Abstract

A new method has been developed for rotation-invariant pattern recognition. One component of the circular harmonic expansion of the target is used in the preparation of the reference. Correlations between the input and reference objects are accomplished by FFT and multiplication in the frequency domain. In an experience with targets from an image with 192 × 192 pixels, target orientations were detected with an accuracy of ~0.1°. This method is also suitable for optical implementation.

© 1982 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. E. Persoon, K.-S. Fu, IEEE Trans. Syst. Man Cybern. SMC-7, 170 (1977).
    [CrossRef]
  2. E. H. J. Persoon, Philips Tech. Rev. 38, 356 (1978/79).
  3. J. D. Dessimoz, M. Kunt, J. M. Zurcher, G. H. Granlund, “Recognition and Handling of Overlapping Industrial Parts,” in Proceedings, Ninth International Symposium on Industrial Robots (Society of Mechanical Engineers, Dearborn, Mich., 1979), p. 357.
  4. D. Psaltis, D. Casasent, Appl. Opt. 16, 2288 (1977).
    [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. A. M. Cormack, J. Appl. Phys. 34, 2722 (1963).
    [CrossRef]
  8. A. M. Cormack, J. Appl. Phys. 35, 2908 (1964).
    [CrossRef]
  9. E. W. Hansen, J. W. Goodman, Opt. Commun. 24, 268 (1978).
    [CrossRef]
  10. E. W. Hansen, Appl. Opt. 20, 2266 (1981).
    [CrossRef] [PubMed]
  11. Y. Yang, H. H. Arsenault, Y.-N. Hsu, “Optimum Circular Symmetrical Filters and Their Uses in Optical Pattern Recognition,” Opt. Acta, in press.
  12. H. H. Arsenault, Y.-N. Hsu, Appl. Opt. 21, 4016 (1982).
    [CrossRef] [PubMed]

1982 (3)

1981 (1)

1978 (1)

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

1977 (2)

E. Persoon, K.-S. Fu, IEEE Trans. Syst. Man Cybern. SMC-7, 170 (1977).
[CrossRef]

D. Psaltis, D. Casasent, Appl. Opt. 16, 2288 (1977).
[CrossRef] [PubMed]

1964 (1)

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

1963 (1)

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

Arsenault, H. H.

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]

Dessimoz, J. D.

J. D. Dessimoz, M. Kunt, J. M. Zurcher, G. H. Granlund, “Recognition and Handling of Overlapping Industrial Parts,” in Proceedings, Ninth International Symposium on Industrial Robots (Society of Mechanical Engineers, Dearborn, Mich., 1979), p. 357.

Fu, K.-S.

E. Persoon, K.-S. Fu, IEEE Trans. Syst. Man Cybern. SMC-7, 170 (1977).
[CrossRef]

Goodman, J. W.

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

Granlund, G. H.

J. D. Dessimoz, M. Kunt, J. M. Zurcher, G. H. Granlund, “Recognition and Handling of Overlapping Industrial Parts,” in Proceedings, Ninth International Symposium on Industrial Robots (Society of Mechanical Engineers, Dearborn, Mich., 1979), p. 357.

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]

Hsu, Y.-N.

Kunt, M.

J. D. Dessimoz, M. Kunt, J. M. Zurcher, G. H. Granlund, “Recognition and Handling of Overlapping Industrial Parts,” in Proceedings, Ninth International Symposium on Industrial Robots (Society of Mechanical Engineers, Dearborn, Mich., 1979), p. 357.

Persoon, E.

E. Persoon, K.-S. Fu, IEEE Trans. Syst. Man Cybern. SMC-7, 170 (1977).
[CrossRef]

Persoon, E. H. J.

E. H. J. Persoon, Philips Tech. Rev. 38, 356 (1978/79).

Psaltis, D.

Yang, Y.

H. H. Arsenault, Y.-N. Hsu, Y. Yang, Appl. Opt. 21, 610 (1982).
[CrossRef] [PubMed]

Y.-N. Hsu, H. H. Arsenault, Y. Yang, Appl. Opt. 21, 616 (1982).
[CrossRef] [PubMed]

Y. Yang, H. H. Arsenault, Y.-N. Hsu, “Optimum Circular Symmetrical Filters and Their Uses in Optical Pattern Recognition,” Opt. Acta, in press.

Zurcher, J. M.

J. D. Dessimoz, M. Kunt, J. M. Zurcher, G. H. Granlund, “Recognition and Handling of Overlapping Industrial Parts,” in Proceedings, Ninth International Symposium on Industrial Robots (Society of Mechanical Engineers, Dearborn, Mich., 1979), p. 357.

Appl. Opt. (5)

IEEE Trans. Syst. Man Cybern. (1)

E. Persoon, K.-S. Fu, IEEE Trans. Syst. Man Cybern. SMC-7, 170 (1977).
[CrossRef]

J. Appl. Phys. (2)

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

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

Opt. Commun. (1)

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

Philips Tech. Rev. (1)

E. H. J. Persoon, Philips Tech. Rev. 38, 356 (1978/79).

Other (2)

J. D. Dessimoz, M. Kunt, J. M. Zurcher, G. H. Granlund, “Recognition and Handling of Overlapping Industrial Parts,” in Proceedings, Ninth International Symposium on Industrial Robots (Society of Mechanical Engineers, Dearborn, Mich., 1979), p. 357.

Y. Yang, H. H. Arsenault, Y.-N. Hsu, “Optimum Circular Symmetrical Filters and Their Uses in Optical Pattern Recognition,” Opt. Acta, in press.

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 (6)

Fig. 1
Fig. 1

System outline.

Fig. 2
Fig. 2

Targets with different orientations.

Fig. 3
Fig. 3

Circular harmonic expansion: (a) target, proper center denoted by X, (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. 4
Fig. 4

System block diagram.

Fig. 5
Fig. 5

Input image and correlation before thresholding.

Fig. 6
Fig. 6

Input image and correlation after thresholding.

Tables (2)

Tables Icon

Table I Locations of Targets with Averaging

Tables Icon

Table II Locations of Targets Without Averaging

Equations (21)

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

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 ) .
f r ( r , θ ) = f M ( r ) exp ( j M θ )
R M ( x , y ) = - f 1 ( ξ , η ) f r 1 * ( ξ - x , η - y ) d ξ d η .
C M ( α ) = 0 r d r 0 2 π f ( r , θ + α ) f r * ( r , θ ) d θ .
C M ( α ) = A exp ( j M α ) ,
A = 2 π 0 r f M ( r ) 2 d r .
A > thd ,
α = arctan Im [ C M ( α ) ] Re [ C M ( α ) ] .
f r ( r , θ + α ) = f M ( r ) exp [ j M ( θ + α ) ] = exp ( j M ) α f r ( r , θ ) .
R 1 ( r , θ ) = f ( r , θ + α ) * f r ( r , θ )
R ( r , θ ) = f ( r , θ ) * f r ( r , θ ) .
δ = θ + α ,
R 1 ( r , δ - α ) = f ( r , δ ) * f r ( r , δ - α ) = exp ( j M α ) R ( r , δ ) .
R 1 ( r , θ ) = exp ( j M α ) R ( r , θ + α ) .
R M ( 0 , 0 ) = maximum R M ( x , y ) .
C 0 - C 1 < 0.02 thd ,
real part = K + 1 K Re ( C 0 ) + 1 Re ( C 1 ) ,
imaginary part = K + 1 K Im ( C 0 ) + 1 Im ( C 1 ) ,
K = 2.

Metrics