Reinstating Floyd-Steinberg: Improved Metrics for Quality Assessment of Error Diffusion Algorithms

  • Sam Hocevar
  • Gary Niger
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5099)


In this contribution we introduce a little-known property of error diffusion halftoning algorithms which we call error diffusion displacement. By accounting for the inherent sub-pixel displacement caused by the error propagation, we correct an important flaw in most metrics used to assess the quality of resulting halftones. We find these metrics to usually highly underestimate the quality of error diffusion in comparison to more modern algorithms such as direct binary search. Using empirical observation, we give a method for creating computationally efficient, image-independent, model-based metrics for this quality assessment. Finally, we use the properties of error diffusion displacement to justify Floyd and Steinberg’s well-known choice of algorithm coefficients.


halftoning error diffusion image quality human visual system color quantization 


  1. 1.
    Bayer, B.: Color imaging array. U.S. patent 3,971,065 (1976)Google Scholar
  2. 2.
    Ulichney, R.A. (Digital Equipment Corporation), Void and cluster apparatus and method for generating dither templates. U.S. patent 5,535,020 (1992)Google Scholar
  3. 3.
    Ancin, H., Bhattacharjya, A., Shu, J. (Seiko Epson Corporation), Void-and-cluster dither-matrix generation for better half-tone uniformity. U.S. patent 6,088,512 (1997)Google Scholar
  4. 4.
    Floyd, R.W., Steinberg, L.: An adaptive algorithm for spatial grey scale. Proceedings of the Society of Information Display 17, 75–77 (1976)Google Scholar
  5. 5.
    Metaxas, P.: Optimal Parallel Error-Diffusion Dithering. In: Color Imaging: Device-Indep. Color, Color Hardcopy, and Graphic Arts IV, Proc. SPIE, vol. 3648, pp. 485–494 (1999)Google Scholar
  6. 6.
    Kite, T.D.: Design and Quality Assessment of Forward and Inverse Error-Diffusion Halftoning Algorithms. PhD thesis, Dept. of ECE, The University of Texas at Austin, Austin, TX (August 1998)Google Scholar
  7. 7.
    Ulichney, R.: Digital Halftoning. MIT Press, Cambridge (1987)Google Scholar
  8. 8.
    Velho, L., Gomes, J.: Digital halftoning with space-filling curves. In: Computer Graphics (Proceedings of SIGGRAPH 1991), vol. 25(4), pp. 81–90 (1991)Google Scholar
  9. 9.
    Nasanen, R.: Visibility of halftone dot textures. IEEE Trans. Syst. Man. Cyb. 14(6), 920–924 (1984)Google Scholar
  10. 10.
    Analoui, M., Allebach, J.P.: Model-based halftoning using direct binary search. In: Proc. of SPIE/IS&T Symp. on Electronic Imaging Science and Tech., San Jose, CA, February 1992, pp. 96–108 (1992)Google Scholar
  11. 11.
    McNamara, A.: Visual Perception in Realistic Image Synthesis. Computer Graphics Forum 20(4), 211–224 (2001)zbMATHCrossRefGoogle Scholar
  12. 12.
    Bhatt, et al.: Direct Binary Search with Adaptive Search and Swap,
  13. 13.
  14. 14.
    Wong, P.W., Allebach, J.P.: Optimum error-diffusion kernel design. In: Proc. SPIE, vol. 3018, pp. 236–242 (1997)Google Scholar
  15. 15.
    Ostromoukhov, V.: A Simple and Efficient Error-Diffusion Algorithm. In: Proceedings of SIGGRAPH 2001, in ACM Computer Graphics, Annual Conference Series, pp. 567–572 (2001)Google Scholar
  16. 16.
    Pappas, T.N., Neuhoff, D.L.: Least-squares model-based halftoning. In: Proc. SPIE, Human Vision, Visual Proc., and Digital Display III, San Jose, CA, February 1992, vol. 1666, pp. 165–176 (1992)Google Scholar
  17. 17.
    Eschbach, R., Fan, Z., Knox, K.T., Marcu, G.: Threshold Modulation and Stability in Error Diffusion. Signal Processing Magazine 20(4), 39–50 (2003)CrossRefGoogle Scholar
  18. 18.
    Sullivan, J., Miller, R., Pios, G.: Image halftoning using a visual model in error diffusion. J. Opt. Soc. Am. A 10, 1714–1724 (1993)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Sam Hocevar
    • 1
  • Gary Niger
    • 2
  1. 1.Laboratoire d’Imagerie Bureautique et de Conception Artistique ParisFrance
  2. 2. Tarzana

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