Abstract

A morphologically preprocessed joint transform correlation is proposed that combines the techniques of morphological filtering and joint transform correlation. We improve on the performance of a joint transform correlator by eliminating noise with morphological preprocessing and by performing edge detection of input images. Computer simulation results show that the corresponding system contributes to a better discrimination capability than gradient operator-based and wavelet-based preprocessed joint transform correlation.

© 1999 Optical Society of America

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  1. C. S. Weaver, J. W. Goodman, “Technique for optically convolving two functions,” Appl. Opt. 5, 1248–1249 (1966).
    [CrossRef] [PubMed]
  2. M. S. Alam, O. Perez, M. A. Karim, “Preprocessed multiobject joint transform correlator,” Appl. Opt. 32, 3102–3107 (1993).
    [CrossRef] [PubMed]
  3. B. Javidi, J. Wang, “Binary nonlinear joint transform correlation with median and subset median thresholding,” Appl. Opt. 30, 967–976 (1991).
    [CrossRef] [PubMed]
  4. D. Feng, H. Zhao, S. Xia, “Amplitude-modulated JTC for improving correlation discrimination,” Opt. Commun. 86, 260–264 (1991).
    [CrossRef]
  5. A. Carnicer, S. Vallmitjana, I. Juvells, “Correlation postprocessing-based method for the detection of defocused images,” Appl. Opt. 20, 4807–4811 (1997).
    [CrossRef]
  6. X. J. Lu, A. Katz, E. G. Kanterakis, N. P. Caviris, “Joint transform correlator that uses wavelet transforms,” Opt. Lett. 17, 1700–1702 (1992).
    [CrossRef] [PubMed]
  7. P. S. Erbach, D. A. Gregory, X. Yang, “Optical wavelet transform by the phase-only joint transform correlator,” Appl. Opt. 35, 3117–3126 (1996).
    [CrossRef] [PubMed]
  8. W. Wang, G. Jin, Y. Yan, M. Wu, “Joint wavelet-transform correlator for image feature extraction,” Appl. Opt. 34, 370–376 (1995).
    [CrossRef] [PubMed]
  9. S. Zhong, S. Liu, X. Zhang, C. Li, “Joint wavelet representation correlator for pattern recognition,” Appl. Opt. 37, 374–379 (1998).
    [CrossRef]
  10. R. Tripathi, K. Singh, “Pattern discrimination using a bank of wavelet filters in a joint transform correlator,” Opt. Eng. 37, 32–538 (1998).
    [CrossRef]
  11. J. Serra, Image Analysis and Mathematical Morphology (Academic, New York, 1982).
  12. P. Maragos, R. W. Schafer, “Morphological systems for multidimensional signal processing,” Proc. IEEE 78, 690–710 (1990).
    [CrossRef]
  13. Y. Li, A. Kostrzewski, D. H. Kim, G. Eichmann, “Compact parallel real-time programmable optical morphological image processor,” Opt. Lett. 14, 981–983 (1989).
    [CrossRef] [PubMed]
  14. E. C. Botha, D. Casasent, “Optical laboratory morphological inspection processor,” Appl. Opt. 28, 5342–5350 (1989).
    [CrossRef] [PubMed]
  15. A. Fedor, M. O. Freeman, “Optical multiscale morphological processor using a complex-valued kernel,” Appl. Opt. 31, 4042–4050 (1992).
    [CrossRef] [PubMed]
  16. J. N. Mait, D. W. Prather, R. A. Athale, “Acousto-optic processing with electronic image feedback for morphological filtering,” Appl. Opt. 31, 5688–5698 (1992).
    [CrossRef] [PubMed]
  17. J. Garcia, T. Szoplik, C. Ferreira, “Optoelectronic morphological image processor,” Opt. Lett. 18, 1952–1954 (1993).
    [CrossRef] [PubMed]
  18. M. Gedziorowski, J. Garcia, “Programmable optical digital processor for rank order and morphological filtering,” Opt. Commun. 119, 207–217 (1995).
    [CrossRef]
  19. D. Casasent, E. Botha, “Optical symbolic substitution for morphological transformations,” Appl. Opt. 27, 3806–3810 (1988).
    [CrossRef] [PubMed]
  20. P. Garcia-Martinex, D. Mas, J. Garcia, C. Ferreira, “Nonlinear morphological correlation: optoelectronic implementation,” Appl. Opt. 37, 2112–2118 (1998).
    [CrossRef]

1998 (3)

1997 (1)

A. Carnicer, S. Vallmitjana, I. Juvells, “Correlation postprocessing-based method for the detection of defocused images,” Appl. Opt. 20, 4807–4811 (1997).
[CrossRef]

1996 (1)

1995 (2)

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

W. Wang, G. Jin, Y. Yan, M. Wu, “Joint wavelet-transform correlator for image feature extraction,” Appl. Opt. 34, 370–376 (1995).
[CrossRef] [PubMed]

1993 (2)

1992 (3)

1991 (2)

B. Javidi, J. Wang, “Binary nonlinear joint transform correlation with median and subset median thresholding,” Appl. Opt. 30, 967–976 (1991).
[CrossRef] [PubMed]

D. Feng, H. Zhao, S. Xia, “Amplitude-modulated JTC for improving correlation discrimination,” Opt. Commun. 86, 260–264 (1991).
[CrossRef]

1990 (1)

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

1989 (2)

1988 (1)

1966 (1)

Alam, M. S.

Athale, R. A.

Botha, E.

Botha, E. C.

Carnicer, A.

A. Carnicer, S. Vallmitjana, I. Juvells, “Correlation postprocessing-based method for the detection of defocused images,” Appl. Opt. 20, 4807–4811 (1997).
[CrossRef]

Casasent, D.

Caviris, N. P.

Eichmann, G.

Erbach, P. S.

Fedor, A.

Feng, D.

D. Feng, H. Zhao, S. Xia, “Amplitude-modulated JTC for improving correlation discrimination,” Opt. Commun. 86, 260–264 (1991).
[CrossRef]

Ferreira, C.

Freeman, M. O.

Garcia, J.

Garcia-Martinex, P.

Gedziorowski, M.

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

Goodman, J. W.

Gregory, D. A.

Javidi, B.

Jin, G.

Juvells, I.

A. Carnicer, S. Vallmitjana, I. Juvells, “Correlation postprocessing-based method for the detection of defocused images,” Appl. Opt. 20, 4807–4811 (1997).
[CrossRef]

Kanterakis, E. G.

Karim, M. A.

Katz, A.

Kim, D. H.

Kostrzewski, A.

Li, C.

Li, Y.

Liu, S.

Lu, X. J.

Mait, J. N.

Maragos, P.

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

Mas, D.

Perez, O.

Prather, D. W.

Schafer, R. W.

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

Serra, J.

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

Singh, K.

R. Tripathi, K. Singh, “Pattern discrimination using a bank of wavelet filters in a joint transform correlator,” Opt. Eng. 37, 32–538 (1998).
[CrossRef]

Szoplik, T.

Tripathi, R.

R. Tripathi, K. Singh, “Pattern discrimination using a bank of wavelet filters in a joint transform correlator,” Opt. Eng. 37, 32–538 (1998).
[CrossRef]

Vallmitjana, S.

A. Carnicer, S. Vallmitjana, I. Juvells, “Correlation postprocessing-based method for the detection of defocused images,” Appl. Opt. 20, 4807–4811 (1997).
[CrossRef]

Wang, J.

Wang, W.

Weaver, C. S.

Wu, M.

Xia, S.

D. Feng, H. Zhao, S. Xia, “Amplitude-modulated JTC for improving correlation discrimination,” Opt. Commun. 86, 260–264 (1991).
[CrossRef]

Yan, Y.

Yang, X.

Zhang, X.

Zhao, H.

D. Feng, H. Zhao, S. Xia, “Amplitude-modulated JTC for improving correlation discrimination,” Opt. Commun. 86, 260–264 (1991).
[CrossRef]

Zhong, S.

Appl. Opt. (12)

A. Carnicer, S. Vallmitjana, I. Juvells, “Correlation postprocessing-based method for the detection of defocused images,” Appl. Opt. 20, 4807–4811 (1997).
[CrossRef]

D. Casasent, E. Botha, “Optical symbolic substitution for morphological transformations,” Appl. Opt. 27, 3806–3810 (1988).
[CrossRef] [PubMed]

E. C. Botha, D. Casasent, “Optical laboratory morphological inspection processor,” Appl. Opt. 28, 5342–5350 (1989).
[CrossRef] [PubMed]

B. Javidi, J. Wang, “Binary nonlinear joint transform correlation with median and subset median thresholding,” Appl. Opt. 30, 967–976 (1991).
[CrossRef] [PubMed]

A. Fedor, M. O. Freeman, “Optical multiscale morphological processor using a complex-valued kernel,” Appl. Opt. 31, 4042–4050 (1992).
[CrossRef] [PubMed]

J. N. Mait, D. W. Prather, R. A. Athale, “Acousto-optic processing with electronic image feedback for morphological filtering,” Appl. Opt. 31, 5688–5698 (1992).
[CrossRef] [PubMed]

M. S. Alam, O. Perez, M. A. Karim, “Preprocessed multiobject joint transform correlator,” Appl. Opt. 32, 3102–3107 (1993).
[CrossRef] [PubMed]

P. Garcia-Martinex, D. Mas, J. Garcia, C. Ferreira, “Nonlinear morphological correlation: optoelectronic implementation,” Appl. Opt. 37, 2112–2118 (1998).
[CrossRef]

W. Wang, G. Jin, Y. Yan, M. Wu, “Joint wavelet-transform correlator for image feature extraction,” Appl. Opt. 34, 370–376 (1995).
[CrossRef] [PubMed]

P. S. Erbach, D. A. Gregory, X. Yang, “Optical wavelet transform by the phase-only joint transform correlator,” Appl. Opt. 35, 3117–3126 (1996).
[CrossRef] [PubMed]

S. Zhong, S. Liu, X. Zhang, C. Li, “Joint wavelet representation correlator for pattern recognition,” Appl. Opt. 37, 374–379 (1998).
[CrossRef]

C. S. Weaver, J. W. Goodman, “Technique for optically convolving two functions,” Appl. Opt. 5, 1248–1249 (1966).
[CrossRef] [PubMed]

Opt. Commun. (2)

D. Feng, H. Zhao, S. Xia, “Amplitude-modulated JTC for improving correlation discrimination,” Opt. Commun. 86, 260–264 (1991).
[CrossRef]

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

Opt. Eng. (1)

R. Tripathi, K. Singh, “Pattern discrimination using a bank of wavelet filters in a joint transform correlator,” Opt. Eng. 37, 32–538 (1998).
[CrossRef]

Opt. Lett. (3)

Proc. IEEE (1)

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

Other (1)

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

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Figures (8)

Fig. 1
Fig. 1

MPJTC setup. SLM, spatial light modulator.

Fig. 2
Fig. 2

Binary aircraft images used in the simulation: (a) noise-free image, (b) noise-corrupted image.

Fig. 3
Fig. 3

Gray-scale aircraft images used in the simulation: (a) noise-free image, (b) noise-corrupted image.

Fig. 4
Fig. 4

(a) Input joint image edges for GBJTC, (b) GBJTC output.

Fig. 5
Fig. 5

WBJTC output.

Fig. 6
Fig. 6

(a) Input joint image of the structuring element and the noisy image, (b) correlation output with threshold for the opening operation, (c) correlation output with threshold for the opening–closing operation.

Fig. 7
Fig. 7

(a) Input joint image edges of the reference image and the opening–closing processed image, (b) the corresponding MPJTC output.

Fig. 8
Fig. 8

Correlation corresponding to the gray-scale input image with (a) GBJTC, (b) WBJTC, (c) MPJTC.

Tables (2)

Tables Icon

Table 1 Correlation Results for the Binary Noisy Imagea

Tables Icon

Table 2 Correlation Results for the Gray-Scale Noisy Imagea

Equations (10)

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

tr=H1tx, yrx, y,
tΘr=HNtx, yrx, y,
tΘr=H1tx, y¯rx, y¯,
t  r=tΘrr,
t  r=trΘr,
tr-tΘr=t¯ΘrtΘr¯,
fx, y=rx, y+d+tx, y-d.
Fu, v=Ru, vexpjvd+Tu, vexp-jvd,
|Fu, v|2=|Ru, v|2+|Tu, v|2+Ru, vT*u, vexpj2vd+R*u, vTu, vexp-j2vd
fx, y=rx, yrx, y+tx, ytx, y+rx, ytx, y+2d+rx, ytx, y-2d.

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