzy and Rough Systems.”Google Scholar
  16. 16.
    Tentush, I., (1995), “On minimal absorbent sets for some types of tolerance relations”, Bull. Polish Acad. Sci. Tech., 43 /1, 79–88.Google Scholar
  17. 17.
    Ulichney,R. (1987). Digital halftoning, MIT Press, Cambridge.Google Scholar
  18. 18.
    Ullman, J. R. (1974). Binarization using associative addressing, Pattern Recognition, Soc. Vol. 6.Google Scholar
  19. 19.
    Vakarelov, D., (1991a), “Logical approach of positive and negative similarity relations in property systems”, Processing of the First World Conference on the Fundamentals of AI, WOCFAI’g1, Paris, July 1–5Google Scholar
  20. 20.
    Weszka, J. S. (1978). “A survey of threshold selection techniques”, Comput. Graphics, Image Processing, Vol.7, PP. 259–265, 1978.CrossRefGoogle Scholar
  21. 21.
    Yao, Y.Y., (1997), “Binary relation based neighborhood operators”, in: P.P. Wang (ed.), Joint Conference of Information Sciences, March 1–5, Duke University, Vol. 3, 169–172.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Huanglin Zeng
    • 1
  • R. Swiniarski
    • 2
  1. 1.Sichuan Institute of Light Industry and Chemical TechnologyP.R. China
  2. 2.Department of Mathematical and Computer SciencesSan Diego State UniversitySan DiegoUSA

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