Abstract

A hybrid optical/electronic system performs median filtering and related ranked-order operations using threshold decomposition to encode the image. Threshold decomposition transforms the nonlinear neighborhood ranking operation into a linear space-invariant filtering step followed by a point-to-point threshold comparison step. Spatial multiplexing allows parallel processing of all the threshold components as well as recombination by a second linear space-invariant filtering step. An incoherent optical correlation system performs the linear filtering, using a magnetooptic spatial light modulator as the input device and a computer-generated hologram in the filter plane. Thresholding is done electronically. By adjusting the value of the threshold, the same architecture is used to perform median, minimum, and maximum filtering of images.

© 1987 Optical Society of America

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References

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  1. J. W. Tukey, Exploratory Data Analysis (Addison-Wesley, Reading, MA, 1977).
  2. N. C. Gallagher, G. L. Wise, “A Theoretical Analysis of the Properties of Median Filters,” IEEE Trans. Acoust. Speech Signal Process. ASSP-29, 1136 (1981).
    [CrossRef]
  3. T. S. Huang, G. J. Yang, “Median Filters and Their Applications to Image Processing,” School of Electronic Engineering, Purdue U., West Lafayette, IN, Tech. Rep. EE 80-1 (Jan.1980).
  4. A. C. Bovik, T. S. Huang, D. C. Munson, “A Generalization of Median Filtering using Linear Combinations of Order Statistics,” IEEE Trans. Acoust. Speech Signal Process. ASSP-31, 1342 (1983).
    [CrossRef]
  5. A. Rosenfeld, A. C. Kak, Digital Picture Processing, Vol. 2 (Academic, New York, 1982), Chap. 11.
  6. Y. Nakagawa, A. Rosenfeld, “A Note on the Use of Local Min and Max Operations in Digital Picture Processing,” IEEE Trans. Syst. Man Cybernet. SMC-8, 632 (1978).
  7. J. Serra, Image Analysis and Mathematical Morphology (Academic, London, 1982), Chap. 2.
  8. T. S. Huang, G. J. Yang, G. Y. Tang, “A Fast Two-Dimensional Median Filtering Algorithm,” IEEE Trans. Acoust. Speech Signal Process. ASSP-27, 13 (1979).
    [CrossRef]
  9. G. R. Arce, P. J. Warter, “A Median Filter Architecture Suitable for VLSI Implementation,” in Proceedings, Twenty-second Annual Allerton Conference on Communication, Control, and Computing, Monticello, IL, 3–5 Oct. 1984, p. 172.
  10. J. P. Fitch, E. J. Coyle, N. C. Gallagher, “Median Filtering by Threshold Decomposition,” IEEE Trans. Acoust. Speech Signal Process. ASSP-32, 1183 (1984).
    [CrossRef]
  11. J. P. Fitch, E. J. Coyle, N. C. Gallagher, “Threshold Decomposition of Multidimensional Ranked-Order Operations,” IEEE Trans. Circuits Syst. CAS-32, 445 (1985).
    [CrossRef]
  12. D. E. Dudgeon, R. M. Mersereau, Multidimensional Digital Signal Processing (Prentice-Hall, Englewood Cliffs, NJ, 1984), pp. 116–118.
  13. W. T. Rhodes, A. A. Sawchuk, “Incoherent Optical Processing,” in Optical Information Processing, S. H. Lee, Ed. (Springer-Verlag, Berlin, 1981).
    [CrossRef]
  14. H. Bartelt, S. K. Case, R. Hauck, “Incoherent-Optical Processing,” in Applications of Optical Fourier Transforms, H. Stark, Ed. (Academic, Orlando, FL, 1982).
    [CrossRef]
  15. W. E. Ross, K. M. Snapp, R. H. Anderson, “Fundamental Characteristics of the Litton Iron Garnet Magneto-optic Spatial Light Modulator,” Proc. Soc. Photo-Opt. Instrum. Eng. 388, 55 (1983).
  16. N. C. Gallagher, J. A. Bucklew, “Nondetour Phase Digital Holograms; An Analysis,” Appl. Opt. 19, 4266 (1980).
    [CrossRef] [PubMed]
  17. “MEBES Software Manual A900-0102G,” Perkin-Elmer Electron Beam Technology, 26460 Corporate Ave., Hayward, CA 94545.
  18. Micro Mask, Inc., 695 Vaqueros Ave., Sunnyvale, CA 94086.
  19. S. A. Benton, “Special Problems: Photographic Materials and their Handling,” in Handbook of Optical Holography, H. J. Caulfield, Ed. (Academic, New York, 1979).
  20. Chalnicon is a trademark of Toshiba.
  21. R. G. Harber, S. C. Bass, G. Neudeck, “VLSI Implementation of a Fast Rank Order Algorithm,” in Proceedings, International Conference on Acoustics, Speech, and Signal Processing ’85 (1985), p. 1396.
    [CrossRef]
  22. J. P. Fitch, “Software and VLSI Algorithms for Generalized Ranked Order Filtering,” IEEE Trans. Circuits Syst. in press, 1987. (UCRL-92674, Mar. 1985).
    [CrossRef]
  23. R. G. Harber, S. C. Bass, J. P. Fitch, E. J. Coyle, N. C. Gallagher, “The VLSI Implementation of Rank Order Filters,” Proc. IEEE submitted for publication June1986.
  24. K. S. O’Neill, W. T. Rhodes, “Morphological Transformations by Hybrid Optical-Electronic Methods,” Proc. Soc. Photo-Opt. Instrum. Eng. 638, 41 (1986).
  25. P. D. Wendt, E. J. Coyle, N. C. Gallagher, “Stack Filters,” IEEE Trans. Acoust. Speech Signal Process. ASSP-34, 898 (1986).
    [CrossRef]
  26. E. N. Gilbert, “Lattice-Theoretic Properties of Frontal Switching Functions,” J. Math. Phys. 33, 57 (1954).
  27. P. A. Maragos, R. W. Schafer, “A Unification of Linear, Median, Order-Statistics, and Morphological Filters under Mathematical Morphology,” in Proceedings, International Conference on Acoustics, Speech, and Signal Processing (1985), p. 1329.
  28. J. L. Jewell, Y. H. Lee, H. M. Gibbs, N. Peyghambarian, A. C. Gossard, W. Wiegmann, “3-pJ, 82-MHz Optical Logic Gates in a Room-Temperature GaAs-AlGaAs Multiple-Quantum-Well Etalon,” Appl. Phys. Lett. 46, 918 (1985).
    [CrossRef]

1986 (2)

K. S. O’Neill, W. T. Rhodes, “Morphological Transformations by Hybrid Optical-Electronic Methods,” Proc. Soc. Photo-Opt. Instrum. Eng. 638, 41 (1986).

P. D. Wendt, E. J. Coyle, N. C. Gallagher, “Stack Filters,” IEEE Trans. Acoust. Speech Signal Process. ASSP-34, 898 (1986).
[CrossRef]

1985 (2)

J. P. Fitch, E. J. Coyle, N. C. Gallagher, “Threshold Decomposition of Multidimensional Ranked-Order Operations,” IEEE Trans. Circuits Syst. CAS-32, 445 (1985).
[CrossRef]

J. L. Jewell, Y. H. Lee, H. M. Gibbs, N. Peyghambarian, A. C. Gossard, W. Wiegmann, “3-pJ, 82-MHz Optical Logic Gates in a Room-Temperature GaAs-AlGaAs Multiple-Quantum-Well Etalon,” Appl. Phys. Lett. 46, 918 (1985).
[CrossRef]

1984 (1)

J. P. Fitch, E. J. Coyle, N. C. Gallagher, “Median Filtering by Threshold Decomposition,” IEEE Trans. Acoust. Speech Signal Process. ASSP-32, 1183 (1984).
[CrossRef]

1983 (2)

W. E. Ross, K. M. Snapp, R. H. Anderson, “Fundamental Characteristics of the Litton Iron Garnet Magneto-optic Spatial Light Modulator,” Proc. Soc. Photo-Opt. Instrum. Eng. 388, 55 (1983).

A. C. Bovik, T. S. Huang, D. C. Munson, “A Generalization of Median Filtering using Linear Combinations of Order Statistics,” IEEE Trans. Acoust. Speech Signal Process. ASSP-31, 1342 (1983).
[CrossRef]

1981 (1)

N. C. Gallagher, G. L. Wise, “A Theoretical Analysis of the Properties of Median Filters,” IEEE Trans. Acoust. Speech Signal Process. ASSP-29, 1136 (1981).
[CrossRef]

1980 (1)

1979 (1)

T. S. Huang, G. J. Yang, G. Y. Tang, “A Fast Two-Dimensional Median Filtering Algorithm,” IEEE Trans. Acoust. Speech Signal Process. ASSP-27, 13 (1979).
[CrossRef]

1978 (1)

Y. Nakagawa, A. Rosenfeld, “A Note on the Use of Local Min and Max Operations in Digital Picture Processing,” IEEE Trans. Syst. Man Cybernet. SMC-8, 632 (1978).

1954 (1)

E. N. Gilbert, “Lattice-Theoretic Properties of Frontal Switching Functions,” J. Math. Phys. 33, 57 (1954).

Anderson, R. H.

W. E. Ross, K. M. Snapp, R. H. Anderson, “Fundamental Characteristics of the Litton Iron Garnet Magneto-optic Spatial Light Modulator,” Proc. Soc. Photo-Opt. Instrum. Eng. 388, 55 (1983).

Arce, G. R.

G. R. Arce, P. J. Warter, “A Median Filter Architecture Suitable for VLSI Implementation,” in Proceedings, Twenty-second Annual Allerton Conference on Communication, Control, and Computing, Monticello, IL, 3–5 Oct. 1984, p. 172.

Bartelt, H.

H. Bartelt, S. K. Case, R. Hauck, “Incoherent-Optical Processing,” in Applications of Optical Fourier Transforms, H. Stark, Ed. (Academic, Orlando, FL, 1982).
[CrossRef]

Bass, S. C.

R. G. Harber, S. C. Bass, G. Neudeck, “VLSI Implementation of a Fast Rank Order Algorithm,” in Proceedings, International Conference on Acoustics, Speech, and Signal Processing ’85 (1985), p. 1396.
[CrossRef]

R. G. Harber, S. C. Bass, J. P. Fitch, E. J. Coyle, N. C. Gallagher, “The VLSI Implementation of Rank Order Filters,” Proc. IEEE submitted for publication June1986.

Benton, S. A.

S. A. Benton, “Special Problems: Photographic Materials and their Handling,” in Handbook of Optical Holography, H. J. Caulfield, Ed. (Academic, New York, 1979).

Bovik, A. C.

A. C. Bovik, T. S. Huang, D. C. Munson, “A Generalization of Median Filtering using Linear Combinations of Order Statistics,” IEEE Trans. Acoust. Speech Signal Process. ASSP-31, 1342 (1983).
[CrossRef]

Bucklew, J. A.

Case, S. K.

H. Bartelt, S. K. Case, R. Hauck, “Incoherent-Optical Processing,” in Applications of Optical Fourier Transforms, H. Stark, Ed. (Academic, Orlando, FL, 1982).
[CrossRef]

Coyle, E. J.

P. D. Wendt, E. J. Coyle, N. C. Gallagher, “Stack Filters,” IEEE Trans. Acoust. Speech Signal Process. ASSP-34, 898 (1986).
[CrossRef]

J. P. Fitch, E. J. Coyle, N. C. Gallagher, “Threshold Decomposition of Multidimensional Ranked-Order Operations,” IEEE Trans. Circuits Syst. CAS-32, 445 (1985).
[CrossRef]

J. P. Fitch, E. J. Coyle, N. C. Gallagher, “Median Filtering by Threshold Decomposition,” IEEE Trans. Acoust. Speech Signal Process. ASSP-32, 1183 (1984).
[CrossRef]

R. G. Harber, S. C. Bass, J. P. Fitch, E. J. Coyle, N. C. Gallagher, “The VLSI Implementation of Rank Order Filters,” Proc. IEEE submitted for publication June1986.

Dudgeon, D. E.

D. E. Dudgeon, R. M. Mersereau, Multidimensional Digital Signal Processing (Prentice-Hall, Englewood Cliffs, NJ, 1984), pp. 116–118.

Fitch, J. P.

J. P. Fitch, E. J. Coyle, N. C. Gallagher, “Threshold Decomposition of Multidimensional Ranked-Order Operations,” IEEE Trans. Circuits Syst. CAS-32, 445 (1985).
[CrossRef]

J. P. Fitch, E. J. Coyle, N. C. Gallagher, “Median Filtering by Threshold Decomposition,” IEEE Trans. Acoust. Speech Signal Process. ASSP-32, 1183 (1984).
[CrossRef]

R. G. Harber, S. C. Bass, J. P. Fitch, E. J. Coyle, N. C. Gallagher, “The VLSI Implementation of Rank Order Filters,” Proc. IEEE submitted for publication June1986.

J. P. Fitch, “Software and VLSI Algorithms for Generalized Ranked Order Filtering,” IEEE Trans. Circuits Syst. in press, 1987. (UCRL-92674, Mar. 1985).
[CrossRef]

Gallagher, N. C.

P. D. Wendt, E. J. Coyle, N. C. Gallagher, “Stack Filters,” IEEE Trans. Acoust. Speech Signal Process. ASSP-34, 898 (1986).
[CrossRef]

J. P. Fitch, E. J. Coyle, N. C. Gallagher, “Threshold Decomposition of Multidimensional Ranked-Order Operations,” IEEE Trans. Circuits Syst. CAS-32, 445 (1985).
[CrossRef]

J. P. Fitch, E. J. Coyle, N. C. Gallagher, “Median Filtering by Threshold Decomposition,” IEEE Trans. Acoust. Speech Signal Process. ASSP-32, 1183 (1984).
[CrossRef]

N. C. Gallagher, G. L. Wise, “A Theoretical Analysis of the Properties of Median Filters,” IEEE Trans. Acoust. Speech Signal Process. ASSP-29, 1136 (1981).
[CrossRef]

N. C. Gallagher, J. A. Bucklew, “Nondetour Phase Digital Holograms; An Analysis,” Appl. Opt. 19, 4266 (1980).
[CrossRef] [PubMed]

R. G. Harber, S. C. Bass, J. P. Fitch, E. J. Coyle, N. C. Gallagher, “The VLSI Implementation of Rank Order Filters,” Proc. IEEE submitted for publication June1986.

Gibbs, H. M.

J. L. Jewell, Y. H. Lee, H. M. Gibbs, N. Peyghambarian, A. C. Gossard, W. Wiegmann, “3-pJ, 82-MHz Optical Logic Gates in a Room-Temperature GaAs-AlGaAs Multiple-Quantum-Well Etalon,” Appl. Phys. Lett. 46, 918 (1985).
[CrossRef]

Gilbert, E. N.

E. N. Gilbert, “Lattice-Theoretic Properties of Frontal Switching Functions,” J. Math. Phys. 33, 57 (1954).

Gossard, A. C.

J. L. Jewell, Y. H. Lee, H. M. Gibbs, N. Peyghambarian, A. C. Gossard, W. Wiegmann, “3-pJ, 82-MHz Optical Logic Gates in a Room-Temperature GaAs-AlGaAs Multiple-Quantum-Well Etalon,” Appl. Phys. Lett. 46, 918 (1985).
[CrossRef]

Harber, R. G.

R. G. Harber, S. C. Bass, G. Neudeck, “VLSI Implementation of a Fast Rank Order Algorithm,” in Proceedings, International Conference on Acoustics, Speech, and Signal Processing ’85 (1985), p. 1396.
[CrossRef]

R. G. Harber, S. C. Bass, J. P. Fitch, E. J. Coyle, N. C. Gallagher, “The VLSI Implementation of Rank Order Filters,” Proc. IEEE submitted for publication June1986.

Hauck, R.

H. Bartelt, S. K. Case, R. Hauck, “Incoherent-Optical Processing,” in Applications of Optical Fourier Transforms, H. Stark, Ed. (Academic, Orlando, FL, 1982).
[CrossRef]

Huang, T. S.

A. C. Bovik, T. S. Huang, D. C. Munson, “A Generalization of Median Filtering using Linear Combinations of Order Statistics,” IEEE Trans. Acoust. Speech Signal Process. ASSP-31, 1342 (1983).
[CrossRef]

T. S. Huang, G. J. Yang, G. Y. Tang, “A Fast Two-Dimensional Median Filtering Algorithm,” IEEE Trans. Acoust. Speech Signal Process. ASSP-27, 13 (1979).
[CrossRef]

T. S. Huang, G. J. Yang, “Median Filters and Their Applications to Image Processing,” School of Electronic Engineering, Purdue U., West Lafayette, IN, Tech. Rep. EE 80-1 (Jan.1980).

Jewell, J. L.

J. L. Jewell, Y. H. Lee, H. M. Gibbs, N. Peyghambarian, A. C. Gossard, W. Wiegmann, “3-pJ, 82-MHz Optical Logic Gates in a Room-Temperature GaAs-AlGaAs Multiple-Quantum-Well Etalon,” Appl. Phys. Lett. 46, 918 (1985).
[CrossRef]

Kak, A. C.

A. Rosenfeld, A. C. Kak, Digital Picture Processing, Vol. 2 (Academic, New York, 1982), Chap. 11.

Lee, Y. H.

J. L. Jewell, Y. H. Lee, H. M. Gibbs, N. Peyghambarian, A. C. Gossard, W. Wiegmann, “3-pJ, 82-MHz Optical Logic Gates in a Room-Temperature GaAs-AlGaAs Multiple-Quantum-Well Etalon,” Appl. Phys. Lett. 46, 918 (1985).
[CrossRef]

Maragos, P. A.

P. A. Maragos, R. W. Schafer, “A Unification of Linear, Median, Order-Statistics, and Morphological Filters under Mathematical Morphology,” in Proceedings, International Conference on Acoustics, Speech, and Signal Processing (1985), p. 1329.

Mersereau, R. M.

D. E. Dudgeon, R. M. Mersereau, Multidimensional Digital Signal Processing (Prentice-Hall, Englewood Cliffs, NJ, 1984), pp. 116–118.

Munson, D. C.

A. C. Bovik, T. S. Huang, D. C. Munson, “A Generalization of Median Filtering using Linear Combinations of Order Statistics,” IEEE Trans. Acoust. Speech Signal Process. ASSP-31, 1342 (1983).
[CrossRef]

Nakagawa, Y.

Y. Nakagawa, A. Rosenfeld, “A Note on the Use of Local Min and Max Operations in Digital Picture Processing,” IEEE Trans. Syst. Man Cybernet. SMC-8, 632 (1978).

Neudeck, G.

R. G. Harber, S. C. Bass, G. Neudeck, “VLSI Implementation of a Fast Rank Order Algorithm,” in Proceedings, International Conference on Acoustics, Speech, and Signal Processing ’85 (1985), p. 1396.
[CrossRef]

O’Neill, K. S.

K. S. O’Neill, W. T. Rhodes, “Morphological Transformations by Hybrid Optical-Electronic Methods,” Proc. Soc. Photo-Opt. Instrum. Eng. 638, 41 (1986).

Peyghambarian, N.

J. L. Jewell, Y. H. Lee, H. M. Gibbs, N. Peyghambarian, A. C. Gossard, W. Wiegmann, “3-pJ, 82-MHz Optical Logic Gates in a Room-Temperature GaAs-AlGaAs Multiple-Quantum-Well Etalon,” Appl. Phys. Lett. 46, 918 (1985).
[CrossRef]

Rhodes, W. T.

K. S. O’Neill, W. T. Rhodes, “Morphological Transformations by Hybrid Optical-Electronic Methods,” Proc. Soc. Photo-Opt. Instrum. Eng. 638, 41 (1986).

W. T. Rhodes, A. A. Sawchuk, “Incoherent Optical Processing,” in Optical Information Processing, S. H. Lee, Ed. (Springer-Verlag, Berlin, 1981).
[CrossRef]

Rosenfeld, A.

Y. Nakagawa, A. Rosenfeld, “A Note on the Use of Local Min and Max Operations in Digital Picture Processing,” IEEE Trans. Syst. Man Cybernet. SMC-8, 632 (1978).

A. Rosenfeld, A. C. Kak, Digital Picture Processing, Vol. 2 (Academic, New York, 1982), Chap. 11.

Ross, W. E.

W. E. Ross, K. M. Snapp, R. H. Anderson, “Fundamental Characteristics of the Litton Iron Garnet Magneto-optic Spatial Light Modulator,” Proc. Soc. Photo-Opt. Instrum. Eng. 388, 55 (1983).

Sawchuk, A. A.

W. T. Rhodes, A. A. Sawchuk, “Incoherent Optical Processing,” in Optical Information Processing, S. H. Lee, Ed. (Springer-Verlag, Berlin, 1981).
[CrossRef]

Schafer, R. W.

P. A. Maragos, R. W. Schafer, “A Unification of Linear, Median, Order-Statistics, and Morphological Filters under Mathematical Morphology,” in Proceedings, International Conference on Acoustics, Speech, and Signal Processing (1985), p. 1329.

Serra, J.

J. Serra, Image Analysis and Mathematical Morphology (Academic, London, 1982), Chap. 2.

Snapp, K. M.

W. E. Ross, K. M. Snapp, R. H. Anderson, “Fundamental Characteristics of the Litton Iron Garnet Magneto-optic Spatial Light Modulator,” Proc. Soc. Photo-Opt. Instrum. Eng. 388, 55 (1983).

Tang, G. Y.

T. S. Huang, G. J. Yang, G. Y. Tang, “A Fast Two-Dimensional Median Filtering Algorithm,” IEEE Trans. Acoust. Speech Signal Process. ASSP-27, 13 (1979).
[CrossRef]

Tukey, J. W.

J. W. Tukey, Exploratory Data Analysis (Addison-Wesley, Reading, MA, 1977).

Warter, P. J.

G. R. Arce, P. J. Warter, “A Median Filter Architecture Suitable for VLSI Implementation,” in Proceedings, Twenty-second Annual Allerton Conference on Communication, Control, and Computing, Monticello, IL, 3–5 Oct. 1984, p. 172.

Wendt, P. D.

P. D. Wendt, E. J. Coyle, N. C. Gallagher, “Stack Filters,” IEEE Trans. Acoust. Speech Signal Process. ASSP-34, 898 (1986).
[CrossRef]

Wiegmann, W.

J. L. Jewell, Y. H. Lee, H. M. Gibbs, N. Peyghambarian, A. C. Gossard, W. Wiegmann, “3-pJ, 82-MHz Optical Logic Gates in a Room-Temperature GaAs-AlGaAs Multiple-Quantum-Well Etalon,” Appl. Phys. Lett. 46, 918 (1985).
[CrossRef]

Wise, G. L.

N. C. Gallagher, G. L. Wise, “A Theoretical Analysis of the Properties of Median Filters,” IEEE Trans. Acoust. Speech Signal Process. ASSP-29, 1136 (1981).
[CrossRef]

Yang, G. J.

T. S. Huang, G. J. Yang, G. Y. Tang, “A Fast Two-Dimensional Median Filtering Algorithm,” IEEE Trans. Acoust. Speech Signal Process. ASSP-27, 13 (1979).
[CrossRef]

T. S. Huang, G. J. Yang, “Median Filters and Their Applications to Image Processing,” School of Electronic Engineering, Purdue U., West Lafayette, IN, Tech. Rep. EE 80-1 (Jan.1980).

Appl. Opt. (1)

Appl. Phys. Lett. (1)

J. L. Jewell, Y. H. Lee, H. M. Gibbs, N. Peyghambarian, A. C. Gossard, W. Wiegmann, “3-pJ, 82-MHz Optical Logic Gates in a Room-Temperature GaAs-AlGaAs Multiple-Quantum-Well Etalon,” Appl. Phys. Lett. 46, 918 (1985).
[CrossRef]

IEEE Trans. Acoust. Speech Signal Process. (5)

J. P. Fitch, E. J. Coyle, N. C. Gallagher, “Median Filtering by Threshold Decomposition,” IEEE Trans. Acoust. Speech Signal Process. ASSP-32, 1183 (1984).
[CrossRef]

P. D. Wendt, E. J. Coyle, N. C. Gallagher, “Stack Filters,” IEEE Trans. Acoust. Speech Signal Process. ASSP-34, 898 (1986).
[CrossRef]

N. C. Gallagher, G. L. Wise, “A Theoretical Analysis of the Properties of Median Filters,” IEEE Trans. Acoust. Speech Signal Process. ASSP-29, 1136 (1981).
[CrossRef]

A. C. Bovik, T. S. Huang, D. C. Munson, “A Generalization of Median Filtering using Linear Combinations of Order Statistics,” IEEE Trans. Acoust. Speech Signal Process. ASSP-31, 1342 (1983).
[CrossRef]

T. S. Huang, G. J. Yang, G. Y. Tang, “A Fast Two-Dimensional Median Filtering Algorithm,” IEEE Trans. Acoust. Speech Signal Process. ASSP-27, 13 (1979).
[CrossRef]

IEEE Trans. Circuits Syst. (1)

J. P. Fitch, E. J. Coyle, N. C. Gallagher, “Threshold Decomposition of Multidimensional Ranked-Order Operations,” IEEE Trans. Circuits Syst. CAS-32, 445 (1985).
[CrossRef]

IEEE Trans. Syst. Man Cybernet. (1)

Y. Nakagawa, A. Rosenfeld, “A Note on the Use of Local Min and Max Operations in Digital Picture Processing,” IEEE Trans. Syst. Man Cybernet. SMC-8, 632 (1978).

J. Math. Phys. (1)

E. N. Gilbert, “Lattice-Theoretic Properties of Frontal Switching Functions,” J. Math. Phys. 33, 57 (1954).

Proc. Soc. Photo-Opt. Instrum. Eng. (2)

K. S. O’Neill, W. T. Rhodes, “Morphological Transformations by Hybrid Optical-Electronic Methods,” Proc. Soc. Photo-Opt. Instrum. Eng. 638, 41 (1986).

W. E. Ross, K. M. Snapp, R. H. Anderson, “Fundamental Characteristics of the Litton Iron Garnet Magneto-optic Spatial Light Modulator,” Proc. Soc. Photo-Opt. Instrum. Eng. 388, 55 (1983).

Other (16)

“MEBES Software Manual A900-0102G,” Perkin-Elmer Electron Beam Technology, 26460 Corporate Ave., Hayward, CA 94545.

Micro Mask, Inc., 695 Vaqueros Ave., Sunnyvale, CA 94086.

S. A. Benton, “Special Problems: Photographic Materials and their Handling,” in Handbook of Optical Holography, H. J. Caulfield, Ed. (Academic, New York, 1979).

Chalnicon is a trademark of Toshiba.

R. G. Harber, S. C. Bass, G. Neudeck, “VLSI Implementation of a Fast Rank Order Algorithm,” in Proceedings, International Conference on Acoustics, Speech, and Signal Processing ’85 (1985), p. 1396.
[CrossRef]

J. P. Fitch, “Software and VLSI Algorithms for Generalized Ranked Order Filtering,” IEEE Trans. Circuits Syst. in press, 1987. (UCRL-92674, Mar. 1985).
[CrossRef]

R. G. Harber, S. C. Bass, J. P. Fitch, E. J. Coyle, N. C. Gallagher, “The VLSI Implementation of Rank Order Filters,” Proc. IEEE submitted for publication June1986.

J. Serra, Image Analysis and Mathematical Morphology (Academic, London, 1982), Chap. 2.

G. R. Arce, P. J. Warter, “A Median Filter Architecture Suitable for VLSI Implementation,” in Proceedings, Twenty-second Annual Allerton Conference on Communication, Control, and Computing, Monticello, IL, 3–5 Oct. 1984, p. 172.

A. Rosenfeld, A. C. Kak, Digital Picture Processing, Vol. 2 (Academic, New York, 1982), Chap. 11.

T. S. Huang, G. J. Yang, “Median Filters and Their Applications to Image Processing,” School of Electronic Engineering, Purdue U., West Lafayette, IN, Tech. Rep. EE 80-1 (Jan.1980).

J. W. Tukey, Exploratory Data Analysis (Addison-Wesley, Reading, MA, 1977).

P. A. Maragos, R. W. Schafer, “A Unification of Linear, Median, Order-Statistics, and Morphological Filters under Mathematical Morphology,” in Proceedings, International Conference on Acoustics, Speech, and Signal Processing (1985), p. 1329.

D. E. Dudgeon, R. M. Mersereau, Multidimensional Digital Signal Processing (Prentice-Hall, Englewood Cliffs, NJ, 1984), pp. 116–118.

W. T. Rhodes, A. A. Sawchuk, “Incoherent Optical Processing,” in Optical Information Processing, S. H. Lee, Ed. (Springer-Verlag, Berlin, 1981).
[CrossRef]

H. Bartelt, S. K. Case, R. Hauck, “Incoherent-Optical Processing,” in Applications of Optical Fourier Transforms, H. Stark, Ed. (Academic, Orlando, FL, 1982).
[CrossRef]

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Figures (13)

Fig. 1
Fig. 1

Median filtering by threshold decomposition using a window of width 3.

Fig. 2
Fig. 2

Processing of spatially multiplexed threshold components illustrated for an image of sixteen levels: (a) ranked-order filtering of threshold components; (b) superposition of threshold components.

Fig. 3
Fig. 3

Schematic of the experimental system. The source is an Arion laser. The optical segment uses f/5, 7.6-cm (3-in.) diam lenses. SLM, spatial light modulator; CGH, computer-generated hologram.

Fig. 4
Fig. 4

Optical portion of the experimental system: 1, rotating diffuser; 2, SLM; 3, hologram plane; 4, SLM driver; 5, camera 1; 6, camera 2.

Fig. 5
Fig. 5

(a) Space-plane representation of the two convolution filters. The 3 × 3 filter is used in phase 1 and the 4 × 4 filter in phase 2. (b) Frequency-plane representation of (a) showing the amplitude after clipping at 0.5 of the maximum.

Fig. 6
Fig. 6

Typical output from optical part of phase 1 with patches superimposed to indicate positions where data are acquired.

Fig. 7
Fig. 7

Typical output from optical part of phase 2 with patches superimposed to indicate positions where data are acquired.

Fig. 8
Fig. 8

48 × 48 sixteen-level image used as input for minimum and maximum filtering.

Fig. 9
Fig. 9

48 × 48 sixteen-level image used as input for median filtering.

Fig. 10
Fig. 10

(a) Optical and (b) electronic results of 3 × 3 median filtering of image in Fig. 9.

Fig. 11
Fig. 11

(a) Optical and (b) electronic results of 3 × 3 minimum filtering of image in Fig. 8.

Fig. 12
Fig. 12

(a) Optical and (b) electronic results of 3 × 3 maximum filtering of image in Fig. 8.

Fig. 13
Fig. 13

Fully optical system for ranked-order filtering.

Equations (16)

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2 N T + 1 = ( 2 N x + 1 ) × ( 2 N y + 1 ) .
x k ( i , j ) = { 1 x ( i , j ) k + ½ . 0 else .
z k ( i , j ) = n x = - N x N x n y - N y N y x k ( i + n x , j + n y ) = l = 0 L - 1 ω = 0 W - 1 h R ( i - l , j - w ) x k ( l , w ) ,
h R ( l , w ) = { 1 l N x , w N y . 0 else
y k ( i , j ) = { 1 z k ( i , j ) N T + ½ . 0 else .
z k ( i , j ) ( 2 N T + 1 ) - ½ ,
z k ( i , j ) ½ .
y ( i , j ) = k = 0 K - 1 y k ( i , j ) .
N B = [ L W ( M / K x - J x + 1 ) ( N / K y - J y + 1 ) ] ,
x ˜ ( i , j ) = x ( i ) K x K x + ( j ) K y ( [ i / K x ] , [ j / K y ] ) ,
z ˜ ( i , j ) = l = 0 L ˜ - 1 w = 0 W ˜ - 1 h ˜ R ( i - l , j - w ) x ˜ ( l , w ) ,
h ˜ R ( l , w ) = { h R ( l / K x , w / K y ) ( l ) K x = 0 and ( w ) K y = 0 0 else
y ˜ ( i , j ) = { 1 z ˜ ( i , j ) N T + 1 / 2 0 else .
y ( i , j ) = k x = 0 k x - 1 k y = 0 k y - 1 y ˜ ( K x i + k x , K y j + k y )
= l = 0 L ˜ - 1 w = 0 W ˜ - 1 h ˜ S ( K x i - l , K y j - w ) y ˜ ( l , w ) ,
h ˜ S ( l , w ) = { 1 0 l K x - 1 , 0 w K y - 1 0 else

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