Abstract

We investigate the performance of the binary joint transform correlator (JTC) for three types of thresholding used to binarize the joint power spectrum. The first thresholding method uses the median of the joint power spectrum of the reference image, which is independent of the effect of input scene noise. The second thresholding method uses the median of the joint power spectrum of the input scene and the reference image. The third method is the subset median thresholding. The subset median is computed for each segment of the joint power spectrum and is used to threshold the same segment. The threshold computed by the second or third method is dependent on the effect of the input scene noise. The correlation performance of the binary JTC is determined for each thresholding method and is compared with the linear (conventional) JTC. Computer simulation is used to determine the correlation peak intensity, peak-to-sidelobe ratio, and correlation width for various thresholding techniques. The results indicate that the thresholding of the joint power spectrum using the methods that take into account the input scene noise produces a reasonably good correlation performance.

© 1991 Optical Society of America

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References

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  1. B. Javidi, “Nonlinear Joint Power Spectrum Based Optical Correlation,” Appl. Opt. 28, 2358–2367 (1989).
    [Crossref] [PubMed]
  2. B. Javidi, J. L. Horner, “Single Spatial Light Modulator Joint Transform Correlator,” Appl. Opt. 28, 1027–1032 (1989).
    [Crossref] [PubMed]
  3. B. Javidi, “Comparison of Bipolar Joint Transform Image Correlators and Phase-Only Matched Filter Correlators,” Opt. Eng. 28, 267–272 (1989).
    [Crossref]
  4. B. Javidi, “Synthetic Discriminant Function-Based Binary Nonlinear Correlation,” Appl Opt. 28, 2490 (1989).
    [Crossref] [PubMed]
  5. C. S. Weaver, J. W. Goodman, “A Technique for Optically Convolving Two Functions,” Appl. Opt. 5, 1248(L), (1966).
    [Crossref]
  6. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1967).
  7. K. H. Fielding, J. L. Horner, “1-f Binary Joint Transform Correlator,” Opt. Eng. 29, 1081–1087 (1990).
    [Crossref]
  8. W. B. Hahn, D. L. Flannery, “Basic Design Elements of the Binary Joint Transform Correlation and Selected Optimization Techniques,” Proc. Soc. Photo-Opt. Instrum. Eng. 1347, (July1990).
  9. J. C. Kirsch, D. A. Gregory, “Video Rate Optical Correlation using a Magnetooptic SLM,” Opt. Eng. 29, 1122–1128 (1990).
    [Crossref]
  10. S. K. Rogers, J. D. Kline, M. Kabrisky, J. P. Mills, “New Binarization Techniques for Joint Transform Correlator,” Opt. Eng. 29, 1088–1093 (1990).
    [Crossref]
  11. A. V. Aho et al., The Design and Analysis of Computer Algorithms (Addision-Wesley, Reading, MA, 1974).

1990 (4)

K. H. Fielding, J. L. Horner, “1-f Binary Joint Transform Correlator,” Opt. Eng. 29, 1081–1087 (1990).
[Crossref]

W. B. Hahn, D. L. Flannery, “Basic Design Elements of the Binary Joint Transform Correlation and Selected Optimization Techniques,” Proc. Soc. Photo-Opt. Instrum. Eng. 1347, (July1990).

J. C. Kirsch, D. A. Gregory, “Video Rate Optical Correlation using a Magnetooptic SLM,” Opt. Eng. 29, 1122–1128 (1990).
[Crossref]

S. K. Rogers, J. D. Kline, M. Kabrisky, J. P. Mills, “New Binarization Techniques for Joint Transform Correlator,” Opt. Eng. 29, 1088–1093 (1990).
[Crossref]

1989 (4)

B. Javidi, “Nonlinear Joint Power Spectrum Based Optical Correlation,” Appl. Opt. 28, 2358–2367 (1989).
[Crossref] [PubMed]

B. Javidi, J. L. Horner, “Single Spatial Light Modulator Joint Transform Correlator,” Appl. Opt. 28, 1027–1032 (1989).
[Crossref] [PubMed]

B. Javidi, “Comparison of Bipolar Joint Transform Image Correlators and Phase-Only Matched Filter Correlators,” Opt. Eng. 28, 267–272 (1989).
[Crossref]

B. Javidi, “Synthetic Discriminant Function-Based Binary Nonlinear Correlation,” Appl Opt. 28, 2490 (1989).
[Crossref] [PubMed]

1966 (1)

C. S. Weaver, J. W. Goodman, “A Technique for Optically Convolving Two Functions,” Appl. Opt. 5, 1248(L), (1966).
[Crossref]

Aho, A. V.

A. V. Aho et al., The Design and Analysis of Computer Algorithms (Addision-Wesley, Reading, MA, 1974).

Fielding, K. H.

K. H. Fielding, J. L. Horner, “1-f Binary Joint Transform Correlator,” Opt. Eng. 29, 1081–1087 (1990).
[Crossref]

Flannery, D. L.

W. B. Hahn, D. L. Flannery, “Basic Design Elements of the Binary Joint Transform Correlation and Selected Optimization Techniques,” Proc. Soc. Photo-Opt. Instrum. Eng. 1347, (July1990).

Goodman, J. W.

C. S. Weaver, J. W. Goodman, “A Technique for Optically Convolving Two Functions,” Appl. Opt. 5, 1248(L), (1966).
[Crossref]

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1967).

Gregory, D. A.

J. C. Kirsch, D. A. Gregory, “Video Rate Optical Correlation using a Magnetooptic SLM,” Opt. Eng. 29, 1122–1128 (1990).
[Crossref]

Hahn, W. B.

W. B. Hahn, D. L. Flannery, “Basic Design Elements of the Binary Joint Transform Correlation and Selected Optimization Techniques,” Proc. Soc. Photo-Opt. Instrum. Eng. 1347, (July1990).

Horner, J. L.

K. H. Fielding, J. L. Horner, “1-f Binary Joint Transform Correlator,” Opt. Eng. 29, 1081–1087 (1990).
[Crossref]

B. Javidi, J. L. Horner, “Single Spatial Light Modulator Joint Transform Correlator,” Appl. Opt. 28, 1027–1032 (1989).
[Crossref] [PubMed]

Javidi, B.

B. Javidi, “Nonlinear Joint Power Spectrum Based Optical Correlation,” Appl. Opt. 28, 2358–2367 (1989).
[Crossref] [PubMed]

B. Javidi, “Comparison of Bipolar Joint Transform Image Correlators and Phase-Only Matched Filter Correlators,” Opt. Eng. 28, 267–272 (1989).
[Crossref]

B. Javidi, “Synthetic Discriminant Function-Based Binary Nonlinear Correlation,” Appl Opt. 28, 2490 (1989).
[Crossref] [PubMed]

B. Javidi, J. L. Horner, “Single Spatial Light Modulator Joint Transform Correlator,” Appl. Opt. 28, 1027–1032 (1989).
[Crossref] [PubMed]

Kabrisky, M.

S. K. Rogers, J. D. Kline, M. Kabrisky, J. P. Mills, “New Binarization Techniques for Joint Transform Correlator,” Opt. Eng. 29, 1088–1093 (1990).
[Crossref]

Kirsch, J. C.

J. C. Kirsch, D. A. Gregory, “Video Rate Optical Correlation using a Magnetooptic SLM,” Opt. Eng. 29, 1122–1128 (1990).
[Crossref]

Kline, J. D.

S. K. Rogers, J. D. Kline, M. Kabrisky, J. P. Mills, “New Binarization Techniques for Joint Transform Correlator,” Opt. Eng. 29, 1088–1093 (1990).
[Crossref]

Mills, J. P.

S. K. Rogers, J. D. Kline, M. Kabrisky, J. P. Mills, “New Binarization Techniques for Joint Transform Correlator,” Opt. Eng. 29, 1088–1093 (1990).
[Crossref]

Rogers, S. K.

S. K. Rogers, J. D. Kline, M. Kabrisky, J. P. Mills, “New Binarization Techniques for Joint Transform Correlator,” Opt. Eng. 29, 1088–1093 (1990).
[Crossref]

Weaver, C. S.

C. S. Weaver, J. W. Goodman, “A Technique for Optically Convolving Two Functions,” Appl. Opt. 5, 1248(L), (1966).
[Crossref]

Appl Opt. (1)

B. Javidi, “Synthetic Discriminant Function-Based Binary Nonlinear Correlation,” Appl Opt. 28, 2490 (1989).
[Crossref] [PubMed]

Appl. Opt. (3)

Opt. Eng. (4)

B. Javidi, “Comparison of Bipolar Joint Transform Image Correlators and Phase-Only Matched Filter Correlators,” Opt. Eng. 28, 267–272 (1989).
[Crossref]

K. H. Fielding, J. L. Horner, “1-f Binary Joint Transform Correlator,” Opt. Eng. 29, 1081–1087 (1990).
[Crossref]

J. C. Kirsch, D. A. Gregory, “Video Rate Optical Correlation using a Magnetooptic SLM,” Opt. Eng. 29, 1122–1128 (1990).
[Crossref]

S. K. Rogers, J. D. Kline, M. Kabrisky, J. P. Mills, “New Binarization Techniques for Joint Transform Correlator,” Opt. Eng. 29, 1088–1093 (1990).
[Crossref]

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

W. B. Hahn, D. L. Flannery, “Basic Design Elements of the Binary Joint Transform Correlation and Selected Optimization Techniques,” Proc. Soc. Photo-Opt. Instrum. Eng. 1347, (July1990).

Other (2)

A. V. Aho et al., The Design and Analysis of Computer Algorithms (Addision-Wesley, Reading, MA, 1974).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1967).

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Figures (10)

Fig. 1
Fig. 1

Binary nonlinear joint transform correlator.

Fig. 2
Fig. 2

Images used in the tests: (a) reference image; (b) input image with the limited scene; (c) input image with the complete scene.

Fig. 3
Fig. 3

Joint power spectrum for images shown in Fig. 2: (a) joint power spectrum of the tank and the tank; (b) joint power spectrum of the tank and the tank in the limited input scene; (c) joint power spectrum of the tank and the tank in a complete input scene.

Fig. 4
Fig. 4

Effects of the input scene noise on the joint power spectrum histogram. VTF is the joint power spectrum median of the tank and the tank. VTN is the joint power spectrum median of the tank and the tank in the input scene: (a) joint power spectrum histogram of the tank and tank; (b) joint power spectrum histogram of the tank and the tank in the limited input scene; (c) joint power spectrum histogram of the tank and the tank in the complete input scene.

Fig. 5
Fig. 5

Effects of the threshold value on the binary transmittance pulses of the joint power spectrum of the reference image and the complete input scene. (a) The threshold for binarization of the joint power spectrum is computed without taking into account the effect of the input scene noise. (a) The middle row of the joint power spectrum of the tank and the tank in the complete input scene. (b) The binarized joint power spectrum using the fixed threshold value (first method). (c) The binarized joint power spectrum using its median value (second method).

Fig. 6
Fig. 6

Block diagram of the computer simulation: (a) classic JTC; (b) binary JTC using a fixed threshold value; (c) binary JTC using the median of the joint power spectrum of the reference and the input scene as the threshold; (d) binary JTC using the subset median thresholding.

Fig. 7
Fig. 7

Linear JTC output for the images shown in Fig. 2: (a) autocorrelation result for the tank [see Fig. 2(a)]; (b) correlation results for the limited input scene [see Fig. 2(b)]; (c) correlation results for the complete input scene [see Fig. 2(c)].

Fig. 8
Fig. 8

Binary JTC output using the median of the joint power spectrum of the reference image: (a) autocorrelation result for the tank [see Fig. 2(a)]; (b) correlation results for the limited input scene [see Fig. 2(b)]; (c) correlation results for the complete input scene [see Fig. 2(c)].

Fig. 9
Fig. 9

Binary JTC output using the median of the joint power spectrum of the reference image and the input scene: (a) autocorrelation result for the tank [see Fig. 2(a)]; (b) correlation results for the limited input scene [see Fig. 2(b)]; (c) correlation results for the complete input scene [see Fig. 2(c)].

Fig. 10
Fig. 10

Binary JTC output using the row-by-row thresholding of the joint power spectrum of the reference image and the input scene: (a) autocorrelation result for the tank [see Fig. 2(a)]; (b) correlation results for the limited input scene [see Fig. 2(b)]; (c) correlation results for the complete input scene [see Fig. 2(c)].

Tables (4)

Tables Icon

Table I Conventional JTC

Tables Icon

Table II Binary JTC Using the Fixed Threshold Value

Tables Icon

Table III Binary JTC Using the Noise Dependent Threshold Value

Tables Icon

Table IV Binary JTC Using the Row-by-Row Threshold Method

Equations (11)

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E ( α , β ) = | I ( α , β ) | 2 = S 2 ( α , β ) + R 2 ( α , β ) + S ( α , β ) exp [ j ϕ S ( α , β ) ] R ( α , β ) exp [ j ϕ R ( α , β ) ] exp ( j 2 x 0 α ) + S ( α , β ) exp [ j ϕ S ( α , β ) ] R ( α , β ) exp [ j ϕ R ( α , β ) ] exp ( j 2 x 0 α ) ,
g ( α , β ) = { 1 , E ( α , β ) V T , 0 , E ( α , β ) < V T .
g c ( α , β ) = 2 π 1 [ R 2 ( α , β ) + S 2 ( α , β ) V T 2 R ( α , β ) S ( α , β ) ] 2 × cos [ 2 x 0 α + ϕ S ( α , β ) ϕ R ( α , β ) ] ,
g 1 a [ R ( α , β ) ] = 2 V T π R ( α , β ) 1 V T 4 R 2 ( α , β ) cos ( 2 x 0 α ) 4 R 2 ( α , β ) V T .
E R ( α , β ) = 2 R 2 ( α , β ) + 2 R 2 ( α , β ) cos ( 2 x 0 α ) .
V T F = med { hist [ E R ( α , β ) ] } ,
V T N = med { hist [ E ( α , β ) ] } ,
V T N M = med { hist [ E m ( α , β ) ] } ,
g m ( α , β ) = { 1 , E m ( α , β ) V T N M , 0 , E m ( α , β ) < V T N M ,
H υ m [ R ( α , β ) S ( α , β ) ] = 2 π υ sin { υ cos 1 [ R 2 ( α , β ) + S 2 ( α , β ) V T N M 2 R ( α , β ) S ( α , β ) ] } .
g ( α , β ) = m = 1 M g m ( α , β ) .

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