Abstract

A variable radial coordinate transformation of the phase-only filter (POF) that is dependent on the energy’s angular distribution of the target spectrum is used to perform shift- and scale-invariant pattern recognition. The POF of a basic size target and the cumulative energy of its angular distribution are calculated. The filter function is then transformed by means of stretching along the radial coordinate so that the same energy contribution to the correlation peak is provided for any size target. The maximum ratio for recognizing scaled objects is 1:1.5. Computer simulations and optical experiments showing the performances of the filter are presented.

© 1997 Optical Society of America

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References

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  1. A. Vanderlugt, “Signal detection by complex filtering,” IEEE Trans. Inf. Theory IT-10, 139–146 (1964).
  2. Y.-N. Hsu, H. H. Arsenault, “Optical pattern recognition using circular harmonic expansion,” Appl. Opt. 21, 4016–4019 (1982).
    [CrossRef] [PubMed]
  3. D. Mendlovic, E. Marom, N. Konforti, “Shift and scale invariant pattern recognition using Mellin radial harmonics,” Opt. Commun. 67, 172–176 (1988).
    [CrossRef]
  4. J. Rosen, J. Shamir, “Scale invariant pattern recognition with logarithmic radial harmonic filters,” Appl. Opt. 28, 240–244 (1989).
    [CrossRef] [PubMed]
  5. D. Casasent, “Coherent optical pattern recognition: a review,” Opt. Eng. 24, 26–31 (1985).
  6. D. Casasent, D. Psaltis, “Deformation invariant, space variant optical pattern recognition,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1978), Vol. 16, pp. 289–356.
  7. Y. Saito, S. Komatsu, H. Ohzu, “Scale and rotation invariant real time optical correlator using computer generated hologram,” Opt. Commun. 47, 8–11 (1983).
    [CrossRef]
  8. D. Mendlovic, N. Konforti, E. Marom, “Scale and projection invariant pattern recognition,” Appl. Opt. 28, 4982–4986 (1989).
    [CrossRef] [PubMed]
  9. J. Fleuret, “Geometrical invariances in images: a hybrid characterization method,” Opt. Commun. 44, 311–316 (1983).
    [CrossRef]
  10. T. Minemoto, I. Tsuchimoto, S. Imi, “Hybrid pattern recognition using the Fraunhoffer diffraction pattern,” Opt. Commun. 51, 221–226 (1984).
    [CrossRef]
  11. T. Minemoto, J. Narano, “Hybrid pattern recognition by features extracted from object patterns and Fraunhoffer difraction patterns,” Appl. Opt. 24, 2914–2920 (1985).
    [CrossRef]
  12. T. Szoplik, “Shift- and scale-invariant anamorphic Fourier correlator,” J. Opt. Soc. Am. A 2, 1419–1423 (1985).
    [CrossRef]
  13. T. Szoplik, H. H. Arsenault, “Shift and scale-invariant anamorphic Fourier correlator using multiple circular harmonic filters,” Appl. Opt. 24, 3179–3183 (1985).
    [CrossRef] [PubMed]
  14. J. García, T. Szoplik, C. Ferreira, “Shift-and-scale-invariant pattern recognition using an elliptic coordinate-transformed phase-only filter,” Appl. Opt. 31, 4823–4828 (1992).
    [CrossRef] [PubMed]
  15. J. L. Horner, P. D. Gianino, “Phase-only matched filtering,” Appl. Opt. 23, 812–816 (1984).
    [CrossRef] [PubMed]
  16. A. W. Lohmann, D. P. Paris, “Binary Fraunhofer holograms,” Appl. Opt. 6, 1739–1748, (1967).
    [CrossRef] [PubMed]

1992 (1)

1989 (2)

1988 (1)

D. Mendlovic, E. Marom, N. Konforti, “Shift and scale invariant pattern recognition using Mellin radial harmonics,” Opt. Commun. 67, 172–176 (1988).
[CrossRef]

1985 (4)

1984 (2)

J. L. Horner, P. D. Gianino, “Phase-only matched filtering,” Appl. Opt. 23, 812–816 (1984).
[CrossRef] [PubMed]

T. Minemoto, I. Tsuchimoto, S. Imi, “Hybrid pattern recognition using the Fraunhoffer diffraction pattern,” Opt. Commun. 51, 221–226 (1984).
[CrossRef]

1983 (2)

J. Fleuret, “Geometrical invariances in images: a hybrid characterization method,” Opt. Commun. 44, 311–316 (1983).
[CrossRef]

Y. Saito, S. Komatsu, H. Ohzu, “Scale and rotation invariant real time optical correlator using computer generated hologram,” Opt. Commun. 47, 8–11 (1983).
[CrossRef]

1982 (1)

1967 (1)

1964 (1)

A. Vanderlugt, “Signal detection by complex filtering,” IEEE Trans. Inf. Theory IT-10, 139–146 (1964).

Arsenault, H. H.

Casasent, D.

D. Casasent, “Coherent optical pattern recognition: a review,” Opt. Eng. 24, 26–31 (1985).

D. Casasent, D. Psaltis, “Deformation invariant, space variant optical pattern recognition,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1978), Vol. 16, pp. 289–356.

Ferreira, C.

Fleuret, J.

J. Fleuret, “Geometrical invariances in images: a hybrid characterization method,” Opt. Commun. 44, 311–316 (1983).
[CrossRef]

García, J.

Gianino, P. D.

Horner, J. L.

Hsu, Y.-N.

Imi, S.

T. Minemoto, I. Tsuchimoto, S. Imi, “Hybrid pattern recognition using the Fraunhoffer diffraction pattern,” Opt. Commun. 51, 221–226 (1984).
[CrossRef]

Komatsu, S.

Y. Saito, S. Komatsu, H. Ohzu, “Scale and rotation invariant real time optical correlator using computer generated hologram,” Opt. Commun. 47, 8–11 (1983).
[CrossRef]

Konforti, N.

D. Mendlovic, N. Konforti, E. Marom, “Scale and projection invariant pattern recognition,” Appl. Opt. 28, 4982–4986 (1989).
[CrossRef] [PubMed]

D. Mendlovic, E. Marom, N. Konforti, “Shift and scale invariant pattern recognition using Mellin radial harmonics,” Opt. Commun. 67, 172–176 (1988).
[CrossRef]

Lohmann, A. W.

Marom, E.

D. Mendlovic, N. Konforti, E. Marom, “Scale and projection invariant pattern recognition,” Appl. Opt. 28, 4982–4986 (1989).
[CrossRef] [PubMed]

D. Mendlovic, E. Marom, N. Konforti, “Shift and scale invariant pattern recognition using Mellin radial harmonics,” Opt. Commun. 67, 172–176 (1988).
[CrossRef]

Mendlovic, D.

D. Mendlovic, N. Konforti, E. Marom, “Scale and projection invariant pattern recognition,” Appl. Opt. 28, 4982–4986 (1989).
[CrossRef] [PubMed]

D. Mendlovic, E. Marom, N. Konforti, “Shift and scale invariant pattern recognition using Mellin radial harmonics,” Opt. Commun. 67, 172–176 (1988).
[CrossRef]

Minemoto, T.

T. Minemoto, J. Narano, “Hybrid pattern recognition by features extracted from object patterns and Fraunhoffer difraction patterns,” Appl. Opt. 24, 2914–2920 (1985).
[CrossRef]

T. Minemoto, I. Tsuchimoto, S. Imi, “Hybrid pattern recognition using the Fraunhoffer diffraction pattern,” Opt. Commun. 51, 221–226 (1984).
[CrossRef]

Narano, J.

Ohzu, H.

Y. Saito, S. Komatsu, H. Ohzu, “Scale and rotation invariant real time optical correlator using computer generated hologram,” Opt. Commun. 47, 8–11 (1983).
[CrossRef]

Paris, D. P.

Psaltis, D.

D. Casasent, D. Psaltis, “Deformation invariant, space variant optical pattern recognition,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1978), Vol. 16, pp. 289–356.

Rosen, J.

Saito, Y.

Y. Saito, S. Komatsu, H. Ohzu, “Scale and rotation invariant real time optical correlator using computer generated hologram,” Opt. Commun. 47, 8–11 (1983).
[CrossRef]

Shamir, J.

Szoplik, T.

Tsuchimoto, I.

T. Minemoto, I. Tsuchimoto, S. Imi, “Hybrid pattern recognition using the Fraunhoffer diffraction pattern,” Opt. Commun. 51, 221–226 (1984).
[CrossRef]

Vanderlugt, A.

A. Vanderlugt, “Signal detection by complex filtering,” IEEE Trans. Inf. Theory IT-10, 139–146 (1964).

Appl. Opt. (8)

IEEE Trans. Inf. Theory (1)

A. Vanderlugt, “Signal detection by complex filtering,” IEEE Trans. Inf. Theory IT-10, 139–146 (1964).

J. Opt. Soc. Am. A (1)

Opt. Commun. (4)

Y. Saito, S. Komatsu, H. Ohzu, “Scale and rotation invariant real time optical correlator using computer generated hologram,” Opt. Commun. 47, 8–11 (1983).
[CrossRef]

J. Fleuret, “Geometrical invariances in images: a hybrid characterization method,” Opt. Commun. 44, 311–316 (1983).
[CrossRef]

T. Minemoto, I. Tsuchimoto, S. Imi, “Hybrid pattern recognition using the Fraunhoffer diffraction pattern,” Opt. Commun. 51, 221–226 (1984).
[CrossRef]

D. Mendlovic, E. Marom, N. Konforti, “Shift and scale invariant pattern recognition using Mellin radial harmonics,” Opt. Commun. 67, 172–176 (1988).
[CrossRef]

Opt. Eng. (1)

D. Casasent, “Coherent optical pattern recognition: a review,” Opt. Eng. 24, 26–31 (1985).

Other (1)

D. Casasent, D. Psaltis, “Deformation invariant, space variant optical pattern recognition,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1978), Vol. 16, pp. 289–356.

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Figures (4)

Fig. 1
Fig. 1

Geometrical representation of the stretching of the filter coordinates. Δρ is related to the interval of accepted scales for the target recognition.

Fig. 2
Fig. 2

True target (top row) and two false targets (middle and bottom rows). All targets are scaled by factors of, from left to right, 1, 1.2, and 1.4.

Fig. 3
Fig. 3

Computer-simulation results: Correlation output signals obtained with the RSF interacting with the scene shown in Fig. 2.

Fig. 4
Fig. 4

Experimental results: Optically obtained correlations by use of the RSF recorded as a computer-generated hologram for the scene in Fig. 2.

Equations (12)

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

Eθ=oTpρ, θ2ρdρ,
Cθ=0θEθdθ.
C0=0,  Cπ/2=1.
ρ=ρfθ.
f0=1Smax=min,  fπ/2=1Smin=max.
k=ΔθEθ.
Δθ=dθdfθ.
dfθ=kEθdθ.
fθ=f0+kCθ=1Smax+1Smin-1SmaxCθ.
Tpρ, θFpρ, θ=Tpρfθ, θ.
1max=SminSSmax=1min.
DA=1-mincorrelation for any size of the true targetmaxcorrelation for any size of the false targets,

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