Abstract

In multiobject pattern recognition the height of the correlation peaks should be controlled when the power spectrum of a joint transform correlator is binarized. In this paper a method to predetermine the value of detection peaks is demonstrated. The technique is based on a frequency-variant threshold in order to remove the intraclass terms and on a suitable factor to normalize the binary joint power spectrum. Digital simulations and experimental hybrid implementation of this method were carried out.

© 1994 Optical Society of America

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References

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  1. C. S. Weaver, J. W. Goodman, “A technique for optically convolving two functions,” Appl. Opt. 5, 1248–1249 (1966).
    [Crossref] [PubMed]
  2. F. T. S. Yu, H. J. Lu, “A real-time programmable joint transform correlator,” Opt. Commun. 52, 10–16 (1984).
    [Crossref]
  3. F. T. S. Yu, T. Nagata, “Binary phase-only joint transform correlator,” Microwave Opt. Tech. Lett. 2, 15–19 (1989).
    [Crossref]
  4. B. Javidi, “Nonlinear joint power spectrum based optical correlation,” Appl. Opt. 28, 2358–2367 (1989).
    [Crossref] [PubMed]
  5. B. Javidi, J. Wang, “Binary nonlinear joint transform correlation with median and subset median thresholding,” Appl. Opt. 30, 967–976 (1991).
    [Crossref] [PubMed]
  6. B. Javidi, J. Wang, Q. Tang, “Multiple-object binary joint transform correlation using multiple-level threshold crossing,” Appl. Opt. 30, 4234–4244 (1991).
    [Crossref] [PubMed]
  7. S. Vallmitjana, I. Juvells, A. Carnicer, “Evaluation of a suitable threshold for binarization of power spectrum in a noise-free joint transform correlator,” Opt. Commun. 90, 221–226 (1992).
    [Crossref]
  8. F. T. S. Yu, F. Cheng, T. Nagata, D. A. Gregory, “Effects of fringe binarization of multiobject joint transform correlation,” Appl. Opt. 28, 2988–2990 (1989).
    [Crossref] [PubMed]
  9. J. A. Davis, E. A. Merrill, D. M. Cotrell, R. M. Bunch, “Effects of sampling and binarization in the output of the joint transform correlator,” Opt. Eng. 29, 1094–1100 (1990).
    [Crossref]
  10. A. Carnicer, I. Juvells, S. Vallmitjana, “Effects of thresholding level variation in fringe binarization of multiobject joint transform correlation,” Appl. Opt. 31, 1012–1014 (1992).
    [Crossref] [PubMed]
  11. F. Cheng, P. Andres, F. T. S. Yu, “Removal of intraclass associations in joint transform power spectrum,” Opt. Commun. 99, 7–12 (1993).
    [Crossref]
  12. F. T. S. Yu, S. Jutamulia, T. W. Lin, D. A. Gregory, “Adaptive real-time pattern recognition using a liquid crystal TV based joint transform correlator,” Appl. Opt. 26, 1370–1372 (1987).
    [Crossref] [PubMed]
  13. I. Juvells, A. Carnicer, S. Vallmitjana, “Comparison between experiment and simulation in a real-time joint transform correlator,” Jpn. J. Appl. Phys. 31, 1076–1077 (1992).
    [Crossref]
  14. A. Carnicer, I. Juvells, S. Vallmitjana, J. R. de F. Moneo, “Analysis by digital simulation of the experimental features in real-time joint transform correlator,” J. Opt. (Paris) 23, 63–70 (1992).
    [Crossref]

1993 (1)

F. Cheng, P. Andres, F. T. S. Yu, “Removal of intraclass associations in joint transform power spectrum,” Opt. Commun. 99, 7–12 (1993).
[Crossref]

1992 (4)

I. Juvells, A. Carnicer, S. Vallmitjana, “Comparison between experiment and simulation in a real-time joint transform correlator,” Jpn. J. Appl. Phys. 31, 1076–1077 (1992).
[Crossref]

A. Carnicer, I. Juvells, S. Vallmitjana, J. R. de F. Moneo, “Analysis by digital simulation of the experimental features in real-time joint transform correlator,” J. Opt. (Paris) 23, 63–70 (1992).
[Crossref]

S. Vallmitjana, I. Juvells, A. Carnicer, “Evaluation of a suitable threshold for binarization of power spectrum in a noise-free joint transform correlator,” Opt. Commun. 90, 221–226 (1992).
[Crossref]

A. Carnicer, I. Juvells, S. Vallmitjana, “Effects of thresholding level variation in fringe binarization of multiobject joint transform correlation,” Appl. Opt. 31, 1012–1014 (1992).
[Crossref] [PubMed]

1991 (2)

1990 (1)

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

1989 (3)

1987 (1)

1984 (1)

F. T. S. Yu, H. J. Lu, “A real-time programmable joint transform correlator,” Opt. Commun. 52, 10–16 (1984).
[Crossref]

1966 (1)

Andres, P.

F. Cheng, P. Andres, F. T. S. Yu, “Removal of intraclass associations in joint transform power spectrum,” Opt. Commun. 99, 7–12 (1993).
[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 transform correlator,” Opt. Eng. 29, 1094–1100 (1990).
[Crossref]

Carnicer, A.

A. Carnicer, I. Juvells, S. Vallmitjana, “Effects of thresholding level variation in fringe binarization of multiobject joint transform correlation,” Appl. Opt. 31, 1012–1014 (1992).
[Crossref] [PubMed]

S. Vallmitjana, I. Juvells, A. Carnicer, “Evaluation of a suitable threshold for binarization of power spectrum in a noise-free joint transform correlator,” Opt. Commun. 90, 221–226 (1992).
[Crossref]

I. Juvells, A. Carnicer, S. Vallmitjana, “Comparison between experiment and simulation in a real-time joint transform correlator,” Jpn. J. Appl. Phys. 31, 1076–1077 (1992).
[Crossref]

A. Carnicer, I. Juvells, S. Vallmitjana, J. R. de F. Moneo, “Analysis by digital simulation of the experimental features in real-time joint transform correlator,” J. Opt. (Paris) 23, 63–70 (1992).
[Crossref]

Cheng, F.

F. Cheng, P. Andres, F. T. S. Yu, “Removal of intraclass associations in joint transform power spectrum,” Opt. Commun. 99, 7–12 (1993).
[Crossref]

F. T. S. Yu, F. Cheng, T. Nagata, D. A. Gregory, “Effects of fringe binarization of multiobject joint transform correlation,” Appl. Opt. 28, 2988–2990 (1989).
[Crossref] [PubMed]

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 transform correlator,” 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 transform correlator,” Opt. Eng. 29, 1094–1100 (1990).
[Crossref]

Goodman, J. W.

Gregory, D. A.

Javidi, B.

Jutamulia, S.

Juvells, I.

I. Juvells, A. Carnicer, S. Vallmitjana, “Comparison between experiment and simulation in a real-time joint transform correlator,” Jpn. J. Appl. Phys. 31, 1076–1077 (1992).
[Crossref]

A. Carnicer, I. Juvells, S. Vallmitjana, “Effects of thresholding level variation in fringe binarization of multiobject joint transform correlation,” Appl. Opt. 31, 1012–1014 (1992).
[Crossref] [PubMed]

S. Vallmitjana, I. Juvells, A. Carnicer, “Evaluation of a suitable threshold for binarization of power spectrum in a noise-free joint transform correlator,” Opt. Commun. 90, 221–226 (1992).
[Crossref]

A. Carnicer, I. Juvells, S. Vallmitjana, J. R. de F. Moneo, “Analysis by digital simulation of the experimental features in real-time joint transform correlator,” J. Opt. (Paris) 23, 63–70 (1992).
[Crossref]

Lin, T. W.

Lu, H. J.

F. T. S. Yu, H. J. Lu, “A real-time programmable joint transform correlator,” Opt. Commun. 52, 10–16 (1984).
[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 transform correlator,” Opt. Eng. 29, 1094–1100 (1990).
[Crossref]

Moneo, J. R. de F.

A. Carnicer, I. Juvells, S. Vallmitjana, J. R. de F. Moneo, “Analysis by digital simulation of the experimental features in real-time joint transform correlator,” J. Opt. (Paris) 23, 63–70 (1992).
[Crossref]

Nagata, T.

Tang, Q.

Vallmitjana, S.

S. Vallmitjana, I. Juvells, A. Carnicer, “Evaluation of a suitable threshold for binarization of power spectrum in a noise-free joint transform correlator,” Opt. Commun. 90, 221–226 (1992).
[Crossref]

A. Carnicer, I. Juvells, S. Vallmitjana, “Effects of thresholding level variation in fringe binarization of multiobject joint transform correlation,” Appl. Opt. 31, 1012–1014 (1992).
[Crossref] [PubMed]

A. Carnicer, I. Juvells, S. Vallmitjana, J. R. de F. Moneo, “Analysis by digital simulation of the experimental features in real-time joint transform correlator,” J. Opt. (Paris) 23, 63–70 (1992).
[Crossref]

I. Juvells, A. Carnicer, S. Vallmitjana, “Comparison between experiment and simulation in a real-time joint transform correlator,” Jpn. J. Appl. Phys. 31, 1076–1077 (1992).
[Crossref]

Wang, J.

Weaver, C. S.

Yu, F. T. S.

F. Cheng, P. Andres, F. T. S. Yu, “Removal of intraclass associations in joint transform power spectrum,” Opt. Commun. 99, 7–12 (1993).
[Crossref]

F. T. S. Yu, T. Nagata, “Binary phase-only joint transform correlator,” Microwave Opt. Tech. Lett. 2, 15–19 (1989).
[Crossref]

F. T. S. Yu, F. Cheng, T. Nagata, D. A. Gregory, “Effects of fringe binarization of multiobject joint transform correlation,” Appl. Opt. 28, 2988–2990 (1989).
[Crossref] [PubMed]

F. T. S. Yu, S. Jutamulia, T. W. Lin, D. A. Gregory, “Adaptive real-time pattern recognition using a liquid crystal TV based joint transform correlator,” Appl. Opt. 26, 1370–1372 (1987).
[Crossref] [PubMed]

F. T. S. Yu, H. J. Lu, “A real-time programmable joint transform correlator,” Opt. Commun. 52, 10–16 (1984).
[Crossref]

Appl. Opt. (7)

J. Opt. (Paris) (1)

A. Carnicer, I. Juvells, S. Vallmitjana, J. R. de F. Moneo, “Analysis by digital simulation of the experimental features in real-time joint transform correlator,” J. Opt. (Paris) 23, 63–70 (1992).
[Crossref]

Jpn. J. Appl. Phys. (1)

I. Juvells, A. Carnicer, S. Vallmitjana, “Comparison between experiment and simulation in a real-time joint transform correlator,” Jpn. J. Appl. Phys. 31, 1076–1077 (1992).
[Crossref]

Microwave Opt. Tech. Lett. (1)

F. T. S. Yu, T. Nagata, “Binary phase-only joint transform correlator,” Microwave Opt. Tech. Lett. 2, 15–19 (1989).
[Crossref]

Opt. Commun. (3)

F. Cheng, P. Andres, F. T. S. Yu, “Removal of intraclass associations in joint transform power spectrum,” Opt. Commun. 99, 7–12 (1993).
[Crossref]

F. T. S. Yu, H. J. Lu, “A real-time programmable joint transform correlator,” Opt. Commun. 52, 10–16 (1984).
[Crossref]

S. Vallmitjana, I. Juvells, A. Carnicer, “Evaluation of a suitable threshold for binarization of power spectrum in a noise-free joint transform correlator,” Opt. Commun. 90, 221–226 (1992).
[Crossref]

Opt. Eng. (1)

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

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Figures (6)

Fig. 1
Fig. 1

(a) Butterflies (scene 1), (b) peaks before normalization, (c) normalized peaks with WR(u, v) = |HR(u, v)|−1, (d) normalized peaks with WR = med[|HR(u, v)|2]−1/2.

Fig. 2
Fig. 2

(a) Butterflies (scene 2), (b) peaks before normalization, (c) normalized peaks.

Fig. 3
Fig. 3

(a) Satellite scene, (b) peaks before normalization, (c) normalized peaks.

Fig. 4
Fig. 4

(a) Satellite and Earth scene, (b) peaks before normalization, (c) normalized peaks.

Fig. 5
Fig. 5

Schematic diagram of the optical setup: FL, Fourier-transform lens; PC, personal computer.

Fig. 6
Fig. 6

Three-dimensional representation of optical correlation: (a) Îsum photographically recorded, (b) Îsum displayed on a LCTV.

Tables (4)

Tables Icon

Table 1 Butterflies (Scene 1)

Tables Icon

Table 2 Butterflies (Scene 2)

Tables Icon

Table 3 Satellite Scene

Tables Icon

Table 4 Satellite and Earth Scene

Equations (12)

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

I ( u , v ) = H R ( u , v ) 2 + H ( u , v ) 2 + 2 H R ( u , v ) H ( u , v ) × cos [ x 0 u + y 0 v + ϕ s ( u , v ) - ϕ R ( u , v ) ] ,
I b ( u , v ) = 1 , for I ( u , v ) > I T , I b ( u , v ) = - 1 , for I ( u , v ) < I T ,
I b ( u , v ) = ν A ν ( u , v ) × cos { ν [ x 0 u + y 0 v + ϕ s ( u , v ) - ϕ R ( u , v ) ] } ,
A ν ( u , v ) = ( 2 / π ν ) sin ( ν arccos { [ I T - H R ( u , v ) 2 - H ( u , v ) 2 ] / 2 H R ( u , v ) H ( u , v ) } ) .
I b ( u , v ) = ν odd ( 2 / π ν ) ( - 1 ) ( ν - 1 ) / 2 × cos { ν [ x 0 u + y 0 v + ϕ S ( u , v ) - ϕ R ( u , v ) ] } = ( 2 / π ) cos [ x 0 u + y 0 v + ϕ S ( u , v ) - ϕ R ( u , v ) ] + .
FT [ I b ( 1 ) ( u , v ) ] = δ ( x + x 0 , y + y 0 ) + δ ( x - x 0 , y - y 0 ) ,
I b ( 1 ) ( u , v ) = j I b j ( 1 ) ( u , v ) , I b , j ( 1 ) ( u , v ) = ( 2 / π ) [ H j ( u , v ) / H ( u , v ) ] × cos [ x j u + y j v + ϕ j ( u , v ) - ϕ R ( u , v ) ] ,
I b , R ( 1 ) ( u , v ) = ( 2 / π ) [ H R ( u , v ) / H ( u , v ) ] cos ( x j u + y j v ) .
I ^ b ( 1 ) ( u , v ) = W R ( u , v ) I b ( 1 ) ( u , v ) = j W R ( u , v ) I b , j ( 1 ) ( u , v ) ,
{ med [ H R ( u , v ) 2 ] } 1 / 2 = med [ H R ( u , v ) ] .
I ^ b ( 1 ) ( u , v ) = j W R I b , j ( 1 ) ( u , v ) = j { med [ H R ( u , v ) 2 ] } 1 / 2 I b , j ( 1 ) ( u , v ) .
I ^ sum = Σ I ^ b ( 1 ) ( u , v ) .

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