Abstract

In image halftoning, texture is one of the important parameters that has a major effect on image reproduction as well as perception. We propose a halftoning algorithm based on a numerical texture metric and on the threshold accepting algorithm, which provides control of the occurrence of specific textures in the halftoned image. To conserve the image information a simultaneous control of the graytone rendition is implemented. Moreover, additional parameters may be added to control further image characteristics. The algorithm permits control of textures composed of symmetric as well as asymmetric texels and a weighted balance among the different control parameters.

© 1996 Optical Society of America

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References

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  1. B. E. Bayer, “An optimum method for two-level rendition of continuous tone pictures,” Proc. IEEE 1, 26-11–26-15 (1973).
  2. R. W. Floyd, L. Steinberg, “An adaptive algorithm for spatial greyscale,” Proc. of the Sc. for Inf. Disp. 17, 75–77 (1976).
  3. M. Broja, F. Wyrowski, O. Bryngdahl, “Digital halftoning by iterative procedure,” Opt. Commun. 69, 205–210 (1989).
    [CrossRef]
  4. M. A. Seldowitz, J. P. Allebach, D. W. Sweeney, “Synthesis of digital holograms by direct binary search,” Appl. Opt. 26, 2788–2798 (1987).
    [CrossRef] [PubMed]
  5. D. Anastassiou, S. Kollias, “Digital image halftoning using neural nets,” in Visual Communications and Image Processing ’88, III, T. R. Hsing, ed., Proc. SPIE1001, 1062–1069 (1988).
    [CrossRef]
  6. B. Julesz, “Visual pattern discrimination,”IRE Trans. Inf. Theory IT-8, 84–92 (1962).
    [CrossRef]
  7. B. Julesz, E. N. Gilbert, L. A. Shepp, “Inability of humans to discriminate between visual textures that agree in second-order statistics—revisited,” Perception 2, 391–405 (1973).
    [CrossRef]
  8. R. M. Haralick, “Statistical and structural approaches to texture,” Proc. IEEE 67, 786–804 (1979).
    [CrossRef]
  9. W. K. Pratt, O. D. Faugeras, A. Gagalowicz, “Application of stochastic texture field models to image processing,” Proc. IEEE 69, 542–551 (1981).
    [CrossRef]
  10. S. Weissbach, O. Bryngdahl, “Control of halftone texture by error diffusion,” Opt. Commun. 103, 174–180 (1993).
    [CrossRef]
  11. T. Scheermesser, O. Bryngdahl, “Digital halftoning with texture control,” Electron. Publ. 6(3), 207–212 (1993).
  12. T. Scheermesser, O. Bryngdahl, “Texture metric of halftone images,”J. Opt. Soc. Am. 13, 18–24 (1996).
    [CrossRef]
  13. G. Dueck, T. Scheuer, “Threshold accepting: a general purpose optimization algorithm appearing superior to simulated annealing,”J. Comput. Phys. 90, 161–175 (1990).
    [CrossRef]
  14. Joseph W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  15. R. Ulichney, “Dithering with blue noise,” Proc. IEEE 76, 56–79 (1988).
    [CrossRef]

1996 (1)

T. Scheermesser, O. Bryngdahl, “Texture metric of halftone images,”J. Opt. Soc. Am. 13, 18–24 (1996).
[CrossRef]

1993 (2)

S. Weissbach, O. Bryngdahl, “Control of halftone texture by error diffusion,” Opt. Commun. 103, 174–180 (1993).
[CrossRef]

T. Scheermesser, O. Bryngdahl, “Digital halftoning with texture control,” Electron. Publ. 6(3), 207–212 (1993).

1990 (1)

G. Dueck, T. Scheuer, “Threshold accepting: a general purpose optimization algorithm appearing superior to simulated annealing,”J. Comput. Phys. 90, 161–175 (1990).
[CrossRef]

1989 (1)

M. Broja, F. Wyrowski, O. Bryngdahl, “Digital halftoning by iterative procedure,” Opt. Commun. 69, 205–210 (1989).
[CrossRef]

1988 (1)

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

1987 (1)

1981 (1)

W. K. Pratt, O. D. Faugeras, A. Gagalowicz, “Application of stochastic texture field models to image processing,” Proc. IEEE 69, 542–551 (1981).
[CrossRef]

1979 (1)

R. M. Haralick, “Statistical and structural approaches to texture,” Proc. IEEE 67, 786–804 (1979).
[CrossRef]

1976 (1)

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

1973 (2)

B. Julesz, E. N. Gilbert, L. A. Shepp, “Inability of humans to discriminate between visual textures that agree in second-order statistics—revisited,” Perception 2, 391–405 (1973).
[CrossRef]

B. E. Bayer, “An optimum method for two-level rendition of continuous tone pictures,” Proc. IEEE 1, 26-11–26-15 (1973).

1962 (1)

B. Julesz, “Visual pattern discrimination,”IRE Trans. Inf. Theory IT-8, 84–92 (1962).
[CrossRef]

Allebach, J. P.

Anastassiou, D.

D. Anastassiou, S. Kollias, “Digital image halftoning using neural nets,” in Visual Communications and Image Processing ’88, III, T. R. Hsing, ed., Proc. SPIE1001, 1062–1069 (1988).
[CrossRef]

Bayer, B. E.

B. E. Bayer, “An optimum method for two-level rendition of continuous tone pictures,” Proc. IEEE 1, 26-11–26-15 (1973).

Broja, M.

M. Broja, F. Wyrowski, O. Bryngdahl, “Digital halftoning by iterative procedure,” Opt. Commun. 69, 205–210 (1989).
[CrossRef]

Bryngdahl, O.

T. Scheermesser, O. Bryngdahl, “Texture metric of halftone images,”J. Opt. Soc. Am. 13, 18–24 (1996).
[CrossRef]

T. Scheermesser, O. Bryngdahl, “Digital halftoning with texture control,” Electron. Publ. 6(3), 207–212 (1993).

S. Weissbach, O. Bryngdahl, “Control of halftone texture by error diffusion,” Opt. Commun. 103, 174–180 (1993).
[CrossRef]

M. Broja, F. Wyrowski, O. Bryngdahl, “Digital halftoning by iterative procedure,” Opt. Commun. 69, 205–210 (1989).
[CrossRef]

Dueck, G.

G. Dueck, T. Scheuer, “Threshold accepting: a general purpose optimization algorithm appearing superior to simulated annealing,”J. Comput. Phys. 90, 161–175 (1990).
[CrossRef]

Faugeras, O. D.

W. K. Pratt, O. D. Faugeras, A. Gagalowicz, “Application of stochastic texture field models to image processing,” Proc. IEEE 69, 542–551 (1981).
[CrossRef]

Floyd, R. W.

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

Gagalowicz, A.

W. K. Pratt, O. D. Faugeras, A. Gagalowicz, “Application of stochastic texture field models to image processing,” Proc. IEEE 69, 542–551 (1981).
[CrossRef]

Gilbert, E. N.

B. Julesz, E. N. Gilbert, L. A. Shepp, “Inability of humans to discriminate between visual textures that agree in second-order statistics—revisited,” Perception 2, 391–405 (1973).
[CrossRef]

Goodman, Joseph W.

Joseph W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Haralick, R. M.

R. M. Haralick, “Statistical and structural approaches to texture,” Proc. IEEE 67, 786–804 (1979).
[CrossRef]

Julesz, B.

B. Julesz, E. N. Gilbert, L. A. Shepp, “Inability of humans to discriminate between visual textures that agree in second-order statistics—revisited,” Perception 2, 391–405 (1973).
[CrossRef]

B. Julesz, “Visual pattern discrimination,”IRE Trans. Inf. Theory IT-8, 84–92 (1962).
[CrossRef]

Kollias, S.

D. Anastassiou, S. Kollias, “Digital image halftoning using neural nets,” in Visual Communications and Image Processing ’88, III, T. R. Hsing, ed., Proc. SPIE1001, 1062–1069 (1988).
[CrossRef]

Pratt, W. K.

W. K. Pratt, O. D. Faugeras, A. Gagalowicz, “Application of stochastic texture field models to image processing,” Proc. IEEE 69, 542–551 (1981).
[CrossRef]

Scheermesser, T.

T. Scheermesser, O. Bryngdahl, “Texture metric of halftone images,”J. Opt. Soc. Am. 13, 18–24 (1996).
[CrossRef]

T. Scheermesser, O. Bryngdahl, “Digital halftoning with texture control,” Electron. Publ. 6(3), 207–212 (1993).

Scheuer, T.

G. Dueck, T. Scheuer, “Threshold accepting: a general purpose optimization algorithm appearing superior to simulated annealing,”J. Comput. Phys. 90, 161–175 (1990).
[CrossRef]

Seldowitz, M. A.

Shepp, L. A.

B. Julesz, E. N. Gilbert, L. A. Shepp, “Inability of humans to discriminate between visual textures that agree in second-order statistics—revisited,” Perception 2, 391–405 (1973).
[CrossRef]

Steinberg, L.

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

Sweeney, D. W.

Ulichney, R.

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

Weissbach, S.

S. Weissbach, O. Bryngdahl, “Control of halftone texture by error diffusion,” Opt. Commun. 103, 174–180 (1993).
[CrossRef]

Wyrowski, F.

M. Broja, F. Wyrowski, O. Bryngdahl, “Digital halftoning by iterative procedure,” Opt. Commun. 69, 205–210 (1989).
[CrossRef]

Appl. Opt. (1)

Electron. Publ. (1)

T. Scheermesser, O. Bryngdahl, “Digital halftoning with texture control,” Electron. Publ. 6(3), 207–212 (1993).

IRE Trans. Inf. Theory (1)

B. Julesz, “Visual pattern discrimination,”IRE Trans. Inf. Theory IT-8, 84–92 (1962).
[CrossRef]

J. Comput. Phys. (1)

G. Dueck, T. Scheuer, “Threshold accepting: a general purpose optimization algorithm appearing superior to simulated annealing,”J. Comput. Phys. 90, 161–175 (1990).
[CrossRef]

J. Opt. Soc. Am. (1)

T. Scheermesser, O. Bryngdahl, “Texture metric of halftone images,”J. Opt. Soc. Am. 13, 18–24 (1996).
[CrossRef]

Opt. Commun. (2)

S. Weissbach, O. Bryngdahl, “Control of halftone texture by error diffusion,” Opt. Commun. 103, 174–180 (1993).
[CrossRef]

M. Broja, F. Wyrowski, O. Bryngdahl, “Digital halftoning by iterative procedure,” Opt. Commun. 69, 205–210 (1989).
[CrossRef]

Perception (1)

B. Julesz, E. N. Gilbert, L. A. Shepp, “Inability of humans to discriminate between visual textures that agree in second-order statistics—revisited,” Perception 2, 391–405 (1973).
[CrossRef]

Proc. IEEE (4)

R. M. Haralick, “Statistical and structural approaches to texture,” Proc. IEEE 67, 786–804 (1979).
[CrossRef]

W. K. Pratt, O. D. Faugeras, A. Gagalowicz, “Application of stochastic texture field models to image processing,” Proc. IEEE 69, 542–551 (1981).
[CrossRef]

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

B. E. Bayer, “An optimum method for two-level rendition of continuous tone pictures,” Proc. IEEE 1, 26-11–26-15 (1973).

Proc. of the Sc. for Inf. Disp. (1)

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

Other (2)

Joseph W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

D. Anastassiou, S. Kollias, “Digital image halftoning using neural nets,” in Visual Communications and Image Processing ’88, III, T. R. Hsing, ed., Proc. SPIE1001, 1062–1069 (1988).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Group of four different texels used. The texel pixels are displayed in white; the background pixels, in black. The reference pixel is marked with a circle.

Fig. 2
Fig. 2

Schematic diagram of the TAA.

Fig. 3
Fig. 3

(a), (b) Images generated with an enhancement of texel A. (c) Image generated with a suppression of texel A.

Fig. 4
Fig. 4

(a)–(c) Images generated with increasing enhancement of texel B and decreasing low-pass control.

Fig. 5
Fig. 5

Development of the cost functions σ L 2 and Δ ρ ¯ ( 1 ) during the optimization process for the corresponding images shown in Fig. 4.

Fig. 6
Fig. 6

(a) Halftoned gray wedge {f(m, n)∈[0.8, 1]} generated with an enhancement of texel C. (b) Halftoned gray wedge {f(m, n)∈[0, 0.2]} generated with an enhancement of texel C. (c) Halftoned gray wedge {f(m, n)∈[0.8, 1]} generated with an enhancement of texel C, rotated by 180°.

Fig. 7
Fig. 7

(a)–(c) Images generated with increasing enhancement of texel C and decreasing low-pass control.

Fig. 8
Fig. 8

(a), (b) Images generated with an enhancement of texel C. (c) Halftoned gray wedge {f(m, n)∈[0.8, 1]} generated with an enhancement of texel D.

Tables (3)

Tables Icon

Table 1 Start and Final Values of the Cost Functions σ L 2 and Δ ρ ¯ ( 1 ) for the Images in Figs. 3 and 4, with Symmetric Texels

Tables Icon

Table 2 Start Parameters for the TAA for the Images in Fig. 4 and for Those in Fig. 7 Below

Tables Icon

Table 3 Start and Final Values of the Cost Functions of σ L 2 and Δ ρ ¯ ( 2 ) for the Images in Figs. 6 and 8, with Asymmetric Texels

Equations (9)

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t ( x , t ) = ( ζ , χ ) T δ ( x ζ , y χ ) ,
Δ ρ ¯ ( k ) = ρ u 1 u 2 k + 1 ( m 1 , n 1 ) T ( m l , n l ) T , l = 2 , , k + 1 ( m 1 , n 1 ) ( m k + 1 , n k + 1 ) ρ u 1 u 2 k + 1 ( m 1 , n 1 ) T ( m l , n l ) T , l = 2 , , k + 1 ( m 1 , n 1 ) ( m k + 1 , n k + 1 )
u 2 k + 1 ( i , j ) = { 0 if u 2 ( i , j ) = = u k + 1 ( i , j ) = 0 1 if u 2 ( i , j ) = = u k + 1 ( i , j ) = 1 , u ¯ 2 k + 1 otherwise
ρ u 1 u 2 k + 1 = i , j = 1 N [ u 1 ( i , j ) u ¯ 1 ] [ u 2 k + 1 ( i , j ) u ¯ 2 k + 1 ] N 2 σ u 1 σ u 2 k + 1
σ L 2 = ( μ , ν ) L | G ( μ , ν ) F ( μ , ν ) | 2 ( μ , ν ) L 1 .
σ L 2 ( 1 + δ σ ) σ L 2 Δ ρ ¯ ( k ) ( 1 δ ρ ) Δ ρ ¯ ( k ) ,
g ( m , n ) = g ( j ) ( m , n ) .
δ σ κ σ δ σ , δ ρ κ ρ δ ρ .
Δ ρ ¯ ( k ) ( 1 + δ ρ ) Δ ρ ¯ ( k ) ,

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