Abstract

Screening is an efficient halftoning algorithm that is easy to implement. With multilevel devices, there is a potential to improve the overall image quality by using multilevel screening, which allows us to choose among multiple native tones at each addressable pixel. We propose a methodology for multilevel screen design using direct binary search (DBS). We refer to one period of the screen as a multitone cell. We define a multitone schedule, which for each absorptance level specifies the fraction of each native tone used in the multitone cell. Traditional multitoning uses only one native tone in smooth areas corresponding to absorptance values near the native tones, an approach that introduces contouring artifacts. To reduce contouring, we employ schedules that use more than one native tone at each absorptance level. On the basis of the multitone schedule, multitone patterns are designed level by level by adding native tones under the stacking constraint. At each level the spatial arrangement of the native tones is determined by a modified DBS search. We explore several different multitone schedules that illustrate the image-quality trade-offs in multitone screen design.

© 2002 Optical Society of America

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  1. J. P. Allebach, ed., Selected Papers on Digital Halftoning, SPIE Milestone Series Vol. MS 154 (SPIE Optical Engineering Press, Bellingham, Wash., 1999).
  2. R. S. Gentile, E. Walowit, J. P. Allebach, “Quantization and multilevel halftoning of color images for near-original image quality,” J. Opt. Soc. Am. A 7, 1019–1026 (1990).
    [CrossRef]
  3. R. Miller, C. Smith, “Mean-preserving multilevel halftoning algorithm,” in Human Vision, Visual Processing and Digital Display IV, J. P. Allebach, B. E. Rogowitz, eds., Proc. SPIE1913, 367–377 (1993).
    [CrossRef]
  4. P. A. Delabastita, “Multilevel halftoning,” in Proceedings of the IS&T’s Technical Symposium on Prepress, Proofing and Printing (Society for Imaging Science and Technology, Springfield, Va., 1995), pp. 68–73.
  5. T. Kurosawa, H. Kotera, “Multilevel halftoning algorithm for high-quality hardcopying,” J. Soc. Inf. Disp. 32, 145–151 (1991).
  6. P. R. Bakić, N. S. Vujović, D. P. Brzaković, B. D. Reljin, “Cellular neural network for automatic multilevel halftoning of digital images,” in Circuits and Systems Connecting the World, Proceedings of the IEEE International Symposium on Circuits and Systems (Institute of Electrical and Electronics Engineers, New York, 1996), Vol. 3, pp. 566–569.
  7. P. R. Bakić, N. S. Vujović, D. P. Brzaković, P. D. Kostić, B. D. Reljin, “CNN paradigm based multilevel halftoning of digital images,” IEEE Trans. Circuits Syst., II 44, 50–53 (1997).
    [CrossRef]
  8. D. Kacker, T. Camis, J. P. Allebach, “Electrophotographic process embedded in direct binary search,” in Color Imaging: Device-Independent Color, Color Hardcopy, and Graphic Arts V, R. Eschbach, G. G. Marcu, eds., Proc. SPIE3963, 468–482 (2000).
    [CrossRef]
  9. P. Li, J. P. Allebach, “Block interlaced pinwheel error diffusion,” in Proceedings of the IS&T’s Processing Images, Image Quality, Capturing Images, Systems (PICS) Conference (Society for Imaging Science and Technology, Springfield, Va., 2002), Vol. 5, pp. 245–249.
  10. D. J. Lieberman, J. P. Allebach, “Efficient model based halftoning using direct binary search,” in Proceedings of the 1997 IEEE International Conference on Image Processing (Institute of Electrical and Electronics Engineers, New York, 1997), Vol. 1, pp. 775–778.
  11. B. W. Kolpatzik, C. A. Bouman, “Optimized error diffusion for image display,” J. Electron. Imaging 1, 277–292 (1992).
    [CrossRef]
  12. S. Sugiura, T. Matika, “An improved multilevel error diffusion method,” J. Imaging Sci. Technol. 39, 495–501 (1995).
  13. Q. Yu, K. J. Parker, K. Spaulding, R. Miller, “Digital multitoning with overmodulation for smooth texture transition,” J. Electron. Imaging 8, 311–321 (1999).
    [CrossRef]
  14. Q. Yu, K. Spaulding, “Combining error diffusion, dithering and over-modulation for smooth multilevel printing,” in Color Imaging: Device-Independent Color, Color Hardcopy, and Graphic Arts V, R. Eschbach, G. G. Marcu, eds., Proc. SPIE3963, 446–457 (2000).
    [CrossRef]
  15. F. Faheem, D. L. Lau, G. R. Arce, “Multilevel halftoning using bilevel quantizers,” in Proceedings of IS&T’s 2001 Processing Images, Image Quality, Capturing Images, Systems (PICS) Conference (Society for Imaging Science and Technology, Springfield, Va., 2001), pp. 51–54.
  16. M. Analoui, J. P. Allebach, “Model based halftoning using direct binary search,” in Human Vision, Visual Processing, and Digital Display III, B. E. Rogowitz, ed., Proc. SPIE1666, 96–108 (1992).
    [CrossRef]
  17. D. J. Lieberman, J. P. Allebach, “A dual interpretation for direct binary search and its implications for tone reproduction and texture quality,” IEEE Trans. Image Process. 9, 1950–1963 (2000).
    [CrossRef]
  18. J. P. Allebach, “DBS: retrospective and future directions,” in Color Imaging: Device Independent Color, Color Hardcopy, and Graphic Arts VI, R. Eschbach, G. G. Marcu, eds., Proc. SPIE4300, 358–376 (2001).
    [CrossRef]
  19. T. Pappas, D. Neuhoff, “Least-squares model-based halftoning,” in Human Vision, Visual Processing, and Digital Display III, B. E. Rogowitz, ed., Proc. SPIE1666, 165–176 (1992).
    [CrossRef]
  20. J. J. Mulligan, A. Ahumada, “Principled halftoning based on models of human vision,” in Human Vision, Visual Processing, and Digital Display III, B. E. Rogowitz, ed., Proc. SPIE1666, 109–121 (1992).
    [CrossRef]
  21. R. Näsänen, “Visibility of halftone dot textures,” IEEE Trans. Syst. Man Cybern. SMC-14, 920–924 (1984).
    [CrossRef]
  22. J. P. Allebach, Q. Lin, “FM screen design using DBS algorithm,” in Proceedings of the 1996 IEEE International Conference on Image Processing (Institute of Electrical and Electronics Engineers, New York, 1996), Vol. 1, pp. 549–552.
  23. J.-H. Lee, J. P. Allebach, “CMYK halftoning algorithm based on direct binary search,” in Proceedings of IS&T/SID’s Ninth Color Imaging Conference (Society for Imaging Science and Technology, Springfield, Va., 2001), pp. 199–204.
  24. R. W. Floyd, L. Steinberg, “An adaptive algorithm for spatial greyscale,” J. Soc. Inf. Disp. 17, 75–77 (1976).
  25. V. Ostromoukhov, “A simple and efficient error-diffusion algorithm,” in Proceedings of SIGGRAPH’01: The 28th International Conference on Computer Graphics and Interactive Techniques (Association for Computing Machinery, New York, 2001), pp. 567–572.
  26. P. Li, J. P. Allebach, “Tone dependent error diffusion,” in Color Imaging: Device-Independent Color, Color Hardcopy, and Applications VII, R. Eschbach, G. G. Marcu, eds., Proc. SPIE4663, 310–321 (2002).
    [CrossRef]
  27. R. Ulichney, Digital Halftoning (MIT Press, Cambridge, Mass., 1987).

2000 (1)

D. J. Lieberman, J. P. Allebach, “A dual interpretation for direct binary search and its implications for tone reproduction and texture quality,” IEEE Trans. Image Process. 9, 1950–1963 (2000).
[CrossRef]

1999 (1)

Q. Yu, K. J. Parker, K. Spaulding, R. Miller, “Digital multitoning with overmodulation for smooth texture transition,” J. Electron. Imaging 8, 311–321 (1999).
[CrossRef]

1997 (1)

P. R. Bakić, N. S. Vujović, D. P. Brzaković, P. D. Kostić, B. D. Reljin, “CNN paradigm based multilevel halftoning of digital images,” IEEE Trans. Circuits Syst., II 44, 50–53 (1997).
[CrossRef]

1995 (1)

S. Sugiura, T. Matika, “An improved multilevel error diffusion method,” J. Imaging Sci. Technol. 39, 495–501 (1995).

1992 (1)

B. W. Kolpatzik, C. A. Bouman, “Optimized error diffusion for image display,” J. Electron. Imaging 1, 277–292 (1992).
[CrossRef]

1991 (1)

T. Kurosawa, H. Kotera, “Multilevel halftoning algorithm for high-quality hardcopying,” J. Soc. Inf. Disp. 32, 145–151 (1991).

1990 (1)

1984 (1)

R. Näsänen, “Visibility of halftone dot textures,” IEEE Trans. Syst. Man Cybern. SMC-14, 920–924 (1984).
[CrossRef]

1976 (1)

R. W. Floyd, L. Steinberg, “An adaptive algorithm for spatial greyscale,” J. Soc. Inf. Disp. 17, 75–77 (1976).

Ahumada, A.

J. J. Mulligan, A. Ahumada, “Principled halftoning based on models of human vision,” in Human Vision, Visual Processing, and Digital Display III, B. E. Rogowitz, ed., Proc. SPIE1666, 109–121 (1992).
[CrossRef]

Allebach, J. P.

D. J. Lieberman, J. P. Allebach, “A dual interpretation for direct binary search and its implications for tone reproduction and texture quality,” IEEE Trans. Image Process. 9, 1950–1963 (2000).
[CrossRef]

R. S. Gentile, E. Walowit, J. P. Allebach, “Quantization and multilevel halftoning of color images for near-original image quality,” J. Opt. Soc. Am. A 7, 1019–1026 (1990).
[CrossRef]

J.-H. Lee, J. P. Allebach, “CMYK halftoning algorithm based on direct binary search,” in Proceedings of IS&T/SID’s Ninth Color Imaging Conference (Society for Imaging Science and Technology, Springfield, Va., 2001), pp. 199–204.

D. Kacker, T. Camis, J. P. Allebach, “Electrophotographic process embedded in direct binary search,” in Color Imaging: Device-Independent Color, Color Hardcopy, and Graphic Arts V, R. Eschbach, G. G. Marcu, eds., Proc. SPIE3963, 468–482 (2000).
[CrossRef]

P. Li, J. P. Allebach, “Tone dependent error diffusion,” in Color Imaging: Device-Independent Color, Color Hardcopy, and Applications VII, R. Eschbach, G. G. Marcu, eds., Proc. SPIE4663, 310–321 (2002).
[CrossRef]

M. Analoui, J. P. Allebach, “Model based halftoning using direct binary search,” in Human Vision, Visual Processing, and Digital Display III, B. E. Rogowitz, ed., Proc. SPIE1666, 96–108 (1992).
[CrossRef]

D. J. Lieberman, J. P. Allebach, “Efficient model based halftoning using direct binary search,” in Proceedings of the 1997 IEEE International Conference on Image Processing (Institute of Electrical and Electronics Engineers, New York, 1997), Vol. 1, pp. 775–778.

P. Li, J. P. Allebach, “Block interlaced pinwheel error diffusion,” in Proceedings of the IS&T’s Processing Images, Image Quality, Capturing Images, Systems (PICS) Conference (Society for Imaging Science and Technology, Springfield, Va., 2002), Vol. 5, pp. 245–249.

J. P. Allebach, “DBS: retrospective and future directions,” in Color Imaging: Device Independent Color, Color Hardcopy, and Graphic Arts VI, R. Eschbach, G. G. Marcu, eds., Proc. SPIE4300, 358–376 (2001).
[CrossRef]

J. P. Allebach, Q. Lin, “FM screen design using DBS algorithm,” in Proceedings of the 1996 IEEE International Conference on Image Processing (Institute of Electrical and Electronics Engineers, New York, 1996), Vol. 1, pp. 549–552.

Analoui, M.

M. Analoui, J. P. Allebach, “Model based halftoning using direct binary search,” in Human Vision, Visual Processing, and Digital Display III, B. E. Rogowitz, ed., Proc. SPIE1666, 96–108 (1992).
[CrossRef]

Arce, G. R.

F. Faheem, D. L. Lau, G. R. Arce, “Multilevel halftoning using bilevel quantizers,” in Proceedings of IS&T’s 2001 Processing Images, Image Quality, Capturing Images, Systems (PICS) Conference (Society for Imaging Science and Technology, Springfield, Va., 2001), pp. 51–54.

Bakic, P. R.

P. R. Bakić, N. S. Vujović, D. P. Brzaković, P. D. Kostić, B. D. Reljin, “CNN paradigm based multilevel halftoning of digital images,” IEEE Trans. Circuits Syst., II 44, 50–53 (1997).
[CrossRef]

P. R. Bakić, N. S. Vujović, D. P. Brzaković, B. D. Reljin, “Cellular neural network for automatic multilevel halftoning of digital images,” in Circuits and Systems Connecting the World, Proceedings of the IEEE International Symposium on Circuits and Systems (Institute of Electrical and Electronics Engineers, New York, 1996), Vol. 3, pp. 566–569.

Bouman, C. A.

B. W. Kolpatzik, C. A. Bouman, “Optimized error diffusion for image display,” J. Electron. Imaging 1, 277–292 (1992).
[CrossRef]

Brzakovic, D. P.

P. R. Bakić, N. S. Vujović, D. P. Brzaković, P. D. Kostić, B. D. Reljin, “CNN paradigm based multilevel halftoning of digital images,” IEEE Trans. Circuits Syst., II 44, 50–53 (1997).
[CrossRef]

P. R. Bakić, N. S. Vujović, D. P. Brzaković, B. D. Reljin, “Cellular neural network for automatic multilevel halftoning of digital images,” in Circuits and Systems Connecting the World, Proceedings of the IEEE International Symposium on Circuits and Systems (Institute of Electrical and Electronics Engineers, New York, 1996), Vol. 3, pp. 566–569.

Camis, T.

D. Kacker, T. Camis, J. P. Allebach, “Electrophotographic process embedded in direct binary search,” in Color Imaging: Device-Independent Color, Color Hardcopy, and Graphic Arts V, R. Eschbach, G. G. Marcu, eds., Proc. SPIE3963, 468–482 (2000).
[CrossRef]

Delabastita, P. A.

P. A. Delabastita, “Multilevel halftoning,” in Proceedings of the IS&T’s Technical Symposium on Prepress, Proofing and Printing (Society for Imaging Science and Technology, Springfield, Va., 1995), pp. 68–73.

Faheem, F.

F. Faheem, D. L. Lau, G. R. Arce, “Multilevel halftoning using bilevel quantizers,” in Proceedings of IS&T’s 2001 Processing Images, Image Quality, Capturing Images, Systems (PICS) Conference (Society for Imaging Science and Technology, Springfield, Va., 2001), pp. 51–54.

Floyd, R. W.

R. W. Floyd, L. Steinberg, “An adaptive algorithm for spatial greyscale,” J. Soc. Inf. Disp. 17, 75–77 (1976).

Gentile, R. S.

Kacker, D.

D. Kacker, T. Camis, J. P. Allebach, “Electrophotographic process embedded in direct binary search,” in Color Imaging: Device-Independent Color, Color Hardcopy, and Graphic Arts V, R. Eschbach, G. G. Marcu, eds., Proc. SPIE3963, 468–482 (2000).
[CrossRef]

Kolpatzik, B. W.

B. W. Kolpatzik, C. A. Bouman, “Optimized error diffusion for image display,” J. Electron. Imaging 1, 277–292 (1992).
[CrossRef]

Kostic, P. D.

P. R. Bakić, N. S. Vujović, D. P. Brzaković, P. D. Kostić, B. D. Reljin, “CNN paradigm based multilevel halftoning of digital images,” IEEE Trans. Circuits Syst., II 44, 50–53 (1997).
[CrossRef]

Kotera, H.

T. Kurosawa, H. Kotera, “Multilevel halftoning algorithm for high-quality hardcopying,” J. Soc. Inf. Disp. 32, 145–151 (1991).

Kurosawa, T.

T. Kurosawa, H. Kotera, “Multilevel halftoning algorithm for high-quality hardcopying,” J. Soc. Inf. Disp. 32, 145–151 (1991).

Lau, D. L.

F. Faheem, D. L. Lau, G. R. Arce, “Multilevel halftoning using bilevel quantizers,” in Proceedings of IS&T’s 2001 Processing Images, Image Quality, Capturing Images, Systems (PICS) Conference (Society for Imaging Science and Technology, Springfield, Va., 2001), pp. 51–54.

Lee, J.-H.

J.-H. Lee, J. P. Allebach, “CMYK halftoning algorithm based on direct binary search,” in Proceedings of IS&T/SID’s Ninth Color Imaging Conference (Society for Imaging Science and Technology, Springfield, Va., 2001), pp. 199–204.

Li, P.

P. Li, J. P. Allebach, “Tone dependent error diffusion,” in Color Imaging: Device-Independent Color, Color Hardcopy, and Applications VII, R. Eschbach, G. G. Marcu, eds., Proc. SPIE4663, 310–321 (2002).
[CrossRef]

P. Li, J. P. Allebach, “Block interlaced pinwheel error diffusion,” in Proceedings of the IS&T’s Processing Images, Image Quality, Capturing Images, Systems (PICS) Conference (Society for Imaging Science and Technology, Springfield, Va., 2002), Vol. 5, pp. 245–249.

Lieberman, D. J.

D. J. Lieberman, J. P. Allebach, “A dual interpretation for direct binary search and its implications for tone reproduction and texture quality,” IEEE Trans. Image Process. 9, 1950–1963 (2000).
[CrossRef]

D. J. Lieberman, J. P. Allebach, “Efficient model based halftoning using direct binary search,” in Proceedings of the 1997 IEEE International Conference on Image Processing (Institute of Electrical and Electronics Engineers, New York, 1997), Vol. 1, pp. 775–778.

Lin, Q.

J. P. Allebach, Q. Lin, “FM screen design using DBS algorithm,” in Proceedings of the 1996 IEEE International Conference on Image Processing (Institute of Electrical and Electronics Engineers, New York, 1996), Vol. 1, pp. 549–552.

Matika, T.

S. Sugiura, T. Matika, “An improved multilevel error diffusion method,” J. Imaging Sci. Technol. 39, 495–501 (1995).

Miller, R.

Q. Yu, K. J. Parker, K. Spaulding, R. Miller, “Digital multitoning with overmodulation for smooth texture transition,” J. Electron. Imaging 8, 311–321 (1999).
[CrossRef]

R. Miller, C. Smith, “Mean-preserving multilevel halftoning algorithm,” in Human Vision, Visual Processing and Digital Display IV, J. P. Allebach, B. E. Rogowitz, eds., Proc. SPIE1913, 367–377 (1993).
[CrossRef]

Mulligan, J. J.

J. J. Mulligan, A. Ahumada, “Principled halftoning based on models of human vision,” in Human Vision, Visual Processing, and Digital Display III, B. E. Rogowitz, ed., Proc. SPIE1666, 109–121 (1992).
[CrossRef]

Näsänen, R.

R. Näsänen, “Visibility of halftone dot textures,” IEEE Trans. Syst. Man Cybern. SMC-14, 920–924 (1984).
[CrossRef]

Neuhoff, D.

T. Pappas, D. Neuhoff, “Least-squares model-based halftoning,” in Human Vision, Visual Processing, and Digital Display III, B. E. Rogowitz, ed., Proc. SPIE1666, 165–176 (1992).
[CrossRef]

Ostromoukhov, V.

V. Ostromoukhov, “A simple and efficient error-diffusion algorithm,” in Proceedings of SIGGRAPH’01: The 28th International Conference on Computer Graphics and Interactive Techniques (Association for Computing Machinery, New York, 2001), pp. 567–572.

Pappas, T.

T. Pappas, D. Neuhoff, “Least-squares model-based halftoning,” in Human Vision, Visual Processing, and Digital Display III, B. E. Rogowitz, ed., Proc. SPIE1666, 165–176 (1992).
[CrossRef]

Parker, K. J.

Q. Yu, K. J. Parker, K. Spaulding, R. Miller, “Digital multitoning with overmodulation for smooth texture transition,” J. Electron. Imaging 8, 311–321 (1999).
[CrossRef]

Reljin, B. D.

P. R. Bakić, N. S. Vujović, D. P. Brzaković, P. D. Kostić, B. D. Reljin, “CNN paradigm based multilevel halftoning of digital images,” IEEE Trans. Circuits Syst., II 44, 50–53 (1997).
[CrossRef]

P. R. Bakić, N. S. Vujović, D. P. Brzaković, B. D. Reljin, “Cellular neural network for automatic multilevel halftoning of digital images,” in Circuits and Systems Connecting the World, Proceedings of the IEEE International Symposium on Circuits and Systems (Institute of Electrical and Electronics Engineers, New York, 1996), Vol. 3, pp. 566–569.

Smith, C.

R. Miller, C. Smith, “Mean-preserving multilevel halftoning algorithm,” in Human Vision, Visual Processing and Digital Display IV, J. P. Allebach, B. E. Rogowitz, eds., Proc. SPIE1913, 367–377 (1993).
[CrossRef]

Spaulding, K.

Q. Yu, K. J. Parker, K. Spaulding, R. Miller, “Digital multitoning with overmodulation for smooth texture transition,” J. Electron. Imaging 8, 311–321 (1999).
[CrossRef]

Q. Yu, K. Spaulding, “Combining error diffusion, dithering and over-modulation for smooth multilevel printing,” in Color Imaging: Device-Independent Color, Color Hardcopy, and Graphic Arts V, R. Eschbach, G. G. Marcu, eds., Proc. SPIE3963, 446–457 (2000).
[CrossRef]

Steinberg, L.

R. W. Floyd, L. Steinberg, “An adaptive algorithm for spatial greyscale,” J. Soc. Inf. Disp. 17, 75–77 (1976).

Sugiura, S.

S. Sugiura, T. Matika, “An improved multilevel error diffusion method,” J. Imaging Sci. Technol. 39, 495–501 (1995).

Ulichney, R.

R. Ulichney, Digital Halftoning (MIT Press, Cambridge, Mass., 1987).

Vujovic, N. S.

P. R. Bakić, N. S. Vujović, D. P. Brzaković, P. D. Kostić, B. D. Reljin, “CNN paradigm based multilevel halftoning of digital images,” IEEE Trans. Circuits Syst., II 44, 50–53 (1997).
[CrossRef]

P. R. Bakić, N. S. Vujović, D. P. Brzaković, B. D. Reljin, “Cellular neural network for automatic multilevel halftoning of digital images,” in Circuits and Systems Connecting the World, Proceedings of the IEEE International Symposium on Circuits and Systems (Institute of Electrical and Electronics Engineers, New York, 1996), Vol. 3, pp. 566–569.

Walowit, E.

Yu, Q.

Q. Yu, K. J. Parker, K. Spaulding, R. Miller, “Digital multitoning with overmodulation for smooth texture transition,” J. Electron. Imaging 8, 311–321 (1999).
[CrossRef]

Q. Yu, K. Spaulding, “Combining error diffusion, dithering and over-modulation for smooth multilevel printing,” in Color Imaging: Device-Independent Color, Color Hardcopy, and Graphic Arts V, R. Eschbach, G. G. Marcu, eds., Proc. SPIE3963, 446–457 (2000).
[CrossRef]

IEEE Trans. Circuits Syst., II (1)

P. R. Bakić, N. S. Vujović, D. P. Brzaković, P. D. Kostić, B. D. Reljin, “CNN paradigm based multilevel halftoning of digital images,” IEEE Trans. Circuits Syst., II 44, 50–53 (1997).
[CrossRef]

IEEE Trans. Image Process. (1)

D. J. Lieberman, J. P. Allebach, “A dual interpretation for direct binary search and its implications for tone reproduction and texture quality,” IEEE Trans. Image Process. 9, 1950–1963 (2000).
[CrossRef]

IEEE Trans. Syst. Man Cybern. (1)

R. Näsänen, “Visibility of halftone dot textures,” IEEE Trans. Syst. Man Cybern. SMC-14, 920–924 (1984).
[CrossRef]

J. Electron. Imaging (2)

B. W. Kolpatzik, C. A. Bouman, “Optimized error diffusion for image display,” J. Electron. Imaging 1, 277–292 (1992).
[CrossRef]

Q. Yu, K. J. Parker, K. Spaulding, R. Miller, “Digital multitoning with overmodulation for smooth texture transition,” J. Electron. Imaging 8, 311–321 (1999).
[CrossRef]

J. Imaging Sci. Technol. (1)

S. Sugiura, T. Matika, “An improved multilevel error diffusion method,” J. Imaging Sci. Technol. 39, 495–501 (1995).

J. Opt. Soc. Am. A (1)

J. Soc. Inf. Disp. (2)

R. W. Floyd, L. Steinberg, “An adaptive algorithm for spatial greyscale,” J. Soc. Inf. Disp. 17, 75–77 (1976).

T. Kurosawa, H. Kotera, “Multilevel halftoning algorithm for high-quality hardcopying,” J. Soc. Inf. Disp. 32, 145–151 (1991).

Other (18)

P. R. Bakić, N. S. Vujović, D. P. Brzaković, B. D. Reljin, “Cellular neural network for automatic multilevel halftoning of digital images,” in Circuits and Systems Connecting the World, Proceedings of the IEEE International Symposium on Circuits and Systems (Institute of Electrical and Electronics Engineers, New York, 1996), Vol. 3, pp. 566–569.

R. Miller, C. Smith, “Mean-preserving multilevel halftoning algorithm,” in Human Vision, Visual Processing and Digital Display IV, J. P. Allebach, B. E. Rogowitz, eds., Proc. SPIE1913, 367–377 (1993).
[CrossRef]

P. A. Delabastita, “Multilevel halftoning,” in Proceedings of the IS&T’s Technical Symposium on Prepress, Proofing and Printing (Society for Imaging Science and Technology, Springfield, Va., 1995), pp. 68–73.

D. Kacker, T. Camis, J. P. Allebach, “Electrophotographic process embedded in direct binary search,” in Color Imaging: Device-Independent Color, Color Hardcopy, and Graphic Arts V, R. Eschbach, G. G. Marcu, eds., Proc. SPIE3963, 468–482 (2000).
[CrossRef]

P. Li, J. P. Allebach, “Block interlaced pinwheel error diffusion,” in Proceedings of the IS&T’s Processing Images, Image Quality, Capturing Images, Systems (PICS) Conference (Society for Imaging Science and Technology, Springfield, Va., 2002), Vol. 5, pp. 245–249.

D. J. Lieberman, J. P. Allebach, “Efficient model based halftoning using direct binary search,” in Proceedings of the 1997 IEEE International Conference on Image Processing (Institute of Electrical and Electronics Engineers, New York, 1997), Vol. 1, pp. 775–778.

Q. Yu, K. Spaulding, “Combining error diffusion, dithering and over-modulation for smooth multilevel printing,” in Color Imaging: Device-Independent Color, Color Hardcopy, and Graphic Arts V, R. Eschbach, G. G. Marcu, eds., Proc. SPIE3963, 446–457 (2000).
[CrossRef]

F. Faheem, D. L. Lau, G. R. Arce, “Multilevel halftoning using bilevel quantizers,” in Proceedings of IS&T’s 2001 Processing Images, Image Quality, Capturing Images, Systems (PICS) Conference (Society for Imaging Science and Technology, Springfield, Va., 2001), pp. 51–54.

M. Analoui, J. P. Allebach, “Model based halftoning using direct binary search,” in Human Vision, Visual Processing, and Digital Display III, B. E. Rogowitz, ed., Proc. SPIE1666, 96–108 (1992).
[CrossRef]

J. P. Allebach, “DBS: retrospective and future directions,” in Color Imaging: Device Independent Color, Color Hardcopy, and Graphic Arts VI, R. Eschbach, G. G. Marcu, eds., Proc. SPIE4300, 358–376 (2001).
[CrossRef]

T. Pappas, D. Neuhoff, “Least-squares model-based halftoning,” in Human Vision, Visual Processing, and Digital Display III, B. E. Rogowitz, ed., Proc. SPIE1666, 165–176 (1992).
[CrossRef]

J. J. Mulligan, A. Ahumada, “Principled halftoning based on models of human vision,” in Human Vision, Visual Processing, and Digital Display III, B. E. Rogowitz, ed., Proc. SPIE1666, 109–121 (1992).
[CrossRef]

V. Ostromoukhov, “A simple and efficient error-diffusion algorithm,” in Proceedings of SIGGRAPH’01: The 28th International Conference on Computer Graphics and Interactive Techniques (Association for Computing Machinery, New York, 2001), pp. 567–572.

P. Li, J. P. Allebach, “Tone dependent error diffusion,” in Color Imaging: Device-Independent Color, Color Hardcopy, and Applications VII, R. Eschbach, G. G. Marcu, eds., Proc. SPIE4663, 310–321 (2002).
[CrossRef]

R. Ulichney, Digital Halftoning (MIT Press, Cambridge, Mass., 1987).

J. P. Allebach, ed., Selected Papers on Digital Halftoning, SPIE Milestone Series Vol. MS 154 (SPIE Optical Engineering Press, Bellingham, Wash., 1999).

J. P. Allebach, Q. Lin, “FM screen design using DBS algorithm,” in Proceedings of the 1996 IEEE International Conference on Image Processing (Institute of Electrical and Electronics Engineers, New York, 1996), Vol. 1, pp. 549–552.

J.-H. Lee, J. P. Allebach, “CMYK halftoning algorithm based on direct binary search,” in Proceedings of IS&T/SID’s Ninth Color Imaging Conference (Society for Imaging Science and Technology, Springfield, Va., 2001), pp. 199–204.

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Figures (17)

Fig. 1
Fig. 1

Ramp image generated with the bilevel DBS screen.

Fig. 2
Fig. 2

Schedule for bilevel halftone screen.

Fig. 3
Fig. 3

Schedule S12 for traditional one-two tone mixture multitone screen.

Fig. 4
Fig. 4

Ramp image generated with schedule S12. Contouring artifacts can be observed in segments 2 and 3 of the ramp at a position that is 1/3 of the way from the right side of each segment.

Fig. 5
Fig. 5

Schedule S23 for two–three-tone-mixture multitone screen.

Fig. 6
Fig. 6

Implementation code and the associated formulas for schedule S23. In the code, we first decide in which interval the input f[m, n] falls, and then we quantize f[m, n] with the appropriate threshold tj23[m, n], j{1, 2,, 2K-3}. Note that masks are applied only in the second and fourth intervals for K=4 possible output states.

Fig. 7
Fig. 7

Ramp image generated with schedule S23. The blend-in effect reduces the visibility of contouring in the ramp shown in Fig. 4 that was generated by the traditional S12 screen. However, the noise contrast is higher in the blend-in regions than elsewhere.

Fig. 8
Fig. 8

Schedule S23e for extended two–three-tone-mixture multitone screen.

Fig. 9
Fig. 9

Ramp image generated with schedule S23e. Contouring is reduced compared with schedule S23. However, native tones that occur as sparsely distributed minority pixels can be seen in segments 1 and 4 of the ramp at a position, which is 1/3 of the way from the right side of each segment.

Fig. 10
Fig. 10

Schedule S34 for three–four-tone-mixture multitone screen.

Fig. 11
Fig. 11

Multitone textures at 1/3 from use of (a) simultaneous design and (b) sequential design. Note the clumping of α1 pixels that occurs with the simultaneous design.

Fig. 12
Fig. 12

Ramp image generated with schedule S34. At least three different native tones are used at all levels. We observe less contouring; however, the result appears to be very noisy.

Fig. 13
Fig. 13

Multitone ramp image generated by a screening-based algorithm proposed in Ref. 13. Distinct adjacent tones are grouped together at the intermediate output levels in segments 2 and 3 of the ramp at a position that is 1/3 of the way from the right side of each segment.

Fig. 14
Fig. 14

Multitone ramp image generated by an error-diffusion-based algorithm proposed in Ref. 15 but by using tone-dependent weights and thresholds from Ref. 26. The overall quality is similar to that resulting from the multitone screen with schedule S23, but at a significantly grater computational cost.

Fig. 15
Fig. 15

Error metric for different schedules. Since schedule S12 does not produce texture at intermediate native-tone levels (1/3 and 2/3), there is no error at these levels, but this does result in contouring.

Fig. 16
Fig. 16

Multitone textures at absorptance level 2/3 generated with schedules (a) S23, (b) S23e, and (c) S34.

Fig. 17
Fig. 17

Radially averaged power spectra for the textures in Fig. 16.

Equations (28)

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f(x, y)=m,nf[m, n] p(x-mX, y-nY),
0f[m, n]1.
f˜(x, y)=f(x, y) ** h(x, y),
f˜(x, y)=m,nf[m, n] p˜(x-mX, y-nY).
g˜(x, y)=m,ng[m, n] p˜(x-mX, y-nY).
e˜(x, y)=g˜(x, y)-f˜(x, y).
E=|e˜(x, y)|2dxdy.
g[m, n]=g[m, n]+a0δ[m-m0, n-n0]+a1δ[m-m1, n-n1],
a0=αi0-αi0foratoggleαi1-αi0foraswap,
a1=0foratoggleαi0-αi1foraswap,
i0, i0, i1{0, 1,, K-1},i0i0,i0i1.
ΔE=E-E=(a02+a12)cp˜p˜[0,0]+2(a0cp˜e˜[m0, n0]+a1cp˜e˜[m1, n1]+a0a1cp˜p˜[m0-m1,n0-n1]),
cab[m, n]=a(x, y)b(x-mX, y-nY)dxdy.
cp˜e˜[m, n]=cp˜e˜[m, n]+a0cp˜p˜[m-m0, n-n0]+a1cp˜p˜[m-m1, n-n1].
t[m, n]=1-1N-1i=0N-1pm, n;iN-1.
g[m, n]=1,f[m, n]>t[m, n]0,else
t12[m, n]=13-1N-1i=0i1/3(N-1)pα1m, n;iN-1.
pα1[m, n; a]=1ifthepixelvalueat[m, n]equalsα10else.
g12[m, n]
=αl+1,f[m, n]-αl>t12[m, n]f[m, n][αl, αl+1],l{0, 1, 2}.αl,else
M123[m, n]=pα1[m, n; 1/3-d]
M223[m, n]=pα2[m, n; 2/3-d].
pα2[m, n; 1/3]=1  pα2[m, n; a]=1,
a (1/3, 2/3).
pα1[m, n; 2/3]=1  pα1[m, n; a]=1,
a[1/3, 2/3).
pα0m, n;iN-1=pα3m, n;N-1-iN-1,
0i13(N-1).

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