Abstract

Phase-only circular harmonic filters and binary phase-only circular harmonic filters are proposed. Both filters have full rotation invariance and excellent performance for discrimination between objects and against background noise. Their properties have been studied and implemented for computer applications. The binary filters are appropriate for real-time applications using spatial light modulators.

© 1989 Optical Society of America

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References

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  1. J. L. Horner, P. D. Gianino, “Phase-Only Matched Filtering,” Appl. Opt. 23, 812 (1984).
    [CrossRef] [PubMed]
  2. D. Psaltis, E. G. Paek, S. S. Venkatesh, “Optical Image Correlation with a Binary Spatial Light Modulator,” Opt. Eng. 23, 698 (1984).
    [CrossRef]
  3. J. L. Horner, J. R. Leger, “Pattern Recognition with Binary Phase-Only Filters,” Appl. Opt. 24, 609 (1985).
    [CrossRef] [PubMed]
  4. J. L. Horner, H. O. Bartelt, “Two-Bit Correlation,” Appl. Opt. 24, 2889 (1985).
    [CrossRef] [PubMed]
  5. J. L. Horner, “Light Utilization in Optical Correlators,” Appl. Opt. 21, 4511 (1982).
    [CrossRef] [PubMed]
  6. P. D. Gianino, J. L. Horner, “Additional Properties of the Phase-Only Correlation Filter,” Opt. Eng. 23, 695 (1984).
    [CrossRef]
  7. D. P. Casasent, A. Mahalanobis, “Optical Iconic Filters for Large Class Recognition,” Appl. Opt. 26, 2266 (1987).
    [CrossRef] [PubMed]
  8. H. J. Caulfield, “Smart Optical Pattern Recognition,” J. Opt. Soc. Am. A 4, P58 (1987).
  9. D. Flannery, J. Loomis, M. Milkovich, “Application of Binary Phase-Only Correlation to Machine Vision,” Opt. Eng. 27, 309 (1988).
    [CrossRef]
  10. H. J. Caulfield, W. T. Maloney, “Improved Discrimination in Optical Character Recognition,” Appl. Opt. 8, 2354 (1969).
    [CrossRef] [PubMed]
  11. D. P. Casasent, W. Chang, “Correlation Synthetic Discriminant Functions,” Appl. Opt. 25, 2343 (1986).
    [CrossRef] [PubMed]
  12. Y. N. Hsu, H. H. Arsenault, “Pattern Discrimination by Multiple Circular Harmonic Components,” Appl. Opt. 23, 841 (1984).
    [CrossRef] [PubMed]
  13. R. Wu, H. Stark, “Rotation-Invariant Pattern Recognition Using Optimum Feature Extraction,” Appl. Opt. 24, 179 (1985).
    [CrossRef] [PubMed]
  14. H. H. Arsenault, C. Belisle, “Contrast-Invariant Pattern Recognition Using Circular Harmonic Components,” Appl. Opt. 24, 2072 (1985).
    [CrossRef] [PubMed]
  15. G. F. Schils, D. W. Sweeney, “Iterative Technique for the Synthesis of Optical-Correlation Filters,” J. Opt. Soc. Am. A 3, 1433 (1986).
    [CrossRef]
  16. Y. Sheng, H. H. Arsenault, “Method for Determining Expansion Centers and Predicting Sidelobe Levels for Circular-Harmonic Filter,” J. Opt. Soc. Am. A 4, 1793 (1987).
    [CrossRef]
  17. Y. Sheng, H. H. Arsenault, “Object Detection from a Real Scene Using the Correlation Peak Coordinates of Multiple Circular Harmonic Filters,” Appl. Opt.28 (1989), in press.
    [CrossRef] [PubMed]
  18. W. L. Anderson, “Particle Identification and Counting,” in Applications of Optical Fourier Transforms, H. Stark, Ed. (Academic, New York, 1982), p. 95.
  19. H. H. Arsenault, L. Leclerc, Y. Sheng, “Similarity and Invariance in Pattern Recognition,” Proc. Soc. Photo-Opt. Instrum. Eng.960 (1988), in press.
  20. B. V. K. Vijaya Kumar, Z. Bahri, “Optimality of Phase-Only Filters,” Proc. Soc. Photo-Opt. Instrum. Eng. 884, paper 23 (1988).
  21. D. M. Cottrell, R. A. Lilly, J. A. Davis, T. Day, “Optical Correlator Performance of Binary Phase-Only Filters Using Fourier and Hartley Transforms,” Appl. Opt. 26, 3755 (1987).
    [CrossRef] [PubMed]
  22. H. H. Arsenault, C. Ferreira, M. P. Levesque, T. Szoplik, “Simple Filter with Limited Rotation Invariance,” Appl. Opt. 25, 3230 (1986).
    [CrossRef] [PubMed]

1988 (2)

D. Flannery, J. Loomis, M. Milkovich, “Application of Binary Phase-Only Correlation to Machine Vision,” Opt. Eng. 27, 309 (1988).
[CrossRef]

B. V. K. Vijaya Kumar, Z. Bahri, “Optimality of Phase-Only Filters,” Proc. Soc. Photo-Opt. Instrum. Eng. 884, paper 23 (1988).

1987 (4)

1986 (3)

1985 (4)

1984 (4)

J. L. Horner, P. D. Gianino, “Phase-Only Matched Filtering,” Appl. Opt. 23, 812 (1984).
[CrossRef] [PubMed]

D. Psaltis, E. G. Paek, S. S. Venkatesh, “Optical Image Correlation with a Binary Spatial Light Modulator,” Opt. Eng. 23, 698 (1984).
[CrossRef]

Y. N. Hsu, H. H. Arsenault, “Pattern Discrimination by Multiple Circular Harmonic Components,” Appl. Opt. 23, 841 (1984).
[CrossRef] [PubMed]

P. D. Gianino, J. L. Horner, “Additional Properties of the Phase-Only Correlation Filter,” Opt. Eng. 23, 695 (1984).
[CrossRef]

1982 (1)

1969 (1)

Anderson, W. L.

W. L. Anderson, “Particle Identification and Counting,” in Applications of Optical Fourier Transforms, H. Stark, Ed. (Academic, New York, 1982), p. 95.

Arsenault, H. H.

Bahri, Z.

B. V. K. Vijaya Kumar, Z. Bahri, “Optimality of Phase-Only Filters,” Proc. Soc. Photo-Opt. Instrum. Eng. 884, paper 23 (1988).

Bartelt, H. O.

Belisle, C.

Casasent, D. P.

Caulfield, H. J.

Chang, W.

Cottrell, D. M.

Davis, J. A.

Day, T.

Ferreira, C.

Flannery, D.

D. Flannery, J. Loomis, M. Milkovich, “Application of Binary Phase-Only Correlation to Machine Vision,” Opt. Eng. 27, 309 (1988).
[CrossRef]

Gianino, P. D.

P. D. Gianino, J. L. Horner, “Additional Properties of the Phase-Only Correlation Filter,” Opt. Eng. 23, 695 (1984).
[CrossRef]

J. L. Horner, P. D. Gianino, “Phase-Only Matched Filtering,” Appl. Opt. 23, 812 (1984).
[CrossRef] [PubMed]

Horner, J. L.

Hsu, Y. N.

Leclerc, L.

H. H. Arsenault, L. Leclerc, Y. Sheng, “Similarity and Invariance in Pattern Recognition,” Proc. Soc. Photo-Opt. Instrum. Eng.960 (1988), in press.

Leger, J. R.

Levesque, M. P.

Lilly, R. A.

Loomis, J.

D. Flannery, J. Loomis, M. Milkovich, “Application of Binary Phase-Only Correlation to Machine Vision,” Opt. Eng. 27, 309 (1988).
[CrossRef]

Mahalanobis, A.

Maloney, W. T.

Milkovich, M.

D. Flannery, J. Loomis, M. Milkovich, “Application of Binary Phase-Only Correlation to Machine Vision,” Opt. Eng. 27, 309 (1988).
[CrossRef]

Paek, E. G.

D. Psaltis, E. G. Paek, S. S. Venkatesh, “Optical Image Correlation with a Binary Spatial Light Modulator,” Opt. Eng. 23, 698 (1984).
[CrossRef]

Psaltis, D.

D. Psaltis, E. G. Paek, S. S. Venkatesh, “Optical Image Correlation with a Binary Spatial Light Modulator,” Opt. Eng. 23, 698 (1984).
[CrossRef]

Schils, G. F.

Sheng, Y.

Y. Sheng, H. H. Arsenault, “Method for Determining Expansion Centers and Predicting Sidelobe Levels for Circular-Harmonic Filter,” J. Opt. Soc. Am. A 4, 1793 (1987).
[CrossRef]

H. H. Arsenault, L. Leclerc, Y. Sheng, “Similarity and Invariance in Pattern Recognition,” Proc. Soc. Photo-Opt. Instrum. Eng.960 (1988), in press.

Y. Sheng, H. H. Arsenault, “Object Detection from a Real Scene Using the Correlation Peak Coordinates of Multiple Circular Harmonic Filters,” Appl. Opt.28 (1989), in press.
[CrossRef] [PubMed]

Stark, H.

Sweeney, D. W.

Szoplik, T.

Venkatesh, S. S.

D. Psaltis, E. G. Paek, S. S. Venkatesh, “Optical Image Correlation with a Binary Spatial Light Modulator,” Opt. Eng. 23, 698 (1984).
[CrossRef]

Vijaya Kumar, B. V. K.

B. V. K. Vijaya Kumar, Z. Bahri, “Optimality of Phase-Only Filters,” Proc. Soc. Photo-Opt. Instrum. Eng. 884, paper 23 (1988).

Wu, R.

Appl. Opt. (12)

J. L. Horner, J. R. Leger, “Pattern Recognition with Binary Phase-Only Filters,” Appl. Opt. 24, 609 (1985).
[CrossRef] [PubMed]

J. L. Horner, H. O. Bartelt, “Two-Bit Correlation,” Appl. Opt. 24, 2889 (1985).
[CrossRef] [PubMed]

J. L. Horner, “Light Utilization in Optical Correlators,” Appl. Opt. 21, 4511 (1982).
[CrossRef] [PubMed]

J. L. Horner, P. D. Gianino, “Phase-Only Matched Filtering,” Appl. Opt. 23, 812 (1984).
[CrossRef] [PubMed]

D. P. Casasent, A. Mahalanobis, “Optical Iconic Filters for Large Class Recognition,” Appl. Opt. 26, 2266 (1987).
[CrossRef] [PubMed]

H. J. Caulfield, W. T. Maloney, “Improved Discrimination in Optical Character Recognition,” Appl. Opt. 8, 2354 (1969).
[CrossRef] [PubMed]

D. P. Casasent, W. Chang, “Correlation Synthetic Discriminant Functions,” Appl. Opt. 25, 2343 (1986).
[CrossRef] [PubMed]

Y. N. Hsu, H. H. Arsenault, “Pattern Discrimination by Multiple Circular Harmonic Components,” Appl. Opt. 23, 841 (1984).
[CrossRef] [PubMed]

R. Wu, H. Stark, “Rotation-Invariant Pattern Recognition Using Optimum Feature Extraction,” Appl. Opt. 24, 179 (1985).
[CrossRef] [PubMed]

H. H. Arsenault, C. Belisle, “Contrast-Invariant Pattern Recognition Using Circular Harmonic Components,” Appl. Opt. 24, 2072 (1985).
[CrossRef] [PubMed]

D. M. Cottrell, R. A. Lilly, J. A. Davis, T. Day, “Optical Correlator Performance of Binary Phase-Only Filters Using Fourier and Hartley Transforms,” Appl. Opt. 26, 3755 (1987).
[CrossRef] [PubMed]

H. H. Arsenault, C. Ferreira, M. P. Levesque, T. Szoplik, “Simple Filter with Limited Rotation Invariance,” Appl. Opt. 25, 3230 (1986).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A (3)

Opt. Eng. (3)

D. Flannery, J. Loomis, M. Milkovich, “Application of Binary Phase-Only Correlation to Machine Vision,” Opt. Eng. 27, 309 (1988).
[CrossRef]

D. Psaltis, E. G. Paek, S. S. Venkatesh, “Optical Image Correlation with a Binary Spatial Light Modulator,” Opt. Eng. 23, 698 (1984).
[CrossRef]

P. D. Gianino, J. L. Horner, “Additional Properties of the Phase-Only Correlation Filter,” Opt. Eng. 23, 695 (1984).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

B. V. K. Vijaya Kumar, Z. Bahri, “Optimality of Phase-Only Filters,” Proc. Soc. Photo-Opt. Instrum. Eng. 884, paper 23 (1988).

Other (3)

Y. Sheng, H. H. Arsenault, “Object Detection from a Real Scene Using the Correlation Peak Coordinates of Multiple Circular Harmonic Filters,” Appl. Opt.28 (1989), in press.
[CrossRef] [PubMed]

W. L. Anderson, “Particle Identification and Counting,” in Applications of Optical Fourier Transforms, H. Stark, Ed. (Academic, New York, 1982), p. 95.

H. H. Arsenault, L. Leclerc, Y. Sheng, “Similarity and Invariance in Pattern Recognition,” Proc. Soc. Photo-Opt. Instrum. Eng.960 (1988), in press.

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Figures (7)

Fig. 1
Fig. 1

Circular harmonic function of the Fourier transform ∣Fm(ρ)∣ for images of the Space Shuttle.

Fig. 2
Fig. 2

Images of aircraft. The numbers of the aircraft are incremented from left to right and from top to bottom.

Fig. 3
Fig. 3

Center correlation integration of a circular harmonic filter with an image of the Space Shuttle.

Fig. 4
Fig. 4

Space Shuttle on an air photograph background with a signal-to-noise ratio equal to 1.7.

Fig. 5
Fig. 5

(a) Correlation output of the circular harmonic filter of order m = 2 for the Space Shuttle with Fig. 4. (b) Output of the corresponding phase-only circular harmonic filter. (c) Output of the corresponding binary phase-only circular harmonic filter.

Fig. 6
Fig. 6

Image of the Space Shuttle degraded by random Gaussian noise with a signal-to-noise ratio of 2.

Fig. 7
Fig. 7

(a) Correlation output of the circular harmonic filter with m = 2 of the Space Shuttle with Fig. 6. (b) Output of the corresponding phase-only circular harmonic filter. (c) Output of the phase-only circular harmonic filter but with high spatial frequencies removed for ρ > 12. (d) Output of the corresponding binary phase-only circular harmonic filter. (e) Output of the binary phase-only circular harmonic filter with high spatial frequencies removed for ρ > 12.

Tables (1)

Tables Icon

Table I Correlation Peak Intensities for the Aircraft in Fig. 2 with the Circular Harmonic Filter (CHF), Phase-Only Circular Harmonic Filter (POCHF), and Binary Phase-Only Circular Harmonic Filter (BPOCHF)

Equations (14)

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f m ( r ) = 1 2 π 0 2 π f ( r , θ ) exp ( j m θ ) d θ .
F m ( ρ ) = 2 π ( j ) m 0 f m ( r ) J m ( 2 π r ρ ) r d r ,
H ρ ( ρ , ϕ ) =   exp   [ α m ( ρ ) ] exp   ( j m ϕ ) ,
C m = 0 0 2 π [ m G m ( ρ )   exp   ( j m ϕ ) ] × exp   [ j α m ( ρ ) ]   exp   ( j m ϕ ) ρ d ρ d ϕ = 2 π 0 | G m ( ρ ) |   exp   [ j ( β m ( ρ ) α m ( ρ ) ] ρ d ρ ,
C m = 2 π 0 | F m ( ρ ) | ρ d ρ .
E m ( ξ , η ) = 2 π 0 | F m ( ρ ; , η ) | ρ d ρ
H B ( u , υ ) = { 1 if  Re [ F ( u , υ ) ] > 0 , 1 otherwise .
H B ( u , υ ) = { 1 if  Im [ F ( u , υ ) ] > 0 , 1 otherwise .
H B ( ρ , ϕ ) = { 1 if  cos [ α m ( ρ ) + m ϕ ] > 0 , 1 otherwise,
H B ( ρ , ϕ ) = { 1 if  sin [ α m ( ρ ) + m ϕ ] > 0 , 1 otherwise,
½ [ f m ( r ) exp   ( j m θ ) + f m * ( r ) exp   ( j m θ ) ] = | f m ( r ) | cos [ m θ + γ m ( r ) ] ,
½ [ F m ( ρ ) exp   ( j m ϕ ) + F m * ( ρ ) exp   ( j m ϕ ) ] = | F m ( ρ ) | cos [ m ϕ + α m ( ρ ) ] .
C c ( δ ) = 0 0 2 π [ m =   f m ( r ) exp   ( j m θ ) ] 1 2 [ f m ( r ) exp   ( j m θ ) + f m * ( r ) exp   ( j m θ ) ] r d r d θ = 2 π 0 | f m ( r ) | 2 r d r cos m δ .
C s ( δ ) = 2 π 0 | f m ( r ) | 2 r d r sin m δ .

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