Abstract

Error diffusion is an important procedure for image and hologram quantization. The spatial distribution of the spectrum of the quantization noise is shaped by a filter function, which depends on the diffusion weights. The customary weights applied during the whole quantization process are optimized to yield the desired filter functions. Stability restrictions limit the optimization process. We suggest optimizing new weights locally after the quantization of each pixel. In this way the eventual occurrence of instabilities can be counteracted and the quality of the filter function improved.

© 1998 Optical Society of America

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References

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  1. R. W. Floyd and L. Steinberg, Proc. Soc. Inf. Disp. 17, 75 (1976).
  2. S. Weissbach and F. Wyrowski, Appl. Opt. 31, 2518 (1992).
    [CrossRef] [PubMed]
  3. R. Eschbach, J. Electron. Imag. 2, 352 (1993).
    [CrossRef]
  4. F. Fetthauer, S. Weissbach, and O. Bryngdahl, Opt. Commun. 94, 44 (1992).
    [CrossRef]
  5. P. van den Bulck, in Proceedings of the Workshop on Circuits, Systems and Signal Processing (Institute of Electrical and Electronics Engineers, Piscataway, N. J., 1992), pp. 271–276.
  6. M. Broja, R. Eschbach, and O. Bryngdahl, Opt. Commun. 60, 353 (1986).
    [CrossRef]
  7. S. Weissbach and F. Wyrowski, Opt. Commun. 93, 151 (1992).
    [CrossRef]
  8. F. Fetthauer, S. Weissbach, and O. Bryngdahl, Opt. Commun. 113, 365 (1995).
    [CrossRef]
  9. B. E. Bayer, in Proceedings of the IEEE International Conference on Communication (Institute of Electrical and Electronics Engineers, New York, 1973), pp. 26-11–26-15.
  10. M. Broja, F. Wyrowski, and O. Bryngdahl, Opt. Commun. 69, 205 (1989).
    [CrossRef]

1995 (1)

F. Fetthauer, S. Weissbach, and O. Bryngdahl, Opt. Commun. 113, 365 (1995).
[CrossRef]

1993 (1)

R. Eschbach, J. Electron. Imag. 2, 352 (1993).
[CrossRef]

1992 (3)

F. Fetthauer, S. Weissbach, and O. Bryngdahl, Opt. Commun. 94, 44 (1992).
[CrossRef]

S. Weissbach and F. Wyrowski, Appl. Opt. 31, 2518 (1992).
[CrossRef] [PubMed]

S. Weissbach and F. Wyrowski, Opt. Commun. 93, 151 (1992).
[CrossRef]

1989 (1)

M. Broja, F. Wyrowski, and O. Bryngdahl, Opt. Commun. 69, 205 (1989).
[CrossRef]

1986 (1)

M. Broja, R. Eschbach, and O. Bryngdahl, Opt. Commun. 60, 353 (1986).
[CrossRef]

1976 (1)

R. W. Floyd and L. Steinberg, Proc. Soc. Inf. Disp. 17, 75 (1976).

Bayer, B. E.

B. E. Bayer, in Proceedings of the IEEE International Conference on Communication (Institute of Electrical and Electronics Engineers, New York, 1973), pp. 26-11–26-15.

Broja, M.

M. Broja, F. Wyrowski, and O. Bryngdahl, Opt. Commun. 69, 205 (1989).
[CrossRef]

M. Broja, R. Eschbach, and O. Bryngdahl, Opt. Commun. 60, 353 (1986).
[CrossRef]

Bryngdahl, O.

F. Fetthauer, S. Weissbach, and O. Bryngdahl, Opt. Commun. 113, 365 (1995).
[CrossRef]

F. Fetthauer, S. Weissbach, and O. Bryngdahl, Opt. Commun. 94, 44 (1992).
[CrossRef]

M. Broja, F. Wyrowski, and O. Bryngdahl, Opt. Commun. 69, 205 (1989).
[CrossRef]

M. Broja, R. Eschbach, and O. Bryngdahl, Opt. Commun. 60, 353 (1986).
[CrossRef]

Eschbach, R.

R. Eschbach, J. Electron. Imag. 2, 352 (1993).
[CrossRef]

M. Broja, R. Eschbach, and O. Bryngdahl, Opt. Commun. 60, 353 (1986).
[CrossRef]

Fetthauer, F.

F. Fetthauer, S. Weissbach, and O. Bryngdahl, Opt. Commun. 113, 365 (1995).
[CrossRef]

F. Fetthauer, S. Weissbach, and O. Bryngdahl, Opt. Commun. 94, 44 (1992).
[CrossRef]

Floyd, R. W.

R. W. Floyd and L. Steinberg, Proc. Soc. Inf. Disp. 17, 75 (1976).

Steinberg, L.

R. W. Floyd and L. Steinberg, Proc. Soc. Inf. Disp. 17, 75 (1976).

van den Bulck, P.

P. van den Bulck, in Proceedings of the Workshop on Circuits, Systems and Signal Processing (Institute of Electrical and Electronics Engineers, Piscataway, N. J., 1992), pp. 271–276.

Weissbach, S.

F. Fetthauer, S. Weissbach, and O. Bryngdahl, Opt. Commun. 113, 365 (1995).
[CrossRef]

S. Weissbach and F. Wyrowski, Appl. Opt. 31, 2518 (1992).
[CrossRef] [PubMed]

F. Fetthauer, S. Weissbach, and O. Bryngdahl, Opt. Commun. 94, 44 (1992).
[CrossRef]

S. Weissbach and F. Wyrowski, Opt. Commun. 93, 151 (1992).
[CrossRef]

Wyrowski, F.

S. Weissbach and F. Wyrowski, Opt. Commun. 93, 151 (1992).
[CrossRef]

S. Weissbach and F. Wyrowski, Appl. Opt. 31, 2518 (1992).
[CrossRef] [PubMed]

M. Broja, F. Wyrowski, and O. Bryngdahl, Opt. Commun. 69, 205 (1989).
[CrossRef]

Appl. Opt. (1)

J. Electron. Imag. (1)

R. Eschbach, J. Electron. Imag. 2, 352 (1993).
[CrossRef]

Opt. Commun. (5)

F. Fetthauer, S. Weissbach, and O. Bryngdahl, Opt. Commun. 94, 44 (1992).
[CrossRef]

M. Broja, R. Eschbach, and O. Bryngdahl, Opt. Commun. 60, 353 (1986).
[CrossRef]

S. Weissbach and F. Wyrowski, Opt. Commun. 93, 151 (1992).
[CrossRef]

F. Fetthauer, S. Weissbach, and O. Bryngdahl, Opt. Commun. 113, 365 (1995).
[CrossRef]

M. Broja, F. Wyrowski, and O. Bryngdahl, Opt. Commun. 69, 205 (1989).
[CrossRef]

Proc. Soc. Inf. Disp. (1)

R. W. Floyd and L. Steinberg, Proc. Soc. Inf. Disp. 17, 75 (1976).

Other (2)

B. E. Bayer, in Proceedings of the IEEE International Conference on Communication (Institute of Electrical and Electronics Engineers, New York, 1973), pp. 26-11–26-15.

P. van den Bulck, in Proceedings of the Workshop on Circuits, Systems and Signal Processing (Institute of Electrical and Electronics Engineers, Piscataway, N. J., 1992), pp. 271–276.

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Figures (3)

Fig. 1
Fig. 1

(a) Gray-tone test image; (b) quantized version with instabilities.

Fig. 2
Fig. 2

(a) Image quantized by the error diffusion algorithm with globally optimized weights with α=0.05; (b) spectrum of the quantization noise.

Fig. 3
Fig. 3

Image quantized by the error diffusion algorithm with (a) locally optimized weights α=0.01 and (b) globally optimized weights α=0.01.

Equations (12)

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fcm, n=fm, n+r, sdr, secm-r, n-s,
gm, n=Pfcm, n
ecm, n=fcm, n-gm, n
em, n=fm, n-gm, n
Ek, l=Hk, lEck, l,
Hk, l=-1+r, sdr, sexp2πikr+ls.
N=k, lFEk, l2=k, lFHk, l2Eck, l2.
I=k, lFHk, l2.
Iˆ=k, lFHk, l2+αr, sdr, s2.
fpcm, n=fm, n+r, sdr, sqm-r, n-s×ecm-r, n-s,
qm, n=1if pixel m, n has been quantized already0otherwise.
-1-fpcma+r, na+secma, nadr, s1-fpcma+r, na+secma, na,

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