The Visual Computer

, Volume 30, Issue 10, pp 1145–1156 | Cite as

Structure-aware error-diffusion approach using entropy-constrained threshold modulation

  • Lingyue Liu
  • Wei Chen
  • Wenting ZhengEmail author
  • Weidong Geng
Original Article


Error diffusion is known as a commonly used digital halftoning technique. We present a novel and efficient error-diffusion algorithm which is capable of preserving appreciable structures and tones with blue-noise property. According to the theoretical analysis of threshold modulation, the extraction of the high-frequency image contents is helpful to preserve human vision-sensitive textures. The pixel intensity’s influence on the structural distortion is observed based on a key statistic phenomenon. This effect leads to the non-uniform conservation of diversiform detail contents. To alleviate this influence, an entropy is introduced to measure the intensity’s impact and adaptively constrain the threshold-modulation strength. Compared with the existing edge-enhancement halftoning, our entropy-based method does not suffer from the failure to detect weak edges or improper emphasis of details. On the other hand, this structural improvement enables the modification of error-diffusion coefficients to eliminate visually harmful tonal artifacts, which results in the seamless integration with the best tone-aware techniques (Ostromoukhov in Proceedings of ACM SIGGRAPH, SIGGRAPH ’01, pp 567–572, 2001, Zhou and Fang in ACM Trans Graph (TOG) 22(3):437–444, 2003). Comparisons with the state-of-the-art structure-preserving error diffusions (Chang et al. in ACM Trans Graph (TOG) 28(5): 162:1–162:8, 2009, Li and Mould in Forum 29(2):273–280, 2010) indicate that our methods can achieve better structural similarity with better tone consistency. Our performance is one order of magnitude faster than (Chang et al. in ACM Trans Graph (TOG) 28(5): 162:1–162:8, 2009, Li and Mould in Forum 29(2): 273–280, 2010) while ensuring higher visual quality on typical images. Due to low computational overhead and high halftone quality, the proposed methods in this paper can be widely applicable in many practical applications.


Error diffusion Entropy Threshold modulation MSSIM 


  1. 1.
    Analoui, M., Allebach, J.P.: Model-based halftoning using direct binary search. In: Proceedings of SPIE, vol. 1666, pp. 96–108 (1992)Google Scholar
  2. 2.
    Asano, T.: Digital halftoning algorithm based on random space-filling curve. In: IEEE International Conference on Image Processing, vol. 1, pp. 545–548 (1996)Google Scholar
  3. 3.
    Balian, R.: Entropy, a protean concept. In: Poincaré Seminar 2003, Progress in Mathematical Physics, p. 119 (2004)Google Scholar
  4. 4.
    Bayer, B.E.: An optimum method for two-level rendition of continuous-tone pictures. In: IEEE International Conference on Communications, pp. 26:11–26:15. IEEE, New York (1973)Google Scholar
  5. 5.
    Chang, J., Alain, B., Ostromoukhov, V.: Structure-aware error diffusion. ACM Trans. Graph. (TOG) 28(5), 162:1–162:8 (2009)Google Scholar
  6. 6.
    Eschbach, R., Knox, K.T.: Error-diffusion algorithm with edge enhancement. J. Opt. Soc. Am. A 8(12), 1844–1850 (1991)CrossRefGoogle Scholar
  7. 7.
    Floyd, R.W., Steinberg, L.: An adaptive algorithm for spatial greyscale. Proc. Soc. Inf. Disp. 17(2), 75–77 (1976)Google Scholar
  8. 8.
    Hwang, B.W., Kang, T.H., Lee, T.S.: Improved edge enhanced error diffusion based on first-order gradient shaping filter. In: IEA/AIE, vol. 3029, pp. 473–482 (2004)Google Scholar
  9. 9.
    Kapur, J.N., Sahoo, P.K., Wong, A.K.C.: A new method for gray-level picture thresholding using the entropy of the histogram. Comput. Vis. Graph. Image Process. 29(3), 273–285 (1985)CrossRefGoogle Scholar
  10. 10.
    Khellaf, A., Beghdadi, A., Dupoisot, H.: Entropic contrast enhancement. IEEE Trans. Med. Imaging 10(4), 589–592 (1991)CrossRefGoogle Scholar
  11. 11.
    Knox, K.T., Eschbach, R.: Threshold modulation in error diffusion. J. Electron. Imaging 2(3), 185–192 (1993)CrossRefGoogle Scholar
  12. 12.
    Kwak, N.J., Ryu, S.P., Ahn, J.H.: Edge-enhanced error diffusion halftoning using human visual properties. In: Proceedings of the 2006 International Conference on Hybrid Information Technology, Vol. 01, ICHIT ’06, pp. 499–504 (2006)Google Scholar
  13. 13.
    Lee, H.S., Kong, K.K., Hong, K.S.: Laplacian based structure-aware error diffusion. In: Proceedings of the International Conference on Image Processing, pp. 525–528 (2010)Google Scholar
  14. 14.
    Li, H., Mould, D.: Contrast-aware halftoning. Comput. Graph. Forum 29(2), 273–280 (2010)CrossRefGoogle Scholar
  15. 15.
    Li, X.: Edge-directed error diffusion halftoning. IEEE Signal Process. Lett. 13(11), 688–690 (2006)CrossRefGoogle Scholar
  16. 16.
    Mitsa, T., Parker, K.J.: Digital halftoning technique using a blue-noise mask. J. Opt. Soc. Am. A 9(11), 1920–1929 (1992)CrossRefGoogle Scholar
  17. 17.
    Neuhoff, D.L., Pappas, T.N., Seshadri, N.: One-dimensional least-squares model-based halftoning. Proc. ICASSP 14, 1997 (1997)Google Scholar
  18. 18.
    Ostromoukhov, V.: A simple and efficient error-diffusion algorithm. In: Proceedings of ACM SIGGRAPH, SIGGRAPH ’01, pp. 567–572 (2001)Google Scholar
  19. 19.
    Pang, W.M., Qu, Y., Wong, T.T., Cohen-Or, D., Heng, P.A.: Structure-aware halftoning. ACM Trans. Graph. (TOG) 27(3), 89:1–89:8 (2008)Google Scholar
  20. 20.
    Pun, T.: Entropic thresholding, a new approach. Comput. Graph. Image Process. 16(3), 210–239 (1981)CrossRefGoogle Scholar
  21. 21.
    Ulichney, R.: Digital Halftoning. MIT Press, Cambridge (1987)Google Scholar
  22. 22.
    Ulichney, R.A.: Dithering with blue noise. Proc. IEEE 76, 56–79 (1988)CrossRefGoogle Scholar
  23. 23.
    Velho, L., Gomes, J.d.M.: Digital halftoning with space filling curves. In: Proceedings of ACM SIGGRAPH, SIGGRAPH ’91, pp. 81–90 (1991)Google Scholar
  24. 24.
    Wang, Z., Bovik, A.C., Sheikh, H.R., Simoncelli, E.P.: Image quality assessment: from error visibility to structural similarity. IEEE Trans. Image Process. 13(4), 600–612 (2004)CrossRefGoogle Scholar
  25. 25.
    Zhang, Y., Webber, R.E.: Space diffusion: an improved parallel halftoning technique using space-filling curves. In: Proceedings of ACM SIGGRAPH, SIGGRAPH ’93, pp. 305–312 (1993)Google Scholar
  26. 26.
    Zhou, B., Fang, X.: Improving mid-tone quality of variable-coefficient error diffusion using threshold modulation. ACM Trans. Graph. (TOG) 22(3), 437–444 (2003)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Lingyue Liu
    • 1
  • Wei Chen
    • 1
  • Wenting Zheng
    • 1
    Email author
  • Weidong Geng
    • 1
  1. 1.State Key Lab of CAD&CG, Zhejiang UniversityHangzhouChina

Personalised recommendations