Abstract

A hybrid optical–digital signal processing system that estimates the trajectory of moving targets in a two-dimensional field at video frame rates was developed and constructed. The hybrid system is particularly well suited to the trajectory estimation of small, barely discernable, moving objects of unknown position and velocity in high-resolution image sequences. The system uses an optical Fourier processor and a point-diffraction interferometer to calculate the frequency-domain representation of moving objects from which their trajectory is estimated by use of conventional electronic processing techniques. In a series of experiments, target velocities were estimated to within 4% of their actual value and direction was estimated to within 3 deg.

© 1999 Optical Society of America

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References

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  1. B. Porat, B. Friedlander, “A frequency domain algorithm for multiframe detection and estimation of dim targets,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 398–401 (1990).
    [CrossRef]
  2. A. E. Cowart, W. E. Snyder, W. H. Ruedger, “The detection of unresolved targets using the Hough transform,” Comput. Vision Graph. Image Process. 21, 222–238 (1983).
    [CrossRef]
  3. L. T. Bruton, N. R. Bartley, “Three-dimensional image processing using the concept of network resonance,” IEEE Trans. Circuits Syst. CAS-32, 664–672 (1985).
    [CrossRef]
  4. L. T. Bruton, N. R. Bartley, “The enhancement and tracking of moving objects in digital images using adaptive three-dimensional recursive filters,” IEEE Trans. Circuits Syst. CAS-33, 604–612 (1986).
    [CrossRef]
  5. N. C. Mohanty, “Computer tracking of moving point targets in space,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-3, 606–611 (1981).
    [CrossRef]
  6. Y. Barniv, “Dynamic programming solution for detecting dim moving targets,” IEEE Trans. Aerosp. Electron. Syst. AES-21, 144–155 (1985).
    [CrossRef]
  7. S. D. Blostein, T. S. Huang, “Detecting small, moving objects in image sequences using sequential hypothesis testing,” IEEE Trans. Signal Process. 39, 1611–1629 (1991).
    [CrossRef]
  8. I. S. Reed, R. M. Gagliardi, H. M. Shao, “Application of three-dimensional filtering to moving target detection,” IEEE Trans. Aerosp. Electron. Syst. AES-19, 898–905 (1983).
    [CrossRef]
  9. S. A. Mahmoud, M. S. Afifi, R. J. Green, “Recognition and velocity computation of large moving objects in images,” IEEE Trans. Acoust. Speech Signal Process. 36, 1790–1791 (1988).
    [CrossRef]
  10. S. A. Mahmoud, “A new technique for velocity estimation of large moving objects,” IEEE Trans. Signal Process. 39, 741–743 (1991).
    [CrossRef]
  11. J. H. Choi, J. W. Jang, S. P. Lee, H. S. Kwak, “Multiple moving object estimation in image sequences of a natural scene,” Opt. Eng. 36, 2176–2183 (1997).
    [CrossRef]
  12. K. S. Knudsen, L. T. Bruton, “Mixed domain filtering of multidimensional signals,” IEEE Trans. Circuits Syst. Video Technol. 1, 260–268 (1991).
    [CrossRef]
  13. K. S. Knudsen, L. T. Bruton, “Moving object detection and trajectory estimation in the transform/spatiotemporal mixed domain,” in Proceedings of the 1992 IEEE International Conference on Acoustics, Speech, and Signal Processing (Institute of Electrical and Electronics Engineers, New York, 1992), Vol. 3, pp. 505–508.
    [CrossRef]
  14. K. S. Knudsen, L. T. Bruton, “Moving object nonlinear trajectory estimation in the transform/spatiotemporal mixed domain,” in Proceedings of the 1992 IEEE Custom Integrated Circuits Conference (Institute of Electrical and Electronics Engineers, New York, 1992), Vol. 5, pp. 2481–2484.
  15. S. Haykin, Adaptive Filter Theory, 3rd ed. (Prentice-Hall, Upper Saddle River, N.J., 1996).
  16. A. B. Watson, A. J. Ahumada, “Model of human visual-motion sensing,” J. Opt. Soc. Am. A 2, 322–341 (1985).
    [CrossRef] [PubMed]
  17. W. P. Linnik, “A simple interferometer for the investigation of optical systems,” C. R. Acad. Sci. URSS 5, 210 (1933) (in Russian).
  18. R. N. Smartt, J. Strong, “Point-diffraction interferometer,” J. Opt. Soc. Am. 62, 737 (1972) (abstract only).
  19. R. N. Smartt, W. H. Steel, “Theory and application of point-diffraction interferometers,” Jpn. J. Appl. Phys. Suppl. 14, 351–356 (1974).
  20. P. M. Lane, S. K. Knudsen, M. Cada, “Moving object trajectory estimation using an optical Fourier processor,” in 1998 International Conference on Applications of Photonic Technology, G. A. Lampropoulos, ed., Proc. SPIE3491, 939–943 (1998).
  21. K. S. Knudsen, Resolute Research Ltd., 24 Midridge Rise, Calgary, Alberta T2X 1E3, Canada, 1995 (personal communication).

1997

J. H. Choi, J. W. Jang, S. P. Lee, H. S. Kwak, “Multiple moving object estimation in image sequences of a natural scene,” Opt. Eng. 36, 2176–2183 (1997).
[CrossRef]

1991

K. S. Knudsen, L. T. Bruton, “Mixed domain filtering of multidimensional signals,” IEEE Trans. Circuits Syst. Video Technol. 1, 260–268 (1991).
[CrossRef]

S. A. Mahmoud, “A new technique for velocity estimation of large moving objects,” IEEE Trans. Signal Process. 39, 741–743 (1991).
[CrossRef]

S. D. Blostein, T. S. Huang, “Detecting small, moving objects in image sequences using sequential hypothesis testing,” IEEE Trans. Signal Process. 39, 1611–1629 (1991).
[CrossRef]

1990

B. Porat, B. Friedlander, “A frequency domain algorithm for multiframe detection and estimation of dim targets,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 398–401 (1990).
[CrossRef]

1988

S. A. Mahmoud, M. S. Afifi, R. J. Green, “Recognition and velocity computation of large moving objects in images,” IEEE Trans. Acoust. Speech Signal Process. 36, 1790–1791 (1988).
[CrossRef]

1986

L. T. Bruton, N. R. Bartley, “The enhancement and tracking of moving objects in digital images using adaptive three-dimensional recursive filters,” IEEE Trans. Circuits Syst. CAS-33, 604–612 (1986).
[CrossRef]

1985

L. T. Bruton, N. R. Bartley, “Three-dimensional image processing using the concept of network resonance,” IEEE Trans. Circuits Syst. CAS-32, 664–672 (1985).
[CrossRef]

Y. Barniv, “Dynamic programming solution for detecting dim moving targets,” IEEE Trans. Aerosp. Electron. Syst. AES-21, 144–155 (1985).
[CrossRef]

A. B. Watson, A. J. Ahumada, “Model of human visual-motion sensing,” J. Opt. Soc. Am. A 2, 322–341 (1985).
[CrossRef] [PubMed]

1983

I. S. Reed, R. M. Gagliardi, H. M. Shao, “Application of three-dimensional filtering to moving target detection,” IEEE Trans. Aerosp. Electron. Syst. AES-19, 898–905 (1983).
[CrossRef]

A. E. Cowart, W. E. Snyder, W. H. Ruedger, “The detection of unresolved targets using the Hough transform,” Comput. Vision Graph. Image Process. 21, 222–238 (1983).
[CrossRef]

1981

N. C. Mohanty, “Computer tracking of moving point targets in space,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-3, 606–611 (1981).
[CrossRef]

1974

R. N. Smartt, W. H. Steel, “Theory and application of point-diffraction interferometers,” Jpn. J. Appl. Phys. Suppl. 14, 351–356 (1974).

1972

R. N. Smartt, J. Strong, “Point-diffraction interferometer,” J. Opt. Soc. Am. 62, 737 (1972) (abstract only).

1933

W. P. Linnik, “A simple interferometer for the investigation of optical systems,” C. R. Acad. Sci. URSS 5, 210 (1933) (in Russian).

Afifi, M. S.

S. A. Mahmoud, M. S. Afifi, R. J. Green, “Recognition and velocity computation of large moving objects in images,” IEEE Trans. Acoust. Speech Signal Process. 36, 1790–1791 (1988).
[CrossRef]

Ahumada, A. J.

Barniv, Y.

Y. Barniv, “Dynamic programming solution for detecting dim moving targets,” IEEE Trans. Aerosp. Electron. Syst. AES-21, 144–155 (1985).
[CrossRef]

Bartley, N. R.

L. T. Bruton, N. R. Bartley, “The enhancement and tracking of moving objects in digital images using adaptive three-dimensional recursive filters,” IEEE Trans. Circuits Syst. CAS-33, 604–612 (1986).
[CrossRef]

L. T. Bruton, N. R. Bartley, “Three-dimensional image processing using the concept of network resonance,” IEEE Trans. Circuits Syst. CAS-32, 664–672 (1985).
[CrossRef]

Blostein, S. D.

S. D. Blostein, T. S. Huang, “Detecting small, moving objects in image sequences using sequential hypothesis testing,” IEEE Trans. Signal Process. 39, 1611–1629 (1991).
[CrossRef]

Bruton, L. T.

K. S. Knudsen, L. T. Bruton, “Mixed domain filtering of multidimensional signals,” IEEE Trans. Circuits Syst. Video Technol. 1, 260–268 (1991).
[CrossRef]

L. T. Bruton, N. R. Bartley, “The enhancement and tracking of moving objects in digital images using adaptive three-dimensional recursive filters,” IEEE Trans. Circuits Syst. CAS-33, 604–612 (1986).
[CrossRef]

L. T. Bruton, N. R. Bartley, “Three-dimensional image processing using the concept of network resonance,” IEEE Trans. Circuits Syst. CAS-32, 664–672 (1985).
[CrossRef]

K. S. Knudsen, L. T. Bruton, “Moving object nonlinear trajectory estimation in the transform/spatiotemporal mixed domain,” in Proceedings of the 1992 IEEE Custom Integrated Circuits Conference (Institute of Electrical and Electronics Engineers, New York, 1992), Vol. 5, pp. 2481–2484.

K. S. Knudsen, L. T. Bruton, “Moving object detection and trajectory estimation in the transform/spatiotemporal mixed domain,” in Proceedings of the 1992 IEEE International Conference on Acoustics, Speech, and Signal Processing (Institute of Electrical and Electronics Engineers, New York, 1992), Vol. 3, pp. 505–508.
[CrossRef]

Cada, M.

P. M. Lane, S. K. Knudsen, M. Cada, “Moving object trajectory estimation using an optical Fourier processor,” in 1998 International Conference on Applications of Photonic Technology, G. A. Lampropoulos, ed., Proc. SPIE3491, 939–943 (1998).

Choi, J. H.

J. H. Choi, J. W. Jang, S. P. Lee, H. S. Kwak, “Multiple moving object estimation in image sequences of a natural scene,” Opt. Eng. 36, 2176–2183 (1997).
[CrossRef]

Cowart, A. E.

A. E. Cowart, W. E. Snyder, W. H. Ruedger, “The detection of unresolved targets using the Hough transform,” Comput. Vision Graph. Image Process. 21, 222–238 (1983).
[CrossRef]

Friedlander, B.

B. Porat, B. Friedlander, “A frequency domain algorithm for multiframe detection and estimation of dim targets,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 398–401 (1990).
[CrossRef]

Gagliardi, R. M.

I. S. Reed, R. M. Gagliardi, H. M. Shao, “Application of three-dimensional filtering to moving target detection,” IEEE Trans. Aerosp. Electron. Syst. AES-19, 898–905 (1983).
[CrossRef]

Green, R. J.

S. A. Mahmoud, M. S. Afifi, R. J. Green, “Recognition and velocity computation of large moving objects in images,” IEEE Trans. Acoust. Speech Signal Process. 36, 1790–1791 (1988).
[CrossRef]

Haykin, S.

S. Haykin, Adaptive Filter Theory, 3rd ed. (Prentice-Hall, Upper Saddle River, N.J., 1996).

Huang, T. S.

S. D. Blostein, T. S. Huang, “Detecting small, moving objects in image sequences using sequential hypothesis testing,” IEEE Trans. Signal Process. 39, 1611–1629 (1991).
[CrossRef]

Jang, J. W.

J. H. Choi, J. W. Jang, S. P. Lee, H. S. Kwak, “Multiple moving object estimation in image sequences of a natural scene,” Opt. Eng. 36, 2176–2183 (1997).
[CrossRef]

Knudsen, K. S.

K. S. Knudsen, L. T. Bruton, “Mixed domain filtering of multidimensional signals,” IEEE Trans. Circuits Syst. Video Technol. 1, 260–268 (1991).
[CrossRef]

K. S. Knudsen, Resolute Research Ltd., 24 Midridge Rise, Calgary, Alberta T2X 1E3, Canada, 1995 (personal communication).

K. S. Knudsen, L. T. Bruton, “Moving object nonlinear trajectory estimation in the transform/spatiotemporal mixed domain,” in Proceedings of the 1992 IEEE Custom Integrated Circuits Conference (Institute of Electrical and Electronics Engineers, New York, 1992), Vol. 5, pp. 2481–2484.

K. S. Knudsen, L. T. Bruton, “Moving object detection and trajectory estimation in the transform/spatiotemporal mixed domain,” in Proceedings of the 1992 IEEE International Conference on Acoustics, Speech, and Signal Processing (Institute of Electrical and Electronics Engineers, New York, 1992), Vol. 3, pp. 505–508.
[CrossRef]

Knudsen, S. K.

P. M. Lane, S. K. Knudsen, M. Cada, “Moving object trajectory estimation using an optical Fourier processor,” in 1998 International Conference on Applications of Photonic Technology, G. A. Lampropoulos, ed., Proc. SPIE3491, 939–943 (1998).

Kwak, H. S.

J. H. Choi, J. W. Jang, S. P. Lee, H. S. Kwak, “Multiple moving object estimation in image sequences of a natural scene,” Opt. Eng. 36, 2176–2183 (1997).
[CrossRef]

Lane, P. M.

P. M. Lane, S. K. Knudsen, M. Cada, “Moving object trajectory estimation using an optical Fourier processor,” in 1998 International Conference on Applications of Photonic Technology, G. A. Lampropoulos, ed., Proc. SPIE3491, 939–943 (1998).

Lee, S. P.

J. H. Choi, J. W. Jang, S. P. Lee, H. S. Kwak, “Multiple moving object estimation in image sequences of a natural scene,” Opt. Eng. 36, 2176–2183 (1997).
[CrossRef]

Linnik, W. P.

W. P. Linnik, “A simple interferometer for the investigation of optical systems,” C. R. Acad. Sci. URSS 5, 210 (1933) (in Russian).

Mahmoud, S. A.

S. A. Mahmoud, “A new technique for velocity estimation of large moving objects,” IEEE Trans. Signal Process. 39, 741–743 (1991).
[CrossRef]

S. A. Mahmoud, M. S. Afifi, R. J. Green, “Recognition and velocity computation of large moving objects in images,” IEEE Trans. Acoust. Speech Signal Process. 36, 1790–1791 (1988).
[CrossRef]

Mohanty, N. C.

N. C. Mohanty, “Computer tracking of moving point targets in space,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-3, 606–611 (1981).
[CrossRef]

Porat, B.

B. Porat, B. Friedlander, “A frequency domain algorithm for multiframe detection and estimation of dim targets,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 398–401 (1990).
[CrossRef]

Reed, I. S.

I. S. Reed, R. M. Gagliardi, H. M. Shao, “Application of three-dimensional filtering to moving target detection,” IEEE Trans. Aerosp. Electron. Syst. AES-19, 898–905 (1983).
[CrossRef]

Ruedger, W. H.

A. E. Cowart, W. E. Snyder, W. H. Ruedger, “The detection of unresolved targets using the Hough transform,” Comput. Vision Graph. Image Process. 21, 222–238 (1983).
[CrossRef]

Shao, H. M.

I. S. Reed, R. M. Gagliardi, H. M. Shao, “Application of three-dimensional filtering to moving target detection,” IEEE Trans. Aerosp. Electron. Syst. AES-19, 898–905 (1983).
[CrossRef]

Smartt, R. N.

R. N. Smartt, W. H. Steel, “Theory and application of point-diffraction interferometers,” Jpn. J. Appl. Phys. Suppl. 14, 351–356 (1974).

R. N. Smartt, J. Strong, “Point-diffraction interferometer,” J. Opt. Soc. Am. 62, 737 (1972) (abstract only).

Snyder, W. E.

A. E. Cowart, W. E. Snyder, W. H. Ruedger, “The detection of unresolved targets using the Hough transform,” Comput. Vision Graph. Image Process. 21, 222–238 (1983).
[CrossRef]

Steel, W. H.

R. N. Smartt, W. H. Steel, “Theory and application of point-diffraction interferometers,” Jpn. J. Appl. Phys. Suppl. 14, 351–356 (1974).

Strong, J.

R. N. Smartt, J. Strong, “Point-diffraction interferometer,” J. Opt. Soc. Am. 62, 737 (1972) (abstract only).

Watson, A. B.

C. R. Acad. Sci. URSS

W. P. Linnik, “A simple interferometer for the investigation of optical systems,” C. R. Acad. Sci. URSS 5, 210 (1933) (in Russian).

Comput. Vision Graph. Image Process.

A. E. Cowart, W. E. Snyder, W. H. Ruedger, “The detection of unresolved targets using the Hough transform,” Comput. Vision Graph. Image Process. 21, 222–238 (1983).
[CrossRef]

IEEE Trans. Acoust. Speech Signal Process.

S. A. Mahmoud, M. S. Afifi, R. J. Green, “Recognition and velocity computation of large moving objects in images,” IEEE Trans. Acoust. Speech Signal Process. 36, 1790–1791 (1988).
[CrossRef]

IEEE Trans. Aerosp. Electron. Syst.

Y. Barniv, “Dynamic programming solution for detecting dim moving targets,” IEEE Trans. Aerosp. Electron. Syst. AES-21, 144–155 (1985).
[CrossRef]

I. S. Reed, R. M. Gagliardi, H. M. Shao, “Application of three-dimensional filtering to moving target detection,” IEEE Trans. Aerosp. Electron. Syst. AES-19, 898–905 (1983).
[CrossRef]

IEEE Trans. Circuits Syst.

L. T. Bruton, N. R. Bartley, “Three-dimensional image processing using the concept of network resonance,” IEEE Trans. Circuits Syst. CAS-32, 664–672 (1985).
[CrossRef]

L. T. Bruton, N. R. Bartley, “The enhancement and tracking of moving objects in digital images using adaptive three-dimensional recursive filters,” IEEE Trans. Circuits Syst. CAS-33, 604–612 (1986).
[CrossRef]

IEEE Trans. Circuits Syst. Video Technol.

K. S. Knudsen, L. T. Bruton, “Mixed domain filtering of multidimensional signals,” IEEE Trans. Circuits Syst. Video Technol. 1, 260–268 (1991).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell.

N. C. Mohanty, “Computer tracking of moving point targets in space,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-3, 606–611 (1981).
[CrossRef]

B. Porat, B. Friedlander, “A frequency domain algorithm for multiframe detection and estimation of dim targets,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 398–401 (1990).
[CrossRef]

IEEE Trans. Signal Process.

S. D. Blostein, T. S. Huang, “Detecting small, moving objects in image sequences using sequential hypothesis testing,” IEEE Trans. Signal Process. 39, 1611–1629 (1991).
[CrossRef]

S. A. Mahmoud, “A new technique for velocity estimation of large moving objects,” IEEE Trans. Signal Process. 39, 741–743 (1991).
[CrossRef]

J. Opt. Soc. Am.

R. N. Smartt, J. Strong, “Point-diffraction interferometer,” J. Opt. Soc. Am. 62, 737 (1972) (abstract only).

J. Opt. Soc. Am. A

Jpn. J. Appl. Phys. Suppl.

R. N. Smartt, W. H. Steel, “Theory and application of point-diffraction interferometers,” Jpn. J. Appl. Phys. Suppl. 14, 351–356 (1974).

Opt. Eng.

J. H. Choi, J. W. Jang, S. P. Lee, H. S. Kwak, “Multiple moving object estimation in image sequences of a natural scene,” Opt. Eng. 36, 2176–2183 (1997).
[CrossRef]

Other

P. M. Lane, S. K. Knudsen, M. Cada, “Moving object trajectory estimation using an optical Fourier processor,” in 1998 International Conference on Applications of Photonic Technology, G. A. Lampropoulos, ed., Proc. SPIE3491, 939–943 (1998).

K. S. Knudsen, Resolute Research Ltd., 24 Midridge Rise, Calgary, Alberta T2X 1E3, Canada, 1995 (personal communication).

K. S. Knudsen, L. T. Bruton, “Moving object detection and trajectory estimation in the transform/spatiotemporal mixed domain,” in Proceedings of the 1992 IEEE International Conference on Acoustics, Speech, and Signal Processing (Institute of Electrical and Electronics Engineers, New York, 1992), Vol. 3, pp. 505–508.
[CrossRef]

K. S. Knudsen, L. T. Bruton, “Moving object nonlinear trajectory estimation in the transform/spatiotemporal mixed domain,” in Proceedings of the 1992 IEEE Custom Integrated Circuits Conference (Institute of Electrical and Electronics Engineers, New York, 1992), Vol. 5, pp. 2481–2484.

S. Haykin, Adaptive Filter Theory, 3rd ed. (Prentice-Hall, Upper Saddle River, N.J., 1996).

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Figures (11)

Fig. 1
Fig. 1

Spatiotemporal-domain representation of a moving point object with velocity vector v = [ν x ν y ] T and angle ϕ.

Fig. 2
Fig. 2

Frequency-domain representation of a moving point object when the temporal Fourier transform is applied to the real part of the mixed-domain representation only.

Fig. 3
Fig. 3

Principle of the PDI.

Fig. 4
Fig. 4

Moving-object trajectories.

Fig. 5
Fig. 5

Real part of the mixed-domain representation of a moving object. Top and bottom images sequences represent the trajectories of the two objects shown in Fig. 4.

Fig. 6
Fig. 6

Relationship between spatial-frequency-plane radius R and maximum target velocity ν max.

Fig. 7
Fig. 7

Block diagram of the optical Fourier processor with PDI (single-pixel reference).

Fig. 8
Fig. 8

Velocity experiment actual trajectories. The duration of each trajectory is 64 frames, and the lengths ranged from 36 pixels (trajectory A–A′) to 282 pixels (trajectory D–D′).

Fig. 9
Fig. 9

Velocity estimation for targets moving with velocities 0.56, 1.12, 2.24, and 4.47 ppf.

Fig. 10
Fig. 10

Direction estimation for targets moving on paths 0, ±45, ±90, ±135, and 180 deg to the x axis.

Fig. 11
Fig. 11

Relationship between absolute estimation error and frequency-domain radius R.

Tables (2)

Tables Icon

Table 1 Actual and Estimated Velocities

Tables Icon

Table 2 Actual and Estimated Directions

Equations (7)

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

ψx, y, n=δx-νxn-x0δy-νyn-y0,
Ψkx, ky, n=-- ψx, y, nexpikxx+kyydxdy=expikxxn+kyyn=expiωtn+ϕt,
Ψkx, ky, ω=n=0 Ψkx, ky, nexp-iωn=2π expiϕtδω-ωt.
nReΨkx, ky, n=cosϕtncosωtn-sinϕtnsinωtn=π exp-iϕtδω+ωt+π expiϕtδω-ωt,
fx, y=sx, y+rectx/a, y/a.
|Fkx, ky|2=1+|Skx, ky|2+2 ReSkx, ky
R=ανmax,

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