Abstract

Rotation-invariant pattern recognition can be achieved with circular-harmonic decomposition. A common problem with such a filter is that, because it is only a single term out of the circular decomposition, it does not contain much of the reference object’s energy. Thus, the obtained correlation selectivity is low. This problem is solved by use of wavelength multiplexing. First, different harmonic terms are encoded by different wavelengths, and then they all are added incoherently in the output correlation plane. This process leads to rotation-invariant pattern recognition with a higher discrimination ability.

© 1997 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).
  2. Y. N. Hsu, H. H. Arsenault, “Optical pattern recognition using the 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 (1988).
    [CrossRef]
  4. D. Mendlovic, N. Konforti, E. Marom, “Shift and projection invariant pattern recognition using logarithmic harmonics,” Appl. Opt. 29, 4784–4789 (1990).
    [CrossRef] [PubMed]
  5. E. Marom, D. Mendlovic, N. Konforti, “Generalized spatial deformation harmonic filter for distortion invariant pattern recognition,” Opt. Commun. 78, 416–424 (1990).
    [CrossRef]
  6. P. García-Martinez, J. García, C. Ferreira, “A new criterion for determining the expansion center for circular-harmonic filters,” Opt. Commun. 117, 399–405 (1995).
    [CrossRef]
  7. D. Mendlovic, Z. Zalevsky, J. García, C. Ferreira, “Logarithmic harmonics proper expansion center and order for efficient projection invariant pattern recognition,” Opt. Commun. 107, 292–299 (1994).
    [CrossRef]
  8. D. Casasent, W. T. Chang, “Correlation synthetic discriminant functions,” Appl. Opt. 25, 2343 (1986).
    [CrossRef] [PubMed]
  9. Y. N. Hsu, H. H. Arsenault, “Pattern discrimination by multiple circular harmonic components,” Appl. Opt. 23, 841–844 (1984).
    [CrossRef] [PubMed]
  10. R. Wu, H. Stark, “Rotation invariant pattern recognition using vector reference,” Appl. Opt. 23, 838–840 (1984).
    [CrossRef]
  11. G. M. Morris, “Diffraction theory for an achromatic Fourier transformation,” Appl. Opt. 20, 2017–2025 (1981).
    [CrossRef] [PubMed]
  12. T. Stone, N. George, “Hybrid diffractive–refractive lenses and achromats,” Appl. Opt. 27, 2960–2971 (1988).
    [CrossRef] [PubMed]
  13. A. W. Lohmann, D. P. Paris, “Binary Fraunhofer holograms, generated by computer,” Appl. Opt. 6, 1739–1748 (1967).
    [CrossRef] [PubMed]
  14. J. García, R. G. Dorsch, D. Mas, “Fractional Fourier transform calculation through fast Fourier transform algorithm,” Appl. Opt. (to be published).

1995 (1)

P. García-Martinez, J. García, C. Ferreira, “A new criterion for determining the expansion center for circular-harmonic filters,” Opt. Commun. 117, 399–405 (1995).
[CrossRef]

1994 (1)

D. Mendlovic, Z. Zalevsky, J. García, C. Ferreira, “Logarithmic harmonics proper expansion center and order for efficient projection invariant pattern recognition,” Opt. Commun. 107, 292–299 (1994).
[CrossRef]

1990 (2)

E. Marom, D. Mendlovic, N. Konforti, “Generalized spatial deformation harmonic filter for distortion invariant pattern recognition,” Opt. Commun. 78, 416–424 (1990).
[CrossRef]

D. Mendlovic, N. Konforti, E. Marom, “Shift and projection invariant pattern recognition using logarithmic harmonics,” Appl. Opt. 29, 4784–4789 (1990).
[CrossRef] [PubMed]

1988 (2)

T. Stone, N. George, “Hybrid diffractive–refractive lenses and achromats,” Appl. Opt. 27, 2960–2971 (1988).
[CrossRef] [PubMed]

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

1986 (1)

1984 (2)

1982 (1)

1981 (1)

1967 (1)

1964 (1)

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

Arsenault, H. H.

Casasent, D.

Chang, W. T.

Dorsch, R. G.

J. García, R. G. Dorsch, D. Mas, “Fractional Fourier transform calculation through fast Fourier transform algorithm,” Appl. Opt. (to be published).

Ferreira, C.

P. García-Martinez, J. García, C. Ferreira, “A new criterion for determining the expansion center for circular-harmonic filters,” Opt. Commun. 117, 399–405 (1995).
[CrossRef]

D. Mendlovic, Z. Zalevsky, J. García, C. Ferreira, “Logarithmic harmonics proper expansion center and order for efficient projection invariant pattern recognition,” Opt. Commun. 107, 292–299 (1994).
[CrossRef]

García, J.

P. García-Martinez, J. García, C. Ferreira, “A new criterion for determining the expansion center for circular-harmonic filters,” Opt. Commun. 117, 399–405 (1995).
[CrossRef]

D. Mendlovic, Z. Zalevsky, J. García, C. Ferreira, “Logarithmic harmonics proper expansion center and order for efficient projection invariant pattern recognition,” Opt. Commun. 107, 292–299 (1994).
[CrossRef]

J. García, R. G. Dorsch, D. Mas, “Fractional Fourier transform calculation through fast Fourier transform algorithm,” Appl. Opt. (to be published).

García-Martinez, P.

P. García-Martinez, J. García, C. Ferreira, “A new criterion for determining the expansion center for circular-harmonic filters,” Opt. Commun. 117, 399–405 (1995).
[CrossRef]

George, N.

Hsu, Y. N.

Konforti, N.

D. Mendlovic, N. Konforti, E. Marom, “Shift and projection invariant pattern recognition using logarithmic harmonics,” Appl. Opt. 29, 4784–4789 (1990).
[CrossRef] [PubMed]

E. Marom, D. Mendlovic, N. Konforti, “Generalized spatial deformation harmonic filter for distortion invariant pattern recognition,” Opt. Commun. 78, 416–424 (1990).
[CrossRef]

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

Lohmann, A. W.

Marom, E.

E. Marom, D. Mendlovic, N. Konforti, “Generalized spatial deformation harmonic filter for distortion invariant pattern recognition,” Opt. Commun. 78, 416–424 (1990).
[CrossRef]

D. Mendlovic, N. Konforti, E. Marom, “Shift and projection invariant pattern recognition using logarithmic harmonics,” Appl. Opt. 29, 4784–4789 (1990).
[CrossRef] [PubMed]

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

Mas, D.

J. García, R. G. Dorsch, D. Mas, “Fractional Fourier transform calculation through fast Fourier transform algorithm,” Appl. Opt. (to be published).

Mendlovic, D.

D. Mendlovic, Z. Zalevsky, J. García, C. Ferreira, “Logarithmic harmonics proper expansion center and order for efficient projection invariant pattern recognition,” Opt. Commun. 107, 292–299 (1994).
[CrossRef]

E. Marom, D. Mendlovic, N. Konforti, “Generalized spatial deformation harmonic filter for distortion invariant pattern recognition,” Opt. Commun. 78, 416–424 (1990).
[CrossRef]

D. Mendlovic, N. Konforti, E. Marom, “Shift and projection invariant pattern recognition using logarithmic harmonics,” Appl. Opt. 29, 4784–4789 (1990).
[CrossRef] [PubMed]

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

Morris, G. M.

Paris, D. P.

Stark, H.

Stone, T.

VanderLugt, A.

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

Wu, R.

Zalevsky, Z.

D. Mendlovic, Z. Zalevsky, J. García, C. Ferreira, “Logarithmic harmonics proper expansion center and order for efficient projection invariant pattern recognition,” Opt. Commun. 107, 292–299 (1994).
[CrossRef]

Appl. Opt. (8)

IEEE Trans. Inf. Theory (1)

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

Opt. Commun. (4)

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

E. Marom, D. Mendlovic, N. Konforti, “Generalized spatial deformation harmonic filter for distortion invariant pattern recognition,” Opt. Commun. 78, 416–424 (1990).
[CrossRef]

P. García-Martinez, J. García, C. Ferreira, “A new criterion for determining the expansion center for circular-harmonic filters,” Opt. Commun. 117, 399–405 (1995).
[CrossRef]

D. Mendlovic, Z. Zalevsky, J. García, C. Ferreira, “Logarithmic harmonics proper expansion center and order for efficient projection invariant pattern recognition,” Opt. Commun. 107, 292–299 (1994).
[CrossRef]

Other (1)

J. García, R. G. Dorsch, D. Mas, “Fractional Fourier transform calculation through fast Fourier transform algorithm,” Appl. Opt. (to be published).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

Suggested optical setup for rotation-invariant pattern recognition.

Fig. 2
Fig. 2

Schematic sketch of the CH filter for three-wavelength multiplexing.

Fig. 3
Fig. 3

Input scene used in the experiments.

Fig. 4
Fig. 4

Experimental output correlation plane.

Fig. 5
Fig. 5

(a) Three-dimensional plot of the obtained output correlation plane. (b) Plot of the peaks’ cross section.

Equations (17)

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

fr, θ=N=-fNr expiNθ,
fNr=12π 02π fr, θ exp-iNθdθ,
CN=2π 0fNr2rdr.
Cα=N=- CN expiNα.
sin α=λiTi=λjTj,
f2λ1/T11-λ12/T12-f2λ2/T11-λ22/T122Lxf2f1,
T1f1Δλ2Lx,
Iα=Cα2=N=-CNλ2,
1FALλ=nλ-1FALλ0nλ0-1,
nλnλ0-dλ-λ0,
1Fλ=1FZPλ+1FALλ,
FZPλ=λλ0FZPλ0.
1Fλ=λ1λ0FZPλ0-dnλ0-1FALλ0+nλ0+dλ0-1FALλ0nλ0-1.
FZPλ0=nλ0-1FALλ0λ0d
n0=Lν/NT1,
LxLν=λf1N.
n02λλ1-λ2.

Metrics