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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
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.
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.
Mohamed, S. A. (1995). “Binary image compression using efficient partitioning into rectangular regions”, IEEE Trans on Comm. Vol. 43, 1888–1893.
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) 161–164
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.
Pawlak, Z. (1991). Rough Sets. Kluwer Academic Publishers.
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.
Shu, J. (1995). “Adaptive Filtering for Error Diffusion Quality Improvement”, SID’95 DIGEST, 833–836.
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.
Skowron, A., and Stepaniuk, J., (1996), “Tolerance approximation spaces”, Fundamenta Informaticae, 27, 245–253.
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.
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.
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.
P. Stuck, P. et al. (1981). “A multiple error correcting computation algorithm for bilevel image hardcopy reproduction”, RZ1060, IBM Research Lab. Switzerland.
Swiniarski, R. (1993). Introduction to Rough Sets“. Materials of The International Short Course Neural Networks. Fuzzy and Rough Systems.”
Tentush, I., (1995), “On minimal absorbent sets for some types of tolerance relations”, Bull. Polish Acad. Sci. Tech., 43 /1, 79–88.
Ulichney,R. (1987). Digital halftoning, MIT Press, Cambridge.
Ullman, J. R. (1974). Binarization using associative addressing, Pattern Recognition, Soc. Vol. 6.
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 1–5
Weszka, J. S. (1978). “A survey of threshold selection techniques”, Comput. Graphics, Image Processing, Vol.7, PP. 259–265, 1978.
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.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Zeng, H., Swiniarski, R. (1998). A New Halftoning Method Based on Error Diffusion with Rough Set Filtering. In: Polkowski, L., Skowron, A. (eds) Rough Sets in Knowledge Discovery 2. Studies in Fuzziness and Soft Computing, vol 19. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1883-3_18
Download citation
DOI: https://doi.org/10.1007/978-3-7908-1883-3_18
Publisher Name: Physica, Heidelberg
Print ISBN: 978-3-7908-2459-9
Online ISBN: 978-3-7908-1883-3
eBook Packages: Springer Book Archive