Abstract

An optoelectronic implementation of the nonlinear morphological correlation by use of a threshold-decomposition technique and a joint transform correlator architecture is presented. This nonlinear morphological correlation provides improved image detection compared with standard linear optical pattern-recognition correlation methods. It also offers a more robust detection of low-intensity images in the presence of high-intensity patterns to be rejected.

© 1998 Optical Society of America

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References

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  1. R. O. Duda, P. E. Hart, Pattern Classification and Scene Analysis (Wiley, New York, 1973), Chap. 7, p. 279.
  2. G. L. Turin, “An introduction to matched filters,” IRE Trans. Inf. Theory IT-6, 311–329 (1960).
    [CrossRef]
  3. E. R. Dougherty, J. Astola, An Introduction to Nonlinear Image Processing, Vol. TT16 of SPIE Tutorial Text Series (SPIE Press, Bellingham, Wash., 1994).
  4. P. Maragos, “Morphological correlation and mean absolute error,” in ICASSP-89: 1989 International Conference on Acoustic, Speech and Signal Processing (Institute of Electrical and Electronics Engineers, New York, 1989), Vol. 3, pp. 1568–1571.
  5. P. Maragos, “Optimal morphological approaches to image matching and object detection,” paper presented at the Second International Conference on Computer Vision, Tampa, Florida, 5–8 December, 1988.
  6. J. Serra, Image Analysis and Mathematical Morphology (Academic, London, 1982).
  7. P. Maragos, R. W. Schafer, “Morphological systems for multidimensional signal processing,” Proc. IEEE 78, 690–710 (1990).
    [CrossRef]
  8. P. Maragos, R. W. Schafer, “Morphological filters. Part I: their set-theoretic analysis and relations to linear shift-invariant filters,” IEEE Trans. Acoust. Speech Signal Process. ASSP-35, 1153–1169 (1987).
    [CrossRef]
  9. P. Maragos, R. W. Schafer, “Morphological filters. Part II: Their relations to median, order-statistic, and stack filters,” IEEE Trans. Acoust. Speech Signal Process. ASSP-35, 1170–1184 (1987).
    [CrossRef]
  10. J. P. Fitch, E. J. Coyle, N. C. Gallagher, “Median filtering by threshold decomposition,” IEEE Trans. Acoust. Speech Signal Process. ASSP-32, 1183–1188 (1984).
    [CrossRef]
  11. P. D. Wendt, E. J. Coyle, N. C. Gallagher, “Stack filters,” IEEE Trans. Acoust. Speech and Signal Process. ASSP-34, 898–911 (1986).
    [CrossRef]
  12. E. Ochoa, J. P. Allebach, D. W. Sweeney, “Optical median filtering using threshold decomposition,” Appl. Opt. 26, 252–260 (1987).
    [CrossRef] [PubMed]
  13. J. M. Hereford, W. T. Rhodes, “Nonlinear optical image filtering by time-sequential threshold decomposition,” Opt. Eng. 27, 274–279 (1988).
    [CrossRef]
  14. R. Schaefer, D. Casasent, “Optical implementation of gray scale morphology,” in Nonlinear Image Processing III, E. R. Dougherty, J. Astola, C. G. Boncelet, eds., Proc. SPIE1658, 287–296 (1992).
    [CrossRef]
  15. J. García, T. Szoplik, C. Ferreira, “Optoelectronic morphological image processor,” Opt. Lett. 18, 1952–1954 (1993).
    [CrossRef] [PubMed]
  16. M. Gedziorowski, J. García, “Programmable optical digital processor for rank-order and morphological image processor,” Opt. Commun. 119, 207–217 (1995).
    [CrossRef]
  17. A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).
  18. C. S. Weaver, J. W. Goodman, “A technique for optically convolving two functions,” Appl. Opt. 5, 1248–1249 (1966).
    [CrossRef] [PubMed]
  19. X. J. Lu, F. T. S. Yu, D. A. Gregory, “Comparison of VanderLugt and joint transform correlators,” Appl. Phys. B 51, 153–164 (1990).
    [CrossRef]
  20. C. Soutar, S. E. Monroe, J. Knopp, “Measurement of the complex transmittance of the Epson liquid crystal television,” Opt. Eng. 33, 1061–1068 (1994).
    [CrossRef]
  21. G. Moddel, “FLC spatial light modulators,” in Spatial Light Modulator Technology: Material, Devices and Applications, U. Efron, ed. (Marcel Dekker, New York, 1995), Chap. 6, pp. 347–349.
  22. B. Noharet, H. Sjöberg, R. Hey, “Fast portable optical information processing,” paper presented at the Euro-American Workshop: Optoelectronic Information Processing, Sitges, Barcelona, Spain, 2–5 June, 1997.
  23. J. P. Karins, S. A. Mills, J. R. Ryan, R. Barry Dydyk, “Performance of a second-generation miniature ruggedized optical correlator module,” Opt. Eng. 36, 2747–2753 (1997).
    [CrossRef]

1997 (1)

J. P. Karins, S. A. Mills, J. R. Ryan, R. Barry Dydyk, “Performance of a second-generation miniature ruggedized optical correlator module,” Opt. Eng. 36, 2747–2753 (1997).
[CrossRef]

1995 (1)

M. Gedziorowski, J. García, “Programmable optical digital processor for rank-order and morphological image processor,” Opt. Commun. 119, 207–217 (1995).
[CrossRef]

1994 (1)

C. Soutar, S. E. Monroe, J. Knopp, “Measurement of the complex transmittance of the Epson liquid crystal television,” Opt. Eng. 33, 1061–1068 (1994).
[CrossRef]

1993 (1)

1990 (2)

X. J. Lu, F. T. S. Yu, D. A. Gregory, “Comparison of VanderLugt and joint transform correlators,” Appl. Phys. B 51, 153–164 (1990).
[CrossRef]

P. Maragos, R. W. Schafer, “Morphological systems for multidimensional signal processing,” Proc. IEEE 78, 690–710 (1990).
[CrossRef]

1988 (1)

J. M. Hereford, W. T. Rhodes, “Nonlinear optical image filtering by time-sequential threshold decomposition,” Opt. Eng. 27, 274–279 (1988).
[CrossRef]

1987 (3)

E. Ochoa, J. P. Allebach, D. W. Sweeney, “Optical median filtering using threshold decomposition,” Appl. Opt. 26, 252–260 (1987).
[CrossRef] [PubMed]

P. Maragos, R. W. Schafer, “Morphological filters. Part I: their set-theoretic analysis and relations to linear shift-invariant filters,” IEEE Trans. Acoust. Speech Signal Process. ASSP-35, 1153–1169 (1987).
[CrossRef]

P. Maragos, R. W. Schafer, “Morphological filters. Part II: Their relations to median, order-statistic, and stack filters,” IEEE Trans. Acoust. Speech Signal Process. ASSP-35, 1170–1184 (1987).
[CrossRef]

1986 (1)

P. D. Wendt, E. J. Coyle, N. C. Gallagher, “Stack filters,” IEEE Trans. Acoust. Speech and Signal Process. ASSP-34, 898–911 (1986).
[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, 1183–1188 (1984).
[CrossRef]

1966 (1)

1964 (1)

A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).

1960 (1)

G. L. Turin, “An introduction to matched filters,” IRE Trans. Inf. Theory IT-6, 311–329 (1960).
[CrossRef]

Allebach, J. P.

Astola, J.

E. R. Dougherty, J. Astola, An Introduction to Nonlinear Image Processing, Vol. TT16 of SPIE Tutorial Text Series (SPIE Press, Bellingham, Wash., 1994).

Barry Dydyk, R.

J. P. Karins, S. A. Mills, J. R. Ryan, R. Barry Dydyk, “Performance of a second-generation miniature ruggedized optical correlator module,” Opt. Eng. 36, 2747–2753 (1997).
[CrossRef]

Casasent, D.

R. Schaefer, D. Casasent, “Optical implementation of gray scale morphology,” in Nonlinear Image Processing III, E. R. Dougherty, J. Astola, C. G. Boncelet, eds., Proc. SPIE1658, 287–296 (1992).
[CrossRef]

Coyle, E. J.

P. D. Wendt, E. J. Coyle, N. C. Gallagher, “Stack filters,” IEEE Trans. Acoust. Speech and Signal Process. ASSP-34, 898–911 (1986).
[CrossRef]

J. P. Fitch, E. J. Coyle, N. C. Gallagher, “Median filtering by threshold decomposition,” IEEE Trans. Acoust. Speech Signal Process. ASSP-32, 1183–1188 (1984).
[CrossRef]

Dougherty, E. R.

E. R. Dougherty, J. Astola, An Introduction to Nonlinear Image Processing, Vol. TT16 of SPIE Tutorial Text Series (SPIE Press, Bellingham, Wash., 1994).

Duda, R. O.

R. O. Duda, P. E. Hart, Pattern Classification and Scene Analysis (Wiley, New York, 1973), Chap. 7, p. 279.

Ferreira, C.

Fitch, J. P.

J. P. Fitch, E. J. Coyle, N. C. Gallagher, “Median filtering by threshold decomposition,” IEEE Trans. Acoust. Speech Signal Process. ASSP-32, 1183–1188 (1984).
[CrossRef]

Gallagher, N. C.

P. D. Wendt, E. J. Coyle, N. C. Gallagher, “Stack filters,” IEEE Trans. Acoust. Speech and Signal Process. ASSP-34, 898–911 (1986).
[CrossRef]

J. P. Fitch, E. J. Coyle, N. C. Gallagher, “Median filtering by threshold decomposition,” IEEE Trans. Acoust. Speech Signal Process. ASSP-32, 1183–1188 (1984).
[CrossRef]

García, J.

M. Gedziorowski, J. García, “Programmable optical digital processor for rank-order and morphological image processor,” Opt. Commun. 119, 207–217 (1995).
[CrossRef]

J. García, T. Szoplik, C. Ferreira, “Optoelectronic morphological image processor,” Opt. Lett. 18, 1952–1954 (1993).
[CrossRef] [PubMed]

Gedziorowski, M.

M. Gedziorowski, J. García, “Programmable optical digital processor for rank-order and morphological image processor,” Opt. Commun. 119, 207–217 (1995).
[CrossRef]

Goodman, J. W.

Gregory, D. A.

X. J. Lu, F. T. S. Yu, D. A. Gregory, “Comparison of VanderLugt and joint transform correlators,” Appl. Phys. B 51, 153–164 (1990).
[CrossRef]

Hart, P. E.

R. O. Duda, P. E. Hart, Pattern Classification and Scene Analysis (Wiley, New York, 1973), Chap. 7, p. 279.

Hereford, J. M.

J. M. Hereford, W. T. Rhodes, “Nonlinear optical image filtering by time-sequential threshold decomposition,” Opt. Eng. 27, 274–279 (1988).
[CrossRef]

Hey, R.

B. Noharet, H. Sjöberg, R. Hey, “Fast portable optical information processing,” paper presented at the Euro-American Workshop: Optoelectronic Information Processing, Sitges, Barcelona, Spain, 2–5 June, 1997.

Karins, J. P.

J. P. Karins, S. A. Mills, J. R. Ryan, R. Barry Dydyk, “Performance of a second-generation miniature ruggedized optical correlator module,” Opt. Eng. 36, 2747–2753 (1997).
[CrossRef]

Knopp, J.

C. Soutar, S. E. Monroe, J. Knopp, “Measurement of the complex transmittance of the Epson liquid crystal television,” Opt. Eng. 33, 1061–1068 (1994).
[CrossRef]

Lu, X. J.

X. J. Lu, F. T. S. Yu, D. A. Gregory, “Comparison of VanderLugt and joint transform correlators,” Appl. Phys. B 51, 153–164 (1990).
[CrossRef]

Maragos, P.

P. Maragos, R. W. Schafer, “Morphological systems for multidimensional signal processing,” Proc. IEEE 78, 690–710 (1990).
[CrossRef]

P. Maragos, R. W. Schafer, “Morphological filters. Part I: their set-theoretic analysis and relations to linear shift-invariant filters,” IEEE Trans. Acoust. Speech Signal Process. ASSP-35, 1153–1169 (1987).
[CrossRef]

P. Maragos, R. W. Schafer, “Morphological filters. Part II: Their relations to median, order-statistic, and stack filters,” IEEE Trans. Acoust. Speech Signal Process. ASSP-35, 1170–1184 (1987).
[CrossRef]

P. Maragos, “Morphological correlation and mean absolute error,” in ICASSP-89: 1989 International Conference on Acoustic, Speech and Signal Processing (Institute of Electrical and Electronics Engineers, New York, 1989), Vol. 3, pp. 1568–1571.

P. Maragos, “Optimal morphological approaches to image matching and object detection,” paper presented at the Second International Conference on Computer Vision, Tampa, Florida, 5–8 December, 1988.

Mills, S. A.

J. P. Karins, S. A. Mills, J. R. Ryan, R. Barry Dydyk, “Performance of a second-generation miniature ruggedized optical correlator module,” Opt. Eng. 36, 2747–2753 (1997).
[CrossRef]

Moddel, G.

G. Moddel, “FLC spatial light modulators,” in Spatial Light Modulator Technology: Material, Devices and Applications, U. Efron, ed. (Marcel Dekker, New York, 1995), Chap. 6, pp. 347–349.

Monroe, S. E.

C. Soutar, S. E. Monroe, J. Knopp, “Measurement of the complex transmittance of the Epson liquid crystal television,” Opt. Eng. 33, 1061–1068 (1994).
[CrossRef]

Noharet, B.

B. Noharet, H. Sjöberg, R. Hey, “Fast portable optical information processing,” paper presented at the Euro-American Workshop: Optoelectronic Information Processing, Sitges, Barcelona, Spain, 2–5 June, 1997.

Ochoa, E.

Rhodes, W. T.

J. M. Hereford, W. T. Rhodes, “Nonlinear optical image filtering by time-sequential threshold decomposition,” Opt. Eng. 27, 274–279 (1988).
[CrossRef]

Ryan, J. R.

J. P. Karins, S. A. Mills, J. R. Ryan, R. Barry Dydyk, “Performance of a second-generation miniature ruggedized optical correlator module,” Opt. Eng. 36, 2747–2753 (1997).
[CrossRef]

Schaefer, R.

R. Schaefer, D. Casasent, “Optical implementation of gray scale morphology,” in Nonlinear Image Processing III, E. R. Dougherty, J. Astola, C. G. Boncelet, eds., Proc. SPIE1658, 287–296 (1992).
[CrossRef]

Schafer, R. W.

P. Maragos, R. W. Schafer, “Morphological systems for multidimensional signal processing,” Proc. IEEE 78, 690–710 (1990).
[CrossRef]

P. Maragos, R. W. Schafer, “Morphological filters. Part II: Their relations to median, order-statistic, and stack filters,” IEEE Trans. Acoust. Speech Signal Process. ASSP-35, 1170–1184 (1987).
[CrossRef]

P. Maragos, R. W. Schafer, “Morphological filters. Part I: their set-theoretic analysis and relations to linear shift-invariant filters,” IEEE Trans. Acoust. Speech Signal Process. ASSP-35, 1153–1169 (1987).
[CrossRef]

Serra, J.

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

Sjöberg, H.

B. Noharet, H. Sjöberg, R. Hey, “Fast portable optical information processing,” paper presented at the Euro-American Workshop: Optoelectronic Information Processing, Sitges, Barcelona, Spain, 2–5 June, 1997.

Soutar, C.

C. Soutar, S. E. Monroe, J. Knopp, “Measurement of the complex transmittance of the Epson liquid crystal television,” Opt. Eng. 33, 1061–1068 (1994).
[CrossRef]

Sweeney, D. W.

Szoplik, T.

Turin, G. L.

G. L. Turin, “An introduction to matched filters,” IRE Trans. Inf. Theory IT-6, 311–329 (1960).
[CrossRef]

VanderLugt, A.

A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).

Weaver, C. S.

Wendt, P. D.

P. D. Wendt, E. J. Coyle, N. C. Gallagher, “Stack filters,” IEEE Trans. Acoust. Speech and Signal Process. ASSP-34, 898–911 (1986).
[CrossRef]

Yu, F. T. S.

X. J. Lu, F. T. S. Yu, D. A. Gregory, “Comparison of VanderLugt and joint transform correlators,” Appl. Phys. B 51, 153–164 (1990).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. B (1)

X. J. Lu, F. T. S. Yu, D. A. Gregory, “Comparison of VanderLugt and joint transform correlators,” Appl. Phys. B 51, 153–164 (1990).
[CrossRef]

IEEE Trans. Acoust. Speech and Signal Process. (1)

P. D. Wendt, E. J. Coyle, N. C. Gallagher, “Stack filters,” IEEE Trans. Acoust. Speech and Signal Process. ASSP-34, 898–911 (1986).
[CrossRef]

IEEE Trans. Acoust. Speech Signal Process. (3)

P. Maragos, R. W. Schafer, “Morphological filters. Part I: their set-theoretic analysis and relations to linear shift-invariant filters,” IEEE Trans. Acoust. Speech Signal Process. ASSP-35, 1153–1169 (1987).
[CrossRef]

P. Maragos, R. W. Schafer, “Morphological filters. Part II: Their relations to median, order-statistic, and stack filters,” IEEE Trans. Acoust. Speech Signal Process. ASSP-35, 1170–1184 (1987).
[CrossRef]

J. P. Fitch, E. J. Coyle, N. C. Gallagher, “Median filtering by threshold decomposition,” IEEE Trans. Acoust. Speech Signal Process. ASSP-32, 1183–1188 (1984).
[CrossRef]

IEEE Trans. Inf. Theory (1)

A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).

IRE Trans. Inf. Theory (1)

G. L. Turin, “An introduction to matched filters,” IRE Trans. Inf. Theory IT-6, 311–329 (1960).
[CrossRef]

Opt. Commun. (1)

M. Gedziorowski, J. García, “Programmable optical digital processor for rank-order and morphological image processor,” Opt. Commun. 119, 207–217 (1995).
[CrossRef]

Opt. Eng. (3)

J. M. Hereford, W. T. Rhodes, “Nonlinear optical image filtering by time-sequential threshold decomposition,” Opt. Eng. 27, 274–279 (1988).
[CrossRef]

C. Soutar, S. E. Monroe, J. Knopp, “Measurement of the complex transmittance of the Epson liquid crystal television,” Opt. Eng. 33, 1061–1068 (1994).
[CrossRef]

J. P. Karins, S. A. Mills, J. R. Ryan, R. Barry Dydyk, “Performance of a second-generation miniature ruggedized optical correlator module,” Opt. Eng. 36, 2747–2753 (1997).
[CrossRef]

Opt. Lett. (1)

Proc. IEEE (1)

P. Maragos, R. W. Schafer, “Morphological systems for multidimensional signal processing,” Proc. IEEE 78, 690–710 (1990).
[CrossRef]

Other (8)

R. O. Duda, P. E. Hart, Pattern Classification and Scene Analysis (Wiley, New York, 1973), Chap. 7, p. 279.

E. R. Dougherty, J. Astola, An Introduction to Nonlinear Image Processing, Vol. TT16 of SPIE Tutorial Text Series (SPIE Press, Bellingham, Wash., 1994).

P. Maragos, “Morphological correlation and mean absolute error,” in ICASSP-89: 1989 International Conference on Acoustic, Speech and Signal Processing (Institute of Electrical and Electronics Engineers, New York, 1989), Vol. 3, pp. 1568–1571.

P. Maragos, “Optimal morphological approaches to image matching and object detection,” paper presented at the Second International Conference on Computer Vision, Tampa, Florida, 5–8 December, 1988.

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

G. Moddel, “FLC spatial light modulators,” in Spatial Light Modulator Technology: Material, Devices and Applications, U. Efron, ed. (Marcel Dekker, New York, 1995), Chap. 6, pp. 347–349.

B. Noharet, H. Sjöberg, R. Hey, “Fast portable optical information processing,” paper presented at the Euro-American Workshop: Optoelectronic Information Processing, Sitges, Barcelona, Spain, 2–5 June, 1997.

R. Schaefer, D. Casasent, “Optical implementation of gray scale morphology,” in Nonlinear Image Processing III, E. R. Dougherty, J. Astola, C. G. Boncelet, eds., Proc. SPIE1658, 287–296 (1992).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Block diagram of the optoelectronic morphological correlator.

Fig. 2
Fig. 2

JTC setup.

Fig. 3
Fig. 3

Two different joint input images, both with an input scene and a reference object.

Fig. 4
Fig. 4

Experimental output plane containing the optical correlations of the scene shown in Fig. 3(a). The three-dimensional plots cover the area around the correlation peaks. (a) Linear correlation γ. (b) MC μ.

Fig. 5
Fig. 5

Experimental output plane containing the optical correlations of the scene shown in Fig. 3(b). The three-dimensional plots cover the area around the correlation peaks. (a) Linear correlation γ. (b) MC μ.

Equations (11)

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

MSE x ,   y = ζ , η W g ζ + x ,   η + y - f ζ ,   η 2 ,
γ gf x ,   y = ζ , η W   g ζ + x ,   η + y f ζ ,   η .
MAE x ,   y = ζ , η W   | g ζ + x ,   η + y - f ζ ,   η | .
μ gf x ,   y = ζ , η W min g ζ + x ,   η + y ,   f ζ ,   η ,
f x ,   y = q = 1 Q - 1   f q x ,   y ,
f q x ,   y = 1 if   f x ,   y q 0 otherwise .
min g x 1 ,   y 1 ,   f x 2 ,   y 2 = q = 1 Q - 1   min g q x 1 ,   y 1 ,   f q x 2 ,   y 2 ,
μ gf x ,   y = q = 1 Q - 1   μ g q f q x ,   y = q = 1 Q - 1   γ g q f q x ,   y = q = 1 Q - 1 g q     f q x ,   y ,
JPS u ,   v = | F u ,   v exp i ϕ u ,   v + G u ,   v exp - i ϕ u ,   v | 2 = | F u ,   v | 2 + | G u ,   v | 2 + F * u ,   v G u ,   v exp - i 2 ϕ u ,   v + F u ,   v G * u ,   v exp i 2 ϕ u ,   v ,
JPS u ,   v = f     f x ,   y + g     g x ,   y + g     f x - 2 x o ,   y +   f     g x   +   2 x o ,   y .
JPS u ,   v = q = 1 Q - 1 JPS q u ,   v = q = 1 Q - 1   | F q u ,   v | 2 + q = 1 Q - 1   | G q u ,   v | 2 + q = 1 Q - 1   F q * u ,   v G q u ,   v exp - i 2 ϕ q u ,   v + q = 1 Q - 1   F q u ,   v G q * u ,   v exp i 2 ϕ q u ,   v .

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