Abstract

Digital halftoning is the process of converting a continuous-tone image into an arrangement of printed and not-printed dots distributed to create an illusion of continuous tone. Traditional halftoning algorithms are inappropriate for lenticular screening where multiple images are columnwise multiplexed into a single image with statistically independent gray levels across neighboring columns. As a means of minimizing intercolumn distortion, we introduce iterative tone correction where gray levels of the spliced image are modified to account for dot overlap. The principal advantage of this new technique is that it preserves the ability to use a traditional, stochastic, halftoning algorithm on the component images prior to spatial multiplexing.

© 2006 Optical Society of America

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References

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  1. F. X. Didik, A Brief History of Stereo Images, Printing and Photography from 1692-2001, Tech. Rep. (Didik/Vari-Vue, 2001). http://www.didik.rom/varivue/3dlowbarhist.htm.
  2. M. Lake, "An art form that's precise but friendly enough to wink," "New York Times," May 20, 1999, p. G11.
  3. T. P. Goggins, "Method of producing multidimensional lithographic separations free of moire interference," U.S. patent 5,488,451 (January 30, 1996).
  4. M. Pilu, "Halftoning of lenticular images," U.S. patent application 20030011824 (January 16, 2003).
  5. K. Yano, "Image forming system, apparatus, and method," U.S. patent application 20030067638 (April 10, 2003).
  6. T. N. Pappas and D. L. Neuhoff, "Printer models and error diffusion," IEEE Trans. Image Process. 4, 66-79 (1995).
    [CrossRef] [PubMed]
  7. T. N. Pappas, C. Dong, and D. L. Neuhoff, "Measurement of printer parameters for model-based halftoning," J. Electron. Imaging 2, 193-204 (1993).
    [CrossRef]
  8. D. L. Lau and T. Smith, "Model-based error-diffusion for high-fidelity lenticular screening," Opt. Express 14, 3214-3224 (2006).
    [CrossRef] [PubMed]
  9. M. Broja, R. Eschbach, and O. Bryngdahl, "Stability of active binarization processes," Opt. Commun. 60, 353-358 (1985).
    [CrossRef]
  10. S. Weissbach and F. Wyrowski, "Numerical stability of the error diffusion concept," Opt. Commun. 93, 151-155 (1992).
    [CrossRef]
  11. Z. Fan, "Stability analysis of error diffusion," in Proceedings of the 1993 IEEE International Conference on Acoustics, Speech, and Signal Processing (IEEE, 1993).
    [CrossRef] [PubMed]
  12. Z. Fan, "Stability analysis of color error diffusion," in Proceedings of the IS&T/SPIE Symposium on Electronic Imaging Science and Technology (SPIE, 2000).
  13. R. A. Ulichney, Digital Halftoning (MIT Press, 1987).
  14. R. W. Floyd and L. Steinberg, "An adaptive algorithm for spatial gray-scale," Proc. S.I.D. 17, 75-78 (1976).
  15. R. A. Ulichney, "Dithering with blue noise," Proc. IEEE 76, 56-79 (1988).
    [CrossRef]
  16. D. L. Lau, G. R. Arce, and N. C. Gallagher, "Green-noise digital halftoning," Proc. IEEE 86, 2424-2444 (1998).
  17. R. A. Ulichney, "The void-and-cluster method for dither array generation," in Human Vision, Visual Processing, Digital Displays IV, B. E. Rogowitz and J. P. Allebach, eds., Proc. SPIE 1913, 332-343 (1993).
  18. T. Mitsa and K. J. Parker, "Digital halftoning technique using a blue noise mask," J. Opt. Soc. Am. A 9, 1920-1929 (1992).
    [CrossRef]
  19. M. Yao and K. J. Parker, "Modified approach to the construction of a blue noise mask," J. Electron. Imaging 3, 92-97 (1994).
    [CrossRef]
  20. J. Mulligan, "Methods for spatio-temporal dithering," in SID International Symposium Digest of Technical Papers (Society for Information Display, 1993), pp. 155-158.
  21. D. P. Hilgenberg, T. J. Flohr, C. B. Atkins, J. P. Allebach, and C. A. Bouman, "Least-squares model-based video halftoning," in Human Vision, Visual Processing, and Digital Display V, B.E.Rogowitz and J.P.Allenbach, eds., Proc. SPIE 2179, pp. 207-217 (1994).
  22. C. B. Atkins, T. J. Flohr, D. P. Hilgenberg, C. A. Bouman, and J. P. Allebach, "Model-based color image sequence quantization," in Human Vision, Visual Processing, and Digital Display V, B.E.Rogowitz and J.P.Allenbach, eds., Proc. SPIE 2179, pp. 310-317 (1994).

2006

1995

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

1994

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

1993

T. N. Pappas, C. Dong, and D. L. Neuhoff, "Measurement of printer parameters for model-based halftoning," J. Electron. Imaging 2, 193-204 (1993).
[CrossRef]

1992

S. Weissbach and F. Wyrowski, "Numerical stability of the error diffusion concept," Opt. Commun. 93, 151-155 (1992).
[CrossRef]

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

1988

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

1985

M. Broja, R. Eschbach, and O. Bryngdahl, "Stability of active binarization processes," Opt. Commun. 60, 353-358 (1985).
[CrossRef]

1976

R. W. Floyd and L. Steinberg, "An adaptive algorithm for spatial gray-scale," Proc. S.I.D. 17, 75-78 (1976).

Allebach, J. P.

D. P. Hilgenberg, T. J. Flohr, C. B. Atkins, J. P. Allebach, and C. A. Bouman, "Least-squares model-based video halftoning," in Human Vision, Visual Processing, and Digital Display V, B.E.Rogowitz and J.P.Allenbach, eds., Proc. SPIE 2179, pp. 207-217 (1994).

C. B. Atkins, T. J. Flohr, D. P. Hilgenberg, C. A. Bouman, and J. P. Allebach, "Model-based color image sequence quantization," in Human Vision, Visual Processing, and Digital Display V, B.E.Rogowitz and J.P.Allenbach, eds., Proc. SPIE 2179, pp. 310-317 (1994).

Arce, G. R.

D. L. Lau, G. R. Arce, and N. C. Gallagher, "Green-noise digital halftoning," Proc. IEEE 86, 2424-2444 (1998).

Atkins, C. B.

C. B. Atkins, T. J. Flohr, D. P. Hilgenberg, C. A. Bouman, and J. P. Allebach, "Model-based color image sequence quantization," in Human Vision, Visual Processing, and Digital Display V, B.E.Rogowitz and J.P.Allenbach, eds., Proc. SPIE 2179, pp. 310-317 (1994).

D. P. Hilgenberg, T. J. Flohr, C. B. Atkins, J. P. Allebach, and C. A. Bouman, "Least-squares model-based video halftoning," in Human Vision, Visual Processing, and Digital Display V, B.E.Rogowitz and J.P.Allenbach, eds., Proc. SPIE 2179, pp. 207-217 (1994).

Bouman, C. A.

C. B. Atkins, T. J. Flohr, D. P. Hilgenberg, C. A. Bouman, and J. P. Allebach, "Model-based color image sequence quantization," in Human Vision, Visual Processing, and Digital Display V, B.E.Rogowitz and J.P.Allenbach, eds., Proc. SPIE 2179, pp. 310-317 (1994).

D. P. Hilgenberg, T. J. Flohr, C. B. Atkins, J. P. Allebach, and C. A. Bouman, "Least-squares model-based video halftoning," in Human Vision, Visual Processing, and Digital Display V, B.E.Rogowitz and J.P.Allenbach, eds., Proc. SPIE 2179, pp. 207-217 (1994).

Broja, M.

M. Broja, R. Eschbach, and O. Bryngdahl, "Stability of active binarization processes," Opt. Commun. 60, 353-358 (1985).
[CrossRef]

Bryngdahl, O.

M. Broja, R. Eschbach, and O. Bryngdahl, "Stability of active binarization processes," Opt. Commun. 60, 353-358 (1985).
[CrossRef]

Didik, F. X.

F. X. Didik, A Brief History of Stereo Images, Printing and Photography from 1692-2001, Tech. Rep. (Didik/Vari-Vue, 2001). http://www.didik.rom/varivue/3dlowbarhist.htm.

Dong, C.

T. N. Pappas, C. Dong, and D. L. Neuhoff, "Measurement of printer parameters for model-based halftoning," J. Electron. Imaging 2, 193-204 (1993).
[CrossRef]

Eschbach, R.

M. Broja, R. Eschbach, and O. Bryngdahl, "Stability of active binarization processes," Opt. Commun. 60, 353-358 (1985).
[CrossRef]

Fan, Z.

Z. Fan, "Stability analysis of error diffusion," in Proceedings of the 1993 IEEE International Conference on Acoustics, Speech, and Signal Processing (IEEE, 1993).
[CrossRef] [PubMed]

Z. Fan, "Stability analysis of color error diffusion," in Proceedings of the IS&T/SPIE Symposium on Electronic Imaging Science and Technology (SPIE, 2000).

Flohr, T. J.

C. B. Atkins, T. J. Flohr, D. P. Hilgenberg, C. A. Bouman, and J. P. Allebach, "Model-based color image sequence quantization," in Human Vision, Visual Processing, and Digital Display V, B.E.Rogowitz and J.P.Allenbach, eds., Proc. SPIE 2179, pp. 310-317 (1994).

D. P. Hilgenberg, T. J. Flohr, C. B. Atkins, J. P. Allebach, and C. A. Bouman, "Least-squares model-based video halftoning," in Human Vision, Visual Processing, and Digital Display V, B.E.Rogowitz and J.P.Allenbach, eds., Proc. SPIE 2179, pp. 207-217 (1994).

Floyd, R. W.

R. W. Floyd and L. Steinberg, "An adaptive algorithm for spatial gray-scale," Proc. S.I.D. 17, 75-78 (1976).

Gallagher, N. C.

D. L. Lau, G. R. Arce, and N. C. Gallagher, "Green-noise digital halftoning," Proc. IEEE 86, 2424-2444 (1998).

Goggins, T. P.

T. P. Goggins, "Method of producing multidimensional lithographic separations free of moire interference," U.S. patent 5,488,451 (January 30, 1996).

Hilgenberg, D. P.

D. P. Hilgenberg, T. J. Flohr, C. B. Atkins, J. P. Allebach, and C. A. Bouman, "Least-squares model-based video halftoning," in Human Vision, Visual Processing, and Digital Display V, B.E.Rogowitz and J.P.Allenbach, eds., Proc. SPIE 2179, pp. 207-217 (1994).

C. B. Atkins, T. J. Flohr, D. P. Hilgenberg, C. A. Bouman, and J. P. Allebach, "Model-based color image sequence quantization," in Human Vision, Visual Processing, and Digital Display V, B.E.Rogowitz and J.P.Allenbach, eds., Proc. SPIE 2179, pp. 310-317 (1994).

Lake, M.

M. Lake, "An art form that's precise but friendly enough to wink," "New York Times," May 20, 1999, p. G11.

Lau, D. L.

D. L. Lau and T. Smith, "Model-based error-diffusion for high-fidelity lenticular screening," Opt. Express 14, 3214-3224 (2006).
[CrossRef] [PubMed]

D. L. Lau, G. R. Arce, and N. C. Gallagher, "Green-noise digital halftoning," Proc. IEEE 86, 2424-2444 (1998).

Mitsa, T.

Mulligan, J.

J. Mulligan, "Methods for spatio-temporal dithering," in SID International Symposium Digest of Technical Papers (Society for Information Display, 1993), pp. 155-158.

Neuhoff, D. L.

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

T. N. Pappas, C. Dong, and D. L. Neuhoff, "Measurement of printer parameters for model-based halftoning," J. Electron. Imaging 2, 193-204 (1993).
[CrossRef]

Pappas, T. N.

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

T. N. Pappas, C. Dong, and D. L. Neuhoff, "Measurement of printer parameters for model-based halftoning," J. Electron. Imaging 2, 193-204 (1993).
[CrossRef]

Parker, K. J.

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

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

Pilu, M.

M. Pilu, "Halftoning of lenticular images," U.S. patent application 20030011824 (January 16, 2003).

Smith, T.

Steinberg, L.

R. W. Floyd and L. Steinberg, "An adaptive algorithm for spatial gray-scale," Proc. S.I.D. 17, 75-78 (1976).

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, Digital Displays IV, B. E. Rogowitz and J. P. Allebach, eds., Proc. SPIE 1913, 332-343 (1993).

R. A. Ulichney, Digital Halftoning (MIT Press, 1987).

Weissbach, S.

S. Weissbach and F. Wyrowski, "Numerical stability of the error diffusion concept," Opt. Commun. 93, 151-155 (1992).
[CrossRef]

Wyrowski, F.

S. Weissbach and F. Wyrowski, "Numerical stability of the error diffusion concept," Opt. Commun. 93, 151-155 (1992).
[CrossRef]

Yano, K.

K. Yano, "Image forming system, apparatus, and method," U.S. patent application 20030067638 (April 10, 2003).

Yao, M.

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

IEEE Trans. Image Process.

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

J. Electron. Imaging

T. N. Pappas, C. Dong, and D. L. Neuhoff, "Measurement of printer parameters for model-based halftoning," J. Electron. Imaging 2, 193-204 (1993).
[CrossRef]

M. Yao and 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

Opt. Commun.

M. Broja, R. Eschbach, and O. Bryngdahl, "Stability of active binarization processes," Opt. Commun. 60, 353-358 (1985).
[CrossRef]

S. Weissbach and F. Wyrowski, "Numerical stability of the error diffusion concept," Opt. Commun. 93, 151-155 (1992).
[CrossRef]

Opt. Express

Proc. IEEE

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

Proc. S.I.D.

R. W. Floyd and L. Steinberg, "An adaptive algorithm for spatial gray-scale," Proc. S.I.D. 17, 75-78 (1976).

Other

D. L. Lau, G. R. Arce, and N. C. Gallagher, "Green-noise digital halftoning," Proc. IEEE 86, 2424-2444 (1998).

R. A. Ulichney, "The void-and-cluster method for dither array generation," in Human Vision, Visual Processing, Digital Displays IV, B. E. Rogowitz and J. P. Allebach, eds., Proc. SPIE 1913, 332-343 (1993).

J. Mulligan, "Methods for spatio-temporal dithering," in SID International Symposium Digest of Technical Papers (Society for Information Display, 1993), pp. 155-158.

D. P. Hilgenberg, T. J. Flohr, C. B. Atkins, J. P. Allebach, and C. A. Bouman, "Least-squares model-based video halftoning," in Human Vision, Visual Processing, and Digital Display V, B.E.Rogowitz and J.P.Allenbach, eds., Proc. SPIE 2179, pp. 207-217 (1994).

C. B. Atkins, T. J. Flohr, D. P. Hilgenberg, C. A. Bouman, and J. P. Allebach, "Model-based color image sequence quantization," in Human Vision, Visual Processing, and Digital Display V, B.E.Rogowitz and J.P.Allenbach, eds., Proc. SPIE 2179, pp. 310-317 (1994).

Z. Fan, "Stability analysis of error diffusion," in Proceedings of the 1993 IEEE International Conference on Acoustics, Speech, and Signal Processing (IEEE, 1993).
[CrossRef] [PubMed]

Z. Fan, "Stability analysis of color error diffusion," in Proceedings of the IS&T/SPIE Symposium on Electronic Imaging Science and Technology (SPIE, 2000).

R. A. Ulichney, Digital Halftoning (MIT Press, 1987).

F. X. Didik, A Brief History of Stereo Images, Printing and Photography from 1692-2001, Tech. Rep. (Didik/Vari-Vue, 2001). http://www.didik.rom/varivue/3dlowbarhist.htm.

M. Lake, "An art form that's precise but friendly enough to wink," "New York Times," May 20, 1999, p. G11.

T. P. Goggins, "Method of producing multidimensional lithographic separations free of moire interference," U.S. patent 5,488,451 (January 30, 1996).

M. Pilu, "Halftoning of lenticular images," U.S. patent application 20030011824 (January 16, 2003).

K. Yano, "Image forming system, apparatus, and method," U.S. patent application 20030067638 (April 10, 2003).

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Figures (22)

Fig. 1
Fig. 1

Illustration of the lenticular imaging process where (top center) images are divided into strips and are interlaced together into a graphic (right), the graphic is printed directly onto the back of an extruded lens, and (bottom left) the lenticule isolates and magnifies the interlaced image beneath, depending on the angle of observation, such that if the lenticule runs vertically, then a different image is delivered to each eye to create a 3D image. If the lenticule runs horizontally, then a rotation of the lens array creates an animation effect. Reproduced by permission of Barry Johnson, www.lenstar.org.

Fig. 2
Fig. 2

Component images of a 12-frame lenticular sequence. The original dolphin image is available at http://www.uglydogart.com/nature/index.htm. Reproduced by permission of John Connell, Uglydogart.

Fig. 3
Fig. 3

Close up of the spatially multiplexed, lenticular image where each component image is spliced into two, consecutive image columns under each lens.

Fig. 4
Fig. 4

Simulated visual response to the first lenticular image when halftoning is performed by means of error diffusion after spatial multiplexing.

Fig. 5
Fig. 5

Simulated visual response to the first lenticular image when halftoning is performed by means of error diffusion prior to spatial multiplexing.

Fig. 6
Fig. 6

Simulated visual response to the first lenticular image when halftoning is performed by means of error diffusion prior to spatial multiplexing using a printer model and tone correction.

Fig. 7
Fig. 7

Simulated visual response to the first lenticular image when halftoning is performed by means of model-based error diffusion after spatial multiplexing.

Fig. 8
Fig. 8

Lenticular image composed of nine images under each lens with one pixel column per component image.

Fig. 9
Fig. 9

Center, left-, and right-side dot overlap profiles for the simulated printed-dot model.

Fig. 10
Fig. 10

First lenticular image after four iterations of tone correction.

Fig. 11
Fig. 11

First lenticular image after four iterations of tone correction with selected regions histogram equalized.

Fig. 12
Fig. 12

Predicted visual response to the first lenticular image from Fig. 10.

Fig. 13
Fig. 13

Relative position of pixels for extracting g A , g B , and g C for (left) iterative and (right) single-pass lenticular tone correction.

Fig. 14
Fig. 14

First lenticular image after single-pass tone correction.

Fig. 15
Fig. 15

First lenticular image after single-pass tone correction with selected regions histogram equalized.

Fig. 16
Fig. 16

Lenticular image composed of nine images under each lens with three pixel columns per component image.

Fig. 17
Fig. 17

Pixel maps showing the pixels (in black) from the first component image corresponding to (left) light-gray pixels subject to gamut reduction and (right) dark-gray pixels responsible for gamut reduction in neighboring component images for (top) T = 1.0 , (center) T = 1.1 , and (bottom) T = 1.2 .

Fig. 18
Fig. 18

Simulated visual response to the first component image using three iterations of ITC and gamut compensation with T = 1.0 and α = 0.05 .

Fig. 19
Fig. 19

Simulated visual response to the first component image using three iterations of ITC and gamut compensation with T = 1.0 and α = 0.1 .

Fig. 20
Fig. 20

Simulated visual response to the first component image using three iterations of ITC and gamut compensation with T = 1.0 and α = 0.2 .

Fig. 21
Fig. 21

Close-ups of the simulated visual responses of Figs. 18, 19, 20.

Fig. 22
Fig. 22

Stereoscopic halftone pair where (top) images are identical and (bottom) images are independently generated.

Equations (10)

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

g B = LUT r ( g A ( 1 ) ) × LUT c ( g B ( 1 ) ) ,
g I = 1 2 { LUT r [ g H ( 1 ) ] × LUT c [ g I ( 1 ) ] } + 1 2 { LUT c [ g I ( 1 ) ] × LUT l [ g A ( 1 ) ] } = 1 2 LUT c [ g I ( 1 ) ] × { LUT r [ g H ( 1 ) ] + LUT r [ g A ( 1 ) ] } ,
g A = 1 2 LUT c [ g A ( i ) ] × { LUT r [ g I ( i l ) ] + LUT r [ g B ( i l ) ] } ,
g A l = 1 2 [ LUT r , m ( g I r , ( i 1 ) ) × LUT c ( g A l , ( i ) ) ] + 1 2 [ LUT c ( g A l , ( i ) ) + LUT l , a ( g A c , ( i 1 ) ) ] ,
g A c = 1 2 [ LUT r , a ( g A l , ( i ) ) + LUT c ( g A c , ( i ) ) ] + 1 2 [ LUT c ( g A c , ( i ) ) + LUT l , a ( g A r , ( i 1 ) ) ] ,
g A r = 1 2 [ LUT r , a ( g A c , ( i ) ) + LUT c ( g A r , ( i ) ) ] + 1 2 [ LUT c ( g A r , ( i ) ) × LUT l , m ( g B l , ( i 1 ) ) ] ,
LUT c ( g A ( i ) ) = 2.0 × g A LUT r ( g I ( i 1 ) ) + LUT r ( g B ( i 1 ) ) ,
e l = g A LUT r ( g I ( i 1 ) ) , e r = g A LUT r ( g B ( i 1 ) ) .
g E = g E + α e l ,
g B = g B + α e r ,

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