Abstract

A circular harmonic filter illuminated with white light illumination is used to achieve scale, rotation, and shift invariant image recognition. The circular harmonic expansion of an object is utilized to achieve rotation and shift invariant image recognition. Scale invariance is added using a broadband dispersion-compensation technique. When illuminated with broadband light, the frequency-plane filter simply selects the wavelength from the spectrum that produces the same size transform as that recorded in the filter. Laboratory experiments that demonstrate the operation of the technique are presented.

© 1986 Optical Society of America

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References

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  1. A. B. VanderLugt, “Signal Detection By Complex Spatial Filtering,” IEEE Trans. Inf. Theory IT-10, 139 (1964).
    [CrossRef]
  2. Y-N. Hsu, H. H. Arsenault, G. April, “Rotation-Invariant Digital Pattern Recognition Using Circular Harmonic Expansion,” Appl. Opt. 21, 4012 (1982).
    [CrossRef] [PubMed]
  3. Y-N. Hsu, H. H. Arsenault, “Optical Pattern Recognition Using Circular Harmonic Expansion,” Appl. Opt. 21, 4016 (1982).
    [CrossRef] [PubMed]
  4. R. Wu, H. Stark, “Rotation-Invariant Pattern Recognition Using a Vector Reference,” Appl. Opt. 23, 838 (1984).
    [CrossRef] [PubMed]
  5. Y-N. Hsu, H. H. Arsenault, “Pattern Discrimination by Multiple Circular Harmonic Components,” Appl. Opt. 23, 841 (1984).
    [CrossRef] [PubMed]
  6. H. H. Arsenault, C. Delisle, “Contrast-Invariant Pattern Recognition Using Circular Harmonic Components,” Appl. Opt. 24, 2072 (1985).
    [CrossRef] [PubMed]
  7. G. M. Morris, N. George, “Space and Wavelength Dependence of a Dispersion-Compensated Matched Filter,” Appl. Opt. 19, 3843 (1980).
    [CrossRef] [PubMed]
  8. S. P. Almeida, S. K. Case, W. J. Dallas, “Multispectral Size-Averaged Incoherent Spatial Filtering,” Appl. Opt. 18, 4025 (1979).
    [CrossRef] [PubMed]
  9. D. Casasent, D. Psaltis, “Position Rotation and Scale Invariant Optical Correlation,” Appl. Opt. 15, 1795 (1976).
    [CrossRef] [PubMed]
  10. F. T. S. Yu, White-Light Optical Signal Processing (Wiley, New York, 1985), Chap. 3.
  11. J. J. Burch, “A Computer Algorithm for the Synthesis of Spatial Frequency Filters,” Proc. IEEE 55, 599 (1967).
    [CrossRef]
  12. W-H. Lee, “Computer-Generated Holograms: Technique and Applications,” in Progress in Optics, Vol. 16, E. Wolf Ed. (North-Holland, New York, 1978).
    [CrossRef]
  13. G. M. Morris, N. George, “Matched Filtering Using Band-limited Illumination,” Opt. Lett. 5, 202 (1980).
    [CrossRef] [PubMed]

1985 (1)

1984 (2)

1982 (2)

1980 (2)

1979 (1)

1976 (1)

1967 (1)

J. J. Burch, “A Computer Algorithm for the Synthesis of Spatial Frequency Filters,” Proc. IEEE 55, 599 (1967).
[CrossRef]

1964 (1)

A. B. VanderLugt, “Signal Detection By Complex Spatial Filtering,” IEEE Trans. Inf. Theory IT-10, 139 (1964).
[CrossRef]

Almeida, S. P.

April, G.

Arsenault, H. H.

Burch, J. J.

J. J. Burch, “A Computer Algorithm for the Synthesis of Spatial Frequency Filters,” Proc. IEEE 55, 599 (1967).
[CrossRef]

Casasent, D.

Case, S. K.

Dallas, W. J.

Delisle, C.

George, N.

Hsu, Y-N.

Lee, W-H.

W-H. Lee, “Computer-Generated Holograms: Technique and Applications,” in Progress in Optics, Vol. 16, E. Wolf Ed. (North-Holland, New York, 1978).
[CrossRef]

Morris, G. M.

Psaltis, D.

Stark, H.

VanderLugt, A. B.

A. B. VanderLugt, “Signal Detection By Complex Spatial Filtering,” IEEE Trans. Inf. Theory IT-10, 139 (1964).
[CrossRef]

Wu, R.

Yu, F. T. S.

F. T. S. Yu, White-Light Optical Signal Processing (Wiley, New York, 1985), Chap. 3.

Appl. Opt. (8)

IEEE Trans. Inf. Theory (1)

A. B. VanderLugt, “Signal Detection By Complex Spatial Filtering,” IEEE Trans. Inf. Theory IT-10, 139 (1964).
[CrossRef]

Opt. Lett. (1)

Proc. IEEE (1)

J. J. Burch, “A Computer Algorithm for the Synthesis of Spatial Frequency Filters,” Proc. IEEE 55, 599 (1967).
[CrossRef]

Other (2)

W-H. Lee, “Computer-Generated Holograms: Technique and Applications,” in Progress in Optics, Vol. 16, E. Wolf Ed. (North-Holland, New York, 1978).
[CrossRef]

F. T. S. Yu, White-Light Optical Signal Processing (Wiley, New York, 1985), Chap. 3.

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Figures (4)

Fig. 1
Fig. 1

Experimental setup for correlation studies: (I) object plane, (II) and (IV) frequency planes, (III) and (V) correlation planes.

Fig. 2
Fig. 2

Objects and their associated circular harmonics: (a) reference object; (b) test object; (c) square modulus of the N = 2 harmonic for the reference object; (d) square modulus of the N = 2 harmonic for the test object.

Fig. 3
Fig. 3

Experimental correlation between the N = 2 circular harmonic of the reference object and (a) reference object, and (b) test object. The rotation angle of the input object is indicated by angle α. The reference object input is the same size as that used to make the frequency plane filter, i.e., M = 1.0.

Fig. 4
Fig. 4

Experimental correlation between the N = 2 circular harmonic of the reference object and the magnified reference object input. The magnification of the input relative to that used to make the frequency plane filter is M = 0.8. Angle α denotes the rotation angle of the input object.

Equations (10)

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f ( r , θ ) = N = - f N ( r ) exp ( i N θ ) ,
f N ( r ) = 1 2 π 0 2 π f ( r , θ ) exp ( - i N θ ) d θ .
R N ( α ) = 0 r d r 0 2 π f ( r , θ + α ) f * N ( r ) exp ( - i N θ ) d θ .
R N ( α ) = 2 π [ 0 r f N ( r ) 2 d r ] exp ( i N α ) .
R N ( α ) 2 = 4 π 2 [ 0 r f N ( r ) 2 d r ] 2 .
U ( II ) ( x 2 , y 2 ; λ ) = C λ - g ( x 1 , y 1 ) exp [ - i 2 π ( x 1 x 2 + y 1 y 2 ) / ( λ F ) ] d x 1 d y 1
T ( x 2 , y 2 ; λ 0 ) = R ( x 2 , y 2 ; λ 0 ) F * N ( x 2 , y 2 ; λ 0 ) .
U ( III ) ( x 3 , y 3 ; λ ) = C λ - f * N ( x 1 , y 1 ; λ 0 ) g [ x 1 λ / λ 0 + F sin θ 0 ( λ / λ 0 ) - x 3 , y 1 λ / λ 0 - y 3 ] d x 1 d y 1 ,
H ( x 4 , y 4 ; λ 0 ) = exp ( i 2 π x 4 sin θ 0 / λ 0 ) .
U V ( x 5 , y 5 ; λ ) = C λ - f * N ( x 1 , y 1 ; λ 0 ) × g ( x 1 λ / λ 0 + x 5 , y 1 λ / λ 0 + y 5 ) d x 1 d y 1 .

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