Abstract

The incoherent optical correlator was extended to perform rotation-invariant pattern recognition by using a set of two real-positive filters presenting a single-order circular harmonic function.

© 1992 Optical Society of America

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References

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  1. A. W. Lohmann, H. W. Werlich, “Incoherent matched filter with Fourier holograms,” Appl. Opt. 7, 561–563 (1968).
  2. H. Bartelt, S. K. Case, R. Hauck, “Incoherent optical processing,” in Applications of Optical Fourier Transforms, H. Stark, ed. (Academic, Orlando, Fla., 1982).
  3. Y.-N. Hsu, H. H. Arsenault, “Optical pattern recognition using circular harmonic expansion,” Appl. Opt. 21, 4016–4019 (1982).
    [CrossRef] [PubMed]
  4. E. Elizur, A. A. Friesem, “Roatation-invariant correlator with incoherent light,” Appl. Opt. 30, 4175–4178 (1991).
    [CrossRef] [PubMed]
  5. D. Mendlovic, E. Marom, N. Konforti, “Shift and scale invariant pattern recognition using Mellin radial harmonics,” Opt. Commun. 67, 172–176 (1988).
    [CrossRef]

1991

1988

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

1982

1968

Arsenault, H. H.

Bartelt, H.

H. Bartelt, S. K. Case, R. Hauck, “Incoherent optical processing,” in Applications of Optical Fourier Transforms, H. Stark, ed. (Academic, Orlando, Fla., 1982).

Case, S. K.

H. Bartelt, S. K. Case, R. Hauck, “Incoherent optical processing,” in Applications of Optical Fourier Transforms, H. Stark, ed. (Academic, Orlando, Fla., 1982).

Elizur, E.

Friesem, A. A.

Hauck, R.

H. Bartelt, S. K. Case, R. Hauck, “Incoherent optical processing,” in Applications of Optical Fourier Transforms, H. Stark, ed. (Academic, Orlando, Fla., 1982).

Hsu, Y.-N.

Konforti, N.

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

Werlich, H. W.

Appl. Opt.

Opt. Commun.

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

Other

H. Bartelt, S. K. Case, R. Hauck, “Incoherent optical processing,” in Applications of Optical Fourier Transforms, H. Stark, ed. (Academic, Orlando, Fla., 1982).

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Figures (4)

Fig. 1
Fig. 1

(a) Optical setup for incoherent correlation. (b) Schematic block diagram of the incoherent optical correlator postprocessing steps.

Fig. 2
Fig. 2

Target object that was used in correlation simulations and experiments.

Fig. 3
Fig. 3

Correlation results when Fig. 2 was the input: (a), (b) computer simulations of the real and imaginary filter responses; (c), (d) the two filter correlation responses. The left-hand side is the real filter response, and the right-hand side is the imaginary filter response; (c) cross-sectional profile; (d) laboratory experimental result.

Fig. 4
Fig. 4

Same as Figs. 3(c) and 3(d) except that the input pattern was rotated by angles of (a), (b) 7.5°; (c), (d) 15°.

Equations (10)

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I 0 = 0 2 π 0 f ( r , θ + α ) 2 h ( r , θ ) 2 r d r d θ ,
I f ( r , θ ) = N = - I f N ( r ) exp ( i N θ ) ,
I f N ( r ) = 1 2 π 0 2 π I f ( r , θ ) exp ( - i N θ ) .
h 1 ( r , θ ) = { Re [ I f N ( r ) exp ( i N θ ) ] + b 1 } 1 / 2 , h 2 ( r , θ ) = { Im [ I f N ( r ) exp ( i N θ ) ] + b 2 } 1 / 2 ,
I 1 = 0 2 π 0 I f ( r , θ + α ) h 1 ( r , θ ) 2 r d r d θ = Re [ 0 2 π 0 I f ( r , θ + α ) I f N ( r ) exp ( i N θ ) r d r d θ ] + b 1 0 2 π 0 I f ( r , θ + α ) r d r d θ .
I 1 = Re [ 0 2 π 0 M = - I f M ( r ) exp ( i M θ ) × exp ( i M α ) I f N ( r ) exp ( i N θ ) r d r d θ ] + I b 1 .
I 1 - I b 1 = Re [ 2 π 0 I f - N ( r ) I f N ( r ) r d r exp ( - i N α ) ] = 2 π 0 I f N ( r ) 2 r d r cos ( N α ) ,
I 2 - I b 2 = - 2 π 0 I f N ( r , θ ) 2 r d r sin ( N α ) .
I 0 = ( I 1 - I b 1 ) 2 + ( I 2 - I b 2 ) 2 ,
α = 1 N arctan ( I 2 - I b 2 I 1 - I b 1 ) .

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