Abstract

Improved correlation discrimination is achieved by using a fringe-adjusted joint transform correlator (JTC). This technique is found to yield significantly better correlation output than the classical and binary JTC’s for input scenes involving single as well as multiple objects. It also avoids the computation-intensive Fourier-plane joint power spectrum binarization processing of a binary JTC. Two optical implementations for the proposed technique are also suggested.

© 1993 Optical Society of America

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References

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  1. A. B. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).
    [CrossRef]
  2. C. S. Weaver, J. W. Goodman, “Technique for optically convolving two functions,” Appl. Opt. 5, 1248 (1966).
    [CrossRef] [PubMed]
  3. J. C. Kirsch, D. A. Gregory, “Video rate optical correlation using a magneto-optic spatial light modulator,” Opt. Eng. 29, 1122–1128 (1990).
    [CrossRef]
  4. M. S. Alam, A. A. S. Awwal, M. A. Karim, “Improved correlation discrimination using joint Fourier transform optical correlator,” Micro. Opt. Tech. Lett. 4, 103–106 (1991).
    [CrossRef]
  5. F. T. J. Johnson, T. H. Barnes, T. Eiju, T. G. Haskell, K. Matsuda, “Analysis of a joint transform correlator using a phase-only spatial light modulator,” Opt. Eng. 30, 1947–1957 (1991).
    [CrossRef]
  6. B. Javidi, C. Kuo, “Joint transform image correlation using a binary spatial light modulator at the Fourier plane,” Appl. Opt. 27, 663–665 (1988).
    [CrossRef] [PubMed]
  7. F. T. S. Yu, F. Cheng, T. Nagata, D. A. Gregory, “Effect of fringe binarization of multi-object joint transform correlation,” Appl. Opt. 28, 2988–2990 (1989).
    [CrossRef] [PubMed]
  8. J. A. Davis, E. A. Merrill, D. M. Cotrell, R. M. Bunch, “Effects of sampling and binarization in the output of the joint Fourier transform correlation,” Opt. Eng. 29, 1094–1100 (1990).
    [CrossRef]
  9. D. Feng, H. Zhao, S. Xia, “Amplitude-modulated JTC for improving correlation discrimination,” Opt. Commun. 86, 260–264(1991).
    [CrossRef]
  10. M. S. Alam, M. A. Karim, “Improved correlation discrimination in a multiobject bipolar joint Fourier transform correlator,” Opt. Laser Tech. 24, 45–50 (1992).
    [CrossRef]
  11. A. A. S. Awwal, M. A. Karim, S. R. Jahan, “Improved correlation discrimination using an amplitude modulated phase-only filter,” Appl. Opt. 29, 233–236 (1990).
    [CrossRef] [PubMed]
  12. J. L. Horner, “Metrics for assessing pattern recognition performance,” Appl. Opt. 31, 165–166 (1992).
    [CrossRef] [PubMed]
  13. B. Javidi, F. Parchekani, Q. Tang, “Gray-scale nonlinear joint transform correlator,” Opt. Eng. 31, 888–895 (1992).
    [CrossRef]
  14. W. B. Hahn, D. L. Flannery, “Design elements of a binary joint transform correlator and selected optimization techniques,” Opt. Eng. 31, 896–905 (1992).
    [CrossRef]

1992 (4)

M. S. Alam, M. A. Karim, “Improved correlation discrimination in a multiobject bipolar joint Fourier transform correlator,” Opt. Laser Tech. 24, 45–50 (1992).
[CrossRef]

B. Javidi, F. Parchekani, Q. Tang, “Gray-scale nonlinear joint transform correlator,” Opt. Eng. 31, 888–895 (1992).
[CrossRef]

W. B. Hahn, D. L. Flannery, “Design elements of a binary joint transform correlator and selected optimization techniques,” Opt. Eng. 31, 896–905 (1992).
[CrossRef]

J. L. Horner, “Metrics for assessing pattern recognition performance,” Appl. Opt. 31, 165–166 (1992).
[CrossRef] [PubMed]

1991 (3)

M. S. Alam, A. A. S. Awwal, M. A. Karim, “Improved correlation discrimination using joint Fourier transform optical correlator,” Micro. Opt. Tech. Lett. 4, 103–106 (1991).
[CrossRef]

F. T. J. Johnson, T. H. Barnes, T. Eiju, T. G. Haskell, K. Matsuda, “Analysis of a joint transform correlator using a phase-only spatial light modulator,” Opt. Eng. 30, 1947–1957 (1991).
[CrossRef]

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

1990 (3)

J. C. Kirsch, D. A. Gregory, “Video rate optical correlation using a magneto-optic spatial light modulator,” Opt. Eng. 29, 1122–1128 (1990).
[CrossRef]

J. A. Davis, E. A. Merrill, D. M. Cotrell, R. M. Bunch, “Effects of sampling and binarization in the output of the joint Fourier transform correlation,” Opt. Eng. 29, 1094–1100 (1990).
[CrossRef]

A. A. S. Awwal, M. A. Karim, S. R. Jahan, “Improved correlation discrimination using an amplitude modulated phase-only filter,” Appl. Opt. 29, 233–236 (1990).
[CrossRef] [PubMed]

1989 (1)

1988 (1)

1966 (1)

1964 (1)

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

Alam, M. S.

M. S. Alam, M. A. Karim, “Improved correlation discrimination in a multiobject bipolar joint Fourier transform correlator,” Opt. Laser Tech. 24, 45–50 (1992).
[CrossRef]

M. S. Alam, A. A. S. Awwal, M. A. Karim, “Improved correlation discrimination using joint Fourier transform optical correlator,” Micro. Opt. Tech. Lett. 4, 103–106 (1991).
[CrossRef]

Awwal, A. A. S.

M. S. Alam, A. A. S. Awwal, M. A. Karim, “Improved correlation discrimination using joint Fourier transform optical correlator,” Micro. Opt. Tech. Lett. 4, 103–106 (1991).
[CrossRef]

A. A. S. Awwal, M. A. Karim, S. R. Jahan, “Improved correlation discrimination using an amplitude modulated phase-only filter,” Appl. Opt. 29, 233–236 (1990).
[CrossRef] [PubMed]

Barnes, T. H.

F. T. J. Johnson, T. H. Barnes, T. Eiju, T. G. Haskell, K. Matsuda, “Analysis of a joint transform correlator using a phase-only spatial light modulator,” Opt. Eng. 30, 1947–1957 (1991).
[CrossRef]

Bunch, R. M.

J. A. Davis, E. A. Merrill, D. M. Cotrell, R. M. Bunch, “Effects of sampling and binarization in the output of the joint Fourier transform correlation,” Opt. Eng. 29, 1094–1100 (1990).
[CrossRef]

Cheng, F.

Cotrell, D. M.

J. A. Davis, E. A. Merrill, D. M. Cotrell, R. M. Bunch, “Effects of sampling and binarization in the output of the joint Fourier transform correlation,” Opt. Eng. 29, 1094–1100 (1990).
[CrossRef]

Davis, J. A.

J. A. Davis, E. A. Merrill, D. M. Cotrell, R. M. Bunch, “Effects of sampling and binarization in the output of the joint Fourier transform correlation,” Opt. Eng. 29, 1094–1100 (1990).
[CrossRef]

Eiju, T.

F. T. J. Johnson, T. H. Barnes, T. Eiju, T. G. Haskell, K. Matsuda, “Analysis of a joint transform correlator using a phase-only spatial light modulator,” Opt. Eng. 30, 1947–1957 (1991).
[CrossRef]

Feng, D.

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

Flannery, D. L.

W. B. Hahn, D. L. Flannery, “Design elements of a binary joint transform correlator and selected optimization techniques,” Opt. Eng. 31, 896–905 (1992).
[CrossRef]

Goodman, J. W.

Gregory, D. A.

J. C. Kirsch, D. A. Gregory, “Video rate optical correlation using a magneto-optic spatial light modulator,” Opt. Eng. 29, 1122–1128 (1990).
[CrossRef]

F. T. S. Yu, F. Cheng, T. Nagata, D. A. Gregory, “Effect of fringe binarization of multi-object joint transform correlation,” Appl. Opt. 28, 2988–2990 (1989).
[CrossRef] [PubMed]

Hahn, W. B.

W. B. Hahn, D. L. Flannery, “Design elements of a binary joint transform correlator and selected optimization techniques,” Opt. Eng. 31, 896–905 (1992).
[CrossRef]

Haskell, T. G.

F. T. J. Johnson, T. H. Barnes, T. Eiju, T. G. Haskell, K. Matsuda, “Analysis of a joint transform correlator using a phase-only spatial light modulator,” Opt. Eng. 30, 1947–1957 (1991).
[CrossRef]

Horner, J. L.

Jahan, S. R.

Javidi, B.

B. Javidi, F. Parchekani, Q. Tang, “Gray-scale nonlinear joint transform correlator,” Opt. Eng. 31, 888–895 (1992).
[CrossRef]

B. Javidi, C. Kuo, “Joint transform image correlation using a binary spatial light modulator at the Fourier plane,” Appl. Opt. 27, 663–665 (1988).
[CrossRef] [PubMed]

Johnson, F. T. J.

F. T. J. Johnson, T. H. Barnes, T. Eiju, T. G. Haskell, K. Matsuda, “Analysis of a joint transform correlator using a phase-only spatial light modulator,” Opt. Eng. 30, 1947–1957 (1991).
[CrossRef]

Karim, M. A.

M. S. Alam, M. A. Karim, “Improved correlation discrimination in a multiobject bipolar joint Fourier transform correlator,” Opt. Laser Tech. 24, 45–50 (1992).
[CrossRef]

M. S. Alam, A. A. S. Awwal, M. A. Karim, “Improved correlation discrimination using joint Fourier transform optical correlator,” Micro. Opt. Tech. Lett. 4, 103–106 (1991).
[CrossRef]

A. A. S. Awwal, M. A. Karim, S. R. Jahan, “Improved correlation discrimination using an amplitude modulated phase-only filter,” Appl. Opt. 29, 233–236 (1990).
[CrossRef] [PubMed]

Kirsch, J. C.

J. C. Kirsch, D. A. Gregory, “Video rate optical correlation using a magneto-optic spatial light modulator,” Opt. Eng. 29, 1122–1128 (1990).
[CrossRef]

Kuo, C.

Matsuda, K.

F. T. J. Johnson, T. H. Barnes, T. Eiju, T. G. Haskell, K. Matsuda, “Analysis of a joint transform correlator using a phase-only spatial light modulator,” Opt. Eng. 30, 1947–1957 (1991).
[CrossRef]

Merrill, E. A.

J. A. Davis, E. A. Merrill, D. M. Cotrell, R. M. Bunch, “Effects of sampling and binarization in the output of the joint Fourier transform correlation,” Opt. Eng. 29, 1094–1100 (1990).
[CrossRef]

Nagata, T.

Parchekani, F.

B. Javidi, F. Parchekani, Q. Tang, “Gray-scale nonlinear joint transform correlator,” Opt. Eng. 31, 888–895 (1992).
[CrossRef]

Tang, Q.

B. Javidi, F. Parchekani, Q. Tang, “Gray-scale nonlinear joint transform correlator,” Opt. Eng. 31, 888–895 (1992).
[CrossRef]

VanderLugt, A. B.

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

Weaver, C. S.

Xia, S.

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

Yu, F. T. S.

Zhao, H.

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

Appl. Opt. (5)

IEEE Trans. Inf. Theory (1)

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

Micro. Opt. Tech. Lett. (1)

M. S. Alam, A. A. S. Awwal, M. A. Karim, “Improved correlation discrimination using joint Fourier transform optical correlator,” Micro. Opt. Tech. Lett. 4, 103–106 (1991).
[CrossRef]

Opt. Commun. (1)

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

Opt. Eng. (5)

F. T. J. Johnson, T. H. Barnes, T. Eiju, T. G. Haskell, K. Matsuda, “Analysis of a joint transform correlator using a phase-only spatial light modulator,” Opt. Eng. 30, 1947–1957 (1991).
[CrossRef]

J. A. Davis, E. A. Merrill, D. M. Cotrell, R. M. Bunch, “Effects of sampling and binarization in the output of the joint Fourier transform correlation,” Opt. Eng. 29, 1094–1100 (1990).
[CrossRef]

B. Javidi, F. Parchekani, Q. Tang, “Gray-scale nonlinear joint transform correlator,” Opt. Eng. 31, 888–895 (1992).
[CrossRef]

W. B. Hahn, D. L. Flannery, “Design elements of a binary joint transform correlator and selected optimization techniques,” Opt. Eng. 31, 896–905 (1992).
[CrossRef]

J. C. Kirsch, D. A. Gregory, “Video rate optical correlation using a magneto-optic spatial light modulator,” Opt. Eng. 29, 1122–1128 (1990).
[CrossRef]

Opt. Laser Tech. (1)

M. S. Alam, M. A. Karim, “Improved correlation discrimination in a multiobject bipolar joint Fourier transform correlator,” Opt. Laser Tech. 24, 45–50 (1992).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Fringe-adjusted JTC implementation–1. BS, beam splitter.

Fig. 2
Fig. 2

Fringe-adjusted JTC implementation—2. BS, beam splitter.

Fig. 3
Fig. 3

(a) reference image; (b) input scene containing single object.

Fig. 4
Fig. 4

Correlation output corresponding to the classical JTC.

Fig. 5
Fig. 5

(a) binarized joint power spectrum corresponding to the binary JTC; (b) correlation output corresponding to Fig. 3(b) as the input scene for the binary JTC.

Fig. 6
Fig. 6

(a) fringe-adjusted filter; (b) correlation output corresponding to Fig. 3(b) as the input scene for the fringe-adjusted JTC.

Fig. 7
Fig. 7

(a) input joint image containing single reference and multiple objects; (b) correlation output corresponding to Fig. 7(a) for the binary JTC; (c) correlation output corresponding to Fig. 7(a) for the fringe-adjusted JTC.

Tables (2)

Tables Icon

Table 1 JTC Results for Single Object Case

Tables Icon

Table 2 JTC Results for Multiple Object Case

Equations (14)

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f ( x , y ) = r ( x , y + y ) + t ( x , y - y ) .
F ( u , v ) = R ( u , v ) exp [ ϕ r ( u , v ) ] exp ( j v y ) + T ( u , v ) exp [ ϕ t ( u , v ) ] exp ( - j v y ) ,
F ( u , v ) 2 = R ( u , v ) 2 + T ( u , v ) 2 + 2 R ( u , v ) T ( u , v ) × cos [ ϕ r ( u , v ) - ϕ t ( u , v ) + 2 v y ] .
F ( u , v ) 2 = { + 1 if F ( u , v ) 2 T f - 1 otherwise ,
T f = median [ F ( u , v ) 2 ] .
H amf ( u , v ) = 1 R ( u , v ) 2 .
H faf ( u , v ) = B ( u , v ) A ( u , v ) + R ( u , v ) 2 ,
G ( u , v ) = H faf ( u , v ) F ( u , v ) 2 = [ B ( u , v ) A ( u , v ) + R ( u , v ) 2 ] { R ( u , v ) 2 + T ( u , v ) 2 + 2 R ( u , v ) T ( u , v ) × cos [ ϕ r ( u , v ) - ϕ t ( u , v ) + 2 v y ] } .
H faf ( u , v ) 1 R ( u , v ) 2 .
G ( u , v ) 2 { 1 + cos [ ϕ r ( u , v ) - ϕ t ( u , v ) + 2 v y ] } .
f ( x , y ) = r ( x , y - y ) + i = 1 n t i ( x , y - y i ) ,
F ( u , v ) 2 = R ( u , v ) 2 + i = 1 n T i ( u , v ) 2 + 2 i = 1 n R ( u , v ) T i ( u , v ) × cos [ ϕ r ( u , v ) - ϕ ti ( u , v ) + v ( y + y i ) ] + i = 1 n k = 1 n T i ( u , v ) T k ( u , v ) × cos [ ϕ ti ( u , v ) - ϕ tk ( u , v ) - v ( y i - y k ) ] ;             i k ,
G n ( u , v ) = [ 1 R ( u , v ) 2 ] { R ( u , v ) 2 + i = 1 n T i ( u , v ) 2 + 2 i = 1 n R ( u , v ) T i ( u , v ) × cos [ ϕ r ( u , v ) - ϕ ti ( u , v ) + v ( y + y i ) ] + i = 1 n k = 1 n T i ( u , v ) T k ( u , v ) × cos [ ϕ ti ( u , v ) - ϕ tk ( u , v ) - v ( y i - y k ) ] } ;             i k .
G n ( u , v ) = 2 + 2 cos [ v ( y + y i ) ] + [ 1 R ( u , v ) 2 ] × { 2 i = 2 n T i ( u , v ) 2 + 2 i = 2 n R ( u , v ) T i ( u , v ) × cos [ ϕ r ( u , v ) - ϕ ti ( u , v ) + v ( y + y i ) ] + i = 1 n k = 1 n T i ( u , v ) T k ( u , v ) × cos [ ϕ ti ( u , v ) - ϕ tk ( u , v ) - v ( y i - y k ) ] } ;             i k .

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