Abstract

We introduce a novel technique for generating green-noise halftones—stochastic dither patterns composed of homogeneously distributed pixel clusters. Although techniques employing error diffusion have been proposed previously, the technique here employs a dither array referred to as a green-noise mask, which greatly reduces the computational complexity formerly associated with green noise. Compared with those generated with blue-noise masks, halftones generated with green-noise masks are less susceptible to printer distortions. Because green noise constitutes patterns with widely varying cluster sizes and shapes, the technique introduced here for constructing these green-noise masks is tunable; that is, it allows for specific printer traits, with small clusters reserved for printers with low distortion and large clusters reserved for printers with high distortion. Given that blue noise is a limiting case of green noise, this new technique can even create blue-noise masks.

© 1999 Optical Society of America

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References

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  1. J. E. Adamcewicz, “A study on the effects of dot gain, print contrast and tone reproduction as it relates to increased solid ink density on stochastically screened images with conventionally screened images,” M.S. thesis (Rochester Institute of Technology, Rochester, N.Y., 1994).
  2. R. W. Floyd, L. Steinberg, “An adaptive algorithm for spatial gray-scale,” Proc. Soc. Inf. Disp. 17, 75–78 (1976).
  3. K. Laughlin, “An investigation of amplitude and frequency modulated screening on dot gain and variability,” M.S. thesis (Rochester Institute of Technology, Rochester, N.Y., 1994).
  4. B. Bayer, “An optimum method for two level rendition of continuous-tone pictures,” in IEEE International Conference on Communications, Conference Record (Institute of Electrical and Electronics Engineers, New York, 1973), pp. 11–15.
  5. R. A. Ulichney, “The void-and-cluster method for dither array generation,” in Human Vision, Visual Processing, and Digital Display IV, J. P. Allebach, B. E. Rogowitz, eds., Proc. SPIE1913, 332–343 (1993).
    [CrossRef]
  6. R. A. Ulichney, “Dithering with blue noise,” Proc. IEEE 76, 56–79 (1988).
    [CrossRef]
  7. T. Mitsa, K. J. Parker, “Digital halftoning technique using a blue-noise mask,” J. Opt. Soc. Am. A 9, 1920–1929 (1992).
    [CrossRef]
  8. M. Rodriguez, “Graphic arts perspective on digital halftoning,” in Human Vision, Visual Processing, and Digital Display V, B. E. Rogowitz, J. P. Allebach, eds., Proc. SPIE2179, 144–149 (1994).
    [CrossRef]
  9. M. A. Coudray, “Causes and corrections of dot gain on press,” Screen Print. J. Technol. Manage. 86, 18–26 (1996).
  10. D. L. Lau, G. R. Arce, N. C. Gallagher, “Green-noise digital halftoning,” Proc. IEEE 86, 2424–2444 (1998).
    [CrossRef]
  11. L. Velho, J. M. Gomes, “Digital halftoning with space filling curves,” Comput. Graph. 25, 81–90 (1991).
    [CrossRef]
  12. R. Levien, “Output dependent feedback in error diffusion halftoning,” in IS&T’s Eighth International Congress on Advances in Non-Impact Printing Technologies (Society for Imaging Science and Technology, Springfield, Va., 1992), pp. 280–282.
  13. J. P. Allebach, “Random nucleated halftone screening,” Photograph. Sci. Eng. 22, 89–91 (1978).
  14. V. Ostromoukhov, “Pseudo-random halftone screening for color and black & white printing,” in Recent Progress in Digital Halftoning, R. Eschbach, ed. (Society for Imaging Science and Technology, Society for Imaging Science and Technology, Springfield, Va., 1995), pp. 130–134.
  15. S. Wang, “Stoclustic (stochastic clustered) halftone screen design,” in IS&T’s NIP 13: International Conference on Digital Printing Technologies (Society for Imaging Science and Technology, Springfield, Va., 1997), pp. 516–521.
  16. S. Aoki, “New halftoning method using adaptive cell,” in IS&T’s NIP 14: International Conference on Digital Printing Technologies (Society for Imaging Science and Technology, Springfield, Va., 1998), pp. 277–280.
  17. J. Sullivan, L. Ray, R. Miller, “Design of minimum visual modulation halftone patterns,” IEEE Trans. Syst. Man Cybern. 21, 33–38 (1991).
    [CrossRef]
  18. M. Yao, K. J. Parker, “Modified approach to the construction of a blue noise mask,” J. Electron. Imaging 3, 92–97 (1994).
    [CrossRef]
  19. N. A. C. Cressie, Statistics for Spatial Data (Wiley, New York, 1983).
  20. P. J. Diggle, Statistical Analysis of Spatial Point Patterns (Academic, London, 1983).
  21. D. Stoyan, W. S. Kendall, J. Mecke, Stochastic Geometry and Its Applications (Wiley, New York, 1987).
  22. T. N. Pappas, D. L. Neuhoff, “Printer models and error diffusion,” IEEE Trans. Image Process. 4, 66–79 (1995).
    [CrossRef] [PubMed]

1998 (1)

D. L. Lau, G. R. Arce, N. C. Gallagher, “Green-noise digital halftoning,” Proc. IEEE 86, 2424–2444 (1998).
[CrossRef]

1996 (1)

M. A. Coudray, “Causes and corrections of dot gain on press,” Screen Print. J. Technol. Manage. 86, 18–26 (1996).

1995 (1)

T. N. Pappas, D. L. Neuhoff, “Printer models and error diffusion,” IEEE Trans. Image Process. 4, 66–79 (1995).
[CrossRef] [PubMed]

1994 (1)

M. Yao, K. J. Parker, “Modified approach to the construction of a blue noise mask,” J. Electron. Imaging 3, 92–97 (1994).
[CrossRef]

1992 (1)

1991 (2)

J. Sullivan, L. Ray, R. Miller, “Design of minimum visual modulation halftone patterns,” IEEE Trans. Syst. Man Cybern. 21, 33–38 (1991).
[CrossRef]

L. Velho, J. M. Gomes, “Digital halftoning with space filling curves,” Comput. Graph. 25, 81–90 (1991).
[CrossRef]

1988 (1)

R. A. Ulichney, “Dithering with blue noise,” Proc. IEEE 76, 56–79 (1988).
[CrossRef]

1978 (1)

J. P. Allebach, “Random nucleated halftone screening,” Photograph. Sci. Eng. 22, 89–91 (1978).

1976 (1)

R. W. Floyd, L. Steinberg, “An adaptive algorithm for spatial gray-scale,” Proc. Soc. Inf. Disp. 17, 75–78 (1976).

Adamcewicz, J. E.

J. E. Adamcewicz, “A study on the effects of dot gain, print contrast and tone reproduction as it relates to increased solid ink density on stochastically screened images with conventionally screened images,” M.S. thesis (Rochester Institute of Technology, Rochester, N.Y., 1994).

Allebach, J. P.

J. P. Allebach, “Random nucleated halftone screening,” Photograph. Sci. Eng. 22, 89–91 (1978).

Aoki, S.

S. Aoki, “New halftoning method using adaptive cell,” in IS&T’s NIP 14: International Conference on Digital Printing Technologies (Society for Imaging Science and Technology, Springfield, Va., 1998), pp. 277–280.

Arce, G. R.

D. L. Lau, G. R. Arce, N. C. Gallagher, “Green-noise digital halftoning,” Proc. IEEE 86, 2424–2444 (1998).
[CrossRef]

Bayer, B.

B. Bayer, “An optimum method for two level rendition of continuous-tone pictures,” in IEEE International Conference on Communications, Conference Record (Institute of Electrical and Electronics Engineers, New York, 1973), pp. 11–15.

Coudray, M. A.

M. A. Coudray, “Causes and corrections of dot gain on press,” Screen Print. J. Technol. Manage. 86, 18–26 (1996).

Cressie, N. A. C.

N. A. C. Cressie, Statistics for Spatial Data (Wiley, New York, 1983).

Diggle, P. J.

P. J. Diggle, Statistical Analysis of Spatial Point Patterns (Academic, London, 1983).

Floyd, R. W.

R. W. Floyd, L. Steinberg, “An adaptive algorithm for spatial gray-scale,” Proc. Soc. Inf. Disp. 17, 75–78 (1976).

Gallagher, N. C.

D. L. Lau, G. R. Arce, N. C. Gallagher, “Green-noise digital halftoning,” Proc. IEEE 86, 2424–2444 (1998).
[CrossRef]

Gomes, J. M.

L. Velho, J. M. Gomes, “Digital halftoning with space filling curves,” Comput. Graph. 25, 81–90 (1991).
[CrossRef]

Kendall, W. S.

D. Stoyan, W. S. Kendall, J. Mecke, Stochastic Geometry and Its Applications (Wiley, New York, 1987).

Lau, D. L.

D. L. Lau, G. R. Arce, N. C. Gallagher, “Green-noise digital halftoning,” Proc. IEEE 86, 2424–2444 (1998).
[CrossRef]

Laughlin, K.

K. Laughlin, “An investigation of amplitude and frequency modulated screening on dot gain and variability,” M.S. thesis (Rochester Institute of Technology, Rochester, N.Y., 1994).

Levien, R.

R. Levien, “Output dependent feedback in error diffusion halftoning,” in IS&T’s Eighth International Congress on Advances in Non-Impact Printing Technologies (Society for Imaging Science and Technology, Springfield, Va., 1992), pp. 280–282.

Mecke, J.

D. Stoyan, W. S. Kendall, J. Mecke, Stochastic Geometry and Its Applications (Wiley, New York, 1987).

Miller, R.

J. Sullivan, L. Ray, R. Miller, “Design of minimum visual modulation halftone patterns,” IEEE Trans. Syst. Man Cybern. 21, 33–38 (1991).
[CrossRef]

Mitsa, T.

Neuhoff, D. L.

T. N. Pappas, D. L. Neuhoff, “Printer models and error diffusion,” IEEE Trans. Image Process. 4, 66–79 (1995).
[CrossRef] [PubMed]

Ostromoukhov, V.

V. Ostromoukhov, “Pseudo-random halftone screening for color and black & white printing,” in Recent Progress in Digital Halftoning, R. Eschbach, ed. (Society for Imaging Science and Technology, Society for Imaging Science and Technology, Springfield, Va., 1995), pp. 130–134.

Pappas, T. N.

T. N. Pappas, D. L. Neuhoff, “Printer models and error diffusion,” IEEE Trans. Image Process. 4, 66–79 (1995).
[CrossRef] [PubMed]

Parker, K. J.

M. Yao, K. J. Parker, “Modified approach to the construction of a blue noise mask,” J. Electron. Imaging 3, 92–97 (1994).
[CrossRef]

T. Mitsa, K. J. Parker, “Digital halftoning technique using a blue-noise mask,” J. Opt. Soc. Am. A 9, 1920–1929 (1992).
[CrossRef]

Ray, L.

J. Sullivan, L. Ray, R. Miller, “Design of minimum visual modulation halftone patterns,” IEEE Trans. Syst. Man Cybern. 21, 33–38 (1991).
[CrossRef]

Rodriguez, M.

M. Rodriguez, “Graphic arts perspective on digital halftoning,” in Human Vision, Visual Processing, and Digital Display V, B. E. Rogowitz, J. P. Allebach, eds., Proc. SPIE2179, 144–149 (1994).
[CrossRef]

Steinberg, L.

R. W. Floyd, L. Steinberg, “An adaptive algorithm for spatial gray-scale,” Proc. Soc. Inf. Disp. 17, 75–78 (1976).

Stoyan, D.

D. Stoyan, W. S. Kendall, J. Mecke, Stochastic Geometry and Its Applications (Wiley, New York, 1987).

Sullivan, J.

J. Sullivan, L. Ray, R. Miller, “Design of minimum visual modulation halftone patterns,” IEEE Trans. Syst. Man Cybern. 21, 33–38 (1991).
[CrossRef]

Ulichney, R. A.

R. A. Ulichney, “Dithering with blue noise,” Proc. IEEE 76, 56–79 (1988).
[CrossRef]

R. A. Ulichney, “The void-and-cluster method for dither array generation,” in Human Vision, Visual Processing, and Digital Display IV, J. P. Allebach, B. E. Rogowitz, eds., Proc. SPIE1913, 332–343 (1993).
[CrossRef]

Velho, L.

L. Velho, J. M. Gomes, “Digital halftoning with space filling curves,” Comput. Graph. 25, 81–90 (1991).
[CrossRef]

Wang, S.

S. Wang, “Stoclustic (stochastic clustered) halftone screen design,” in IS&T’s NIP 13: International Conference on Digital Printing Technologies (Society for Imaging Science and Technology, Springfield, Va., 1997), pp. 516–521.

Yao, M.

M. Yao, K. J. Parker, “Modified approach to the construction of a blue noise mask,” J. Electron. Imaging 3, 92–97 (1994).
[CrossRef]

Comput. Graph. (1)

L. Velho, J. M. Gomes, “Digital halftoning with space filling curves,” Comput. Graph. 25, 81–90 (1991).
[CrossRef]

IEEE Trans. Image Process. (1)

T. N. Pappas, D. L. Neuhoff, “Printer models and error diffusion,” IEEE Trans. Image Process. 4, 66–79 (1995).
[CrossRef] [PubMed]

IEEE Trans. Syst. Man Cybern. (1)

J. Sullivan, L. Ray, R. Miller, “Design of minimum visual modulation halftone patterns,” IEEE Trans. Syst. Man Cybern. 21, 33–38 (1991).
[CrossRef]

J. Electron. Imaging (1)

M. Yao, K. J. Parker, “Modified approach to the construction of a blue noise mask,” J. Electron. Imaging 3, 92–97 (1994).
[CrossRef]

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

Photograph. Sci. Eng. (1)

J. P. Allebach, “Random nucleated halftone screening,” Photograph. Sci. Eng. 22, 89–91 (1978).

Proc. IEEE (2)

D. L. Lau, G. R. Arce, N. C. Gallagher, “Green-noise digital halftoning,” Proc. IEEE 86, 2424–2444 (1998).
[CrossRef]

R. A. Ulichney, “Dithering with blue noise,” Proc. IEEE 76, 56–79 (1988).
[CrossRef]

Proc. Soc. Inf. Disp. (1)

R. W. Floyd, L. Steinberg, “An adaptive algorithm for spatial gray-scale,” Proc. Soc. Inf. Disp. 17, 75–78 (1976).

Screen Print. J. Technol. Manage. (1)

M. A. Coudray, “Causes and corrections of dot gain on press,” Screen Print. J. Technol. Manage. 86, 18–26 (1996).

Other (12)

R. Levien, “Output dependent feedback in error diffusion halftoning,” in IS&T’s Eighth International Congress on Advances in Non-Impact Printing Technologies (Society for Imaging Science and Technology, Springfield, Va., 1992), pp. 280–282.

V. Ostromoukhov, “Pseudo-random halftone screening for color and black & white printing,” in Recent Progress in Digital Halftoning, R. Eschbach, ed. (Society for Imaging Science and Technology, Society for Imaging Science and Technology, Springfield, Va., 1995), pp. 130–134.

S. Wang, “Stoclustic (stochastic clustered) halftone screen design,” in IS&T’s NIP 13: International Conference on Digital Printing Technologies (Society for Imaging Science and Technology, Springfield, Va., 1997), pp. 516–521.

S. Aoki, “New halftoning method using adaptive cell,” in IS&T’s NIP 14: International Conference on Digital Printing Technologies (Society for Imaging Science and Technology, Springfield, Va., 1998), pp. 277–280.

K. Laughlin, “An investigation of amplitude and frequency modulated screening on dot gain and variability,” M.S. thesis (Rochester Institute of Technology, Rochester, N.Y., 1994).

B. Bayer, “An optimum method for two level rendition of continuous-tone pictures,” in IEEE International Conference on Communications, Conference Record (Institute of Electrical and Electronics Engineers, New York, 1973), pp. 11–15.

R. A. Ulichney, “The void-and-cluster method for dither array generation,” in Human Vision, Visual Processing, and Digital Display IV, J. P. Allebach, B. E. Rogowitz, eds., Proc. SPIE1913, 332–343 (1993).
[CrossRef]

J. E. Adamcewicz, “A study on the effects of dot gain, print contrast and tone reproduction as it relates to increased solid ink density on stochastically screened images with conventionally screened images,” M.S. thesis (Rochester Institute of Technology, Rochester, N.Y., 1994).

M. Rodriguez, “Graphic arts perspective on digital halftoning,” in Human Vision, Visual Processing, and Digital Display V, B. E. Rogowitz, J. P. Allebach, eds., Proc. SPIE2179, 144–149 (1994).
[CrossRef]

N. A. C. Cressie, Statistics for Spatial Data (Wiley, New York, 1983).

P. J. Diggle, Statistical Analysis of Spatial Point Patterns (Academic, London, 1983).

D. Stoyan, W. S. Kendall, J. Mecke, Stochastic Geometry and Its Applications (Wiley, New York, 1987).

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Figures (12)

Fig. 1
Fig. 1

Binary tomato image generated by using (top left) clustered-dot dithering, (top right) error diffusion, (middle left) a blue-noise dither array, (middle right) error diffusion with printer distortion, (bottom left) error diffusion with output-dependent feedback with printer distortion, and (bottom right) a green-noise mask with printer distortion.

Fig. 2
Fig. 2

With the spectral domain partitioned into a series of annular rings, the power spectrum P(f ) can be studied by using P(fρ) and A(fρ).

Fig. 3
Fig. 3

Spectral characteristics of (top) a blue-noise halftone pattern and (bottom) a green-noise halftone pattern.

Fig. 4
Fig. 4

(a) With the spatial domain divided into a series of annular rings centered on location y, the spatial arrangement of points can be studied through the use of R(r); (b) from the expected number of points per unit area in the segment Γya versus that in the ring Γy, the spatial arrangement can be studied by using Dr1,r2(a).

Fig. 5
Fig. 5

Pair correlation for (top) a blue-noise process and (bottom) a green-noise process.

Fig. 6
Fig. 6

Resulting metrics for dither patterns generated with the use of error diffusion representing gray level g=3/4 for (top left) blue noise, (top right) green noise with small clusters, (bottom left) green noise with medium clusters, and (bottom right) green noise with large clusters.

Fig. 7
Fig. 7

Isotropic shaping function K˜(r) used to construct green-noise dither patterns in BIPPCCA.

Fig. 8
Fig. 8

Mapping function used to construct the concentration matrix C from the output after ϕ is filtered with the low-pass filter HLP by using circular convolution.

Fig. 9
Fig. 9

Resulting metrics for dither patterns generated with the use of BIPPCCA representing gray level g=3/4 with average cluster sizes of (top left) 2.0 pixels, (top right) 3.9 pixels, (bottom left) 6.0 pixels, and (bottom right) 7.9 pixels.

Fig. 10
Fig. 10

(a)–(c) Masks generated by BIPPCCA having cluster sizes that increase symmetrically with equal deviations from black and white toward middle gray, (d) mask generated by BIPPCCA with nonsymmetric deviations with larger clusters for g<1/2.

Fig. 11
Fig. 11

Principal wavelengths for masks (a)–(d), with the blue-noise principal wavelength indicated by a dotted curve.

Fig. 12
Fig. 12

Tomato image halftoned by use of the green-noise masks of Fig. 10 [labeled (a)–(d)].  

Tables (1)

Tables Icon

Table 1 Average Number of Pixels per Cluster M¯, Principal Wavelength λg, and Principal Frequency fg for Masks of Fig. 1 a

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

P(fρ)=1N(R(fρ)) fR(fρ)Pˆ(f ),
A(fρ)=1N(R(fρ))-1 fN(R(fρ)) [Pˆ(f )-P(fρ)]2[P(fρ)]2,
λb=D/gfor0<g1/2D/1-gfor1/2<g1,
fb=g/Dfor0<g1/21-g/Dfor1/2<g1.
λg=D/g/M¯for0<g1/2D/(1-g)/M¯for1/2<g1.
fg=g/M¯/Dfor0<g1/2(1-g)/M¯/Dfor1/2<g1.
K(x; y)=E{ϕ(x)|yϕ}E{ϕ(x)},
R(r)=E{ϕ(Ry(r))|yϕ}E{ϕ(Ry(r))},
Dr1,r2(a)=E{ϕ(Γya)|yϕ}/N(Γya)E{ϕ(Γy)|yϕ}/N(Γy),
πrc2=M¯.
HLP(r)=exp-r22σ2

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