Abstract

Presented in this paper is an optical implementation of a shift- and rotation-invariant pattern recognition technique. A computer-generated hologram is designed to match with one of the circular harmonic components of the target. Experimental results with simple photographic objects show that targets with different locations and orientations can be simultaneously recognized by the optical system.

© 1982 Optical Society of America

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References

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  1. D. Casasent, IEEE Spectrum28 (Mar.1981).
  2. J. R. Leger, S. H. Lee, Appl. Opt. 21, 274 (1982).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  5. H. H. Arsenault, Y.-N. Hsu, Y. Yang, Appl. Opt. 21, 610 (1982).
    [CrossRef] [PubMed]
  6. Y.-N. Hsu, H. H. Arsenault, Y. Yang, Appl. Opt. 21, 616 (1982).
    [CrossRef] [PubMed]
  7. Y.-N. Hsu, H. H. Arsenault, G. April, Appl. Opt. 21, 4012 (1982).
    [CrossRef] [PubMed]
  8. A. M. Cormack, J. Appl. Phys. 34, 2722 (1963).
    [CrossRef]
  9. A. M. Cormack, J. Appl. Phys. 35, 2908 (1964).
    [CrossRef]
  10. E. W. Hansen, J. W. Goodman, Opt. Commun. 24, 268 (1978).
    [CrossRef]
  11. E. W. Hansen, Appl. Opt. 20, 2266 (1981).
    [CrossRef] [PubMed]
  12. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 178.
  13. A. W. Lohmann, D. P. Paris, Appl. Opt. 6, 1739 (1967).
    [CrossRef] [PubMed]

1982

1981

D. Casasent, IEEE Spectrum28 (Mar.1981).

E. W. Hansen, Appl. Opt. 20, 2266 (1981).
[CrossRef] [PubMed]

1978

1977

1967

1964

A. M. Cormack, J. Appl. Phys. 35, 2908 (1964).
[CrossRef]

1963

A. M. Cormack, J. Appl. Phys. 34, 2722 (1963).
[CrossRef]

April, G.

Arsenault, H. H.

Bondurant, R. A.

Casasent, D.

Cormack, A. M.

A. M. Cormack, J. Appl. Phys. 35, 2908 (1964).
[CrossRef]

A. M. Cormack, J. Appl. Phys. 34, 2722 (1963).
[CrossRef]

Goodman, J. W.

E. W. Hansen, J. W. Goodman, Opt. Commun. 24, 268 (1978).
[CrossRef]

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 178.

Hansen, E. W.

E. W. Hansen, Appl. Opt. 20, 2266 (1981).
[CrossRef] [PubMed]

E. W. Hansen, J. W. Goodman, Opt. Commun. 24, 268 (1978).
[CrossRef]

Herold, R.

Hsiao, S.

Hsu, Y.-N.

Lee, S. H.

Leger, J. R.

Leib, K. G.

Lohmann, A. W.

Paris, D. P.

Psaltis, D.

Wohlers, R.

Yang, Y.

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Figures (7)

Fig. 1
Fig. 1

Circular step function: f ( r , θ ) = { 0 , if r > R , 1 , if 0 θ π , r R , - 1 , if - π θ 0 , r R .

Fig. 2
Fig. 2

First-order circular harmonic component: (a) target with X denoting the proper center; (b) amplitude of the circular harmonic component (M = 1); (c) real part of the circular harmonic component; (d) imaginary part of the circular harmonic component.

Fig. 3
Fig. 3

Binary hologram filter matched to the circular harmonic component of Fig. 2.

Fig. 4
Fig. 4

Output of the recognition system.

Fig. 5
Fig. 5

Thresholded output of Fig. 4.

Fig. 6
Fig. 6

Impulse response of the filter of Fig. 3.

Fig. 7
Fig. 7

Experimental optical recognition system with continuous scale adjustment.

Equations (15)

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f ( r , θ ) = M = - f M ( r ) exp ( j M θ ) ,
f M ( r ) = 1 2 π 0 2 π f ( r , θ ) exp ( - j M θ ) d θ .
f ( r , θ + α ) = M = - f M ( r ) exp ( j M α ) exp ( j M θ ) .
V α ( x , y ) = - f α ( ξ , η ) f 1 * ( ξ - x , η - y ) d ξ d η .
V α ( 0 , 0 ) = - f α ( ξ , η ) f 1 * ( ξ , η ) d ξ d η
C ( α ) = 0 r d r 0 2 π f ( r , θ + α ) f * ( r , θ ) d θ .
C ( α ) = 0 r [ M = - f M * ( r ) 0 2 π f ( r , θ + α ) exp ( - j M θ ) d θ ] d r .
1 2 π 0 2 π f ( r , θ + α ) exp ( - j M θ ) d θ = f M ( r ) exp ( j M α ) ,
C ( α ) = 2 π M = - exp ( j M θ ) 0 r f M ( r ) 2 d r .
C step ( α ) = 8 R 2 π ( cos α + 1 9 cos 3 α + 1 25 cos 5 α + ) = π R 2 ( 1 - α π / 2 ) ,             α π .
f r ( r , θ ) = f M ( r ) exp ( j M θ ) .
C M ( α ) = A exp ( j M α ) ,
A = 2 π 0 r f M ( r ) 2 d r .
C M ( α ) 2 = A 2
f ( r , θ ) = { 0 , if r > R , 1 , if 0 θ π , r R , - 1 , if - π θ 0 , r R .

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