Abstract

The idea of a phase-only matched filter [ J. L. Horner and P. D. Gianino, Appl. Opt. 23, 812– 816 ( 1984)] is incorporated in the scheme of circular harmonic component matched filtering [ Y. N. Hsu and H. H. Arsenault, Appl. Opt. 21, 4016– 4019 ( 1982)]. Computer simulation showed that the phase-only circular harmonic matched filter possesses the rotational invariant property for 2-D recognition. Furthermore, it does a better job in recognizing closely placed targets compared with traditional circular harmonic filters. The simulation also demonstrated that a pure phase circular harmonic filter is less liable to give rise to false alarms in recognition because the sidelobe produced by it is much less pronounced and much less extensive than that produced by a traditional circular harmonic filter.

© 1989 Optical Society of America

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References

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  1. A. V. Oppenheim, J. S. Lim, “The Importance of Phase in Signals,” Proc. IEEE 69, 529–541 (1981).
    [CrossRef]
  2. J. L. Horner, P. D. Gianino, “Phase-Only Matched Filtering,” Appl. Opt. 23, 812–816 (1984).
    [CrossRef] [PubMed]
  3. P. D. Gianino, J. L. Horner, “Additional Properties of the Phase-Only Correlation Filter,” Opt. Eng. 23, 695–697 (1984).
    [CrossRef]
  4. H. H. Arsenault, Y. N. Hsu, K. C. Macukow, Y. Yang, “Rotation Invariant Pattern Recognition,” Proc. Soc. Photo-Opt. Instrum. Eng. 359, 266–272 (1982).
  5. Y. N. Hsu, H. H. Arsenault, “Optical Pattern Recognition Using Circular Harmonic Expansion,” Appl. Opt. 21, 4016–4019 (1982).
    [CrossRef] [PubMed]
  6. Y. N. Hsu, H. H. Arsenault, G. April, “Rotational-Invariant Digital Pattern Recognition Using Circular Harmonic Expansion,” Appl. Opt. 21, 4012–4015 (1982).
    [CrossRef] [PubMed]
  7. H. H. Arsenault, Y. N. Hsu, K. C. Macukow, “Rotation Invariant Pattern Recognition,” Opt. Eng. 23, 705–709 (1984).
    [CrossRef]
  8. Y. Sheng, H. H. Arsenault, “Method for Determining Expansion Centers and Predicting Sidelobe Levels for Circular-Harmonic Filters,” J. Opt. Soc. Am. A 4, 1793–1797 (1987).
    [CrossRef]

1987 (1)

1984 (3)

J. L. Horner, P. D. Gianino, “Phase-Only Matched Filtering,” Appl. Opt. 23, 812–816 (1984).
[CrossRef] [PubMed]

P. D. Gianino, J. L. Horner, “Additional Properties of the Phase-Only Correlation Filter,” Opt. Eng. 23, 695–697 (1984).
[CrossRef]

H. H. Arsenault, Y. N. Hsu, K. C. Macukow, “Rotation Invariant Pattern Recognition,” Opt. Eng. 23, 705–709 (1984).
[CrossRef]

1982 (3)

1981 (1)

A. V. Oppenheim, J. S. Lim, “The Importance of Phase in Signals,” Proc. IEEE 69, 529–541 (1981).
[CrossRef]

April, G.

Arsenault, H. H.

Gianino, P. D.

J. L. Horner, P. D. Gianino, “Phase-Only Matched Filtering,” Appl. Opt. 23, 812–816 (1984).
[CrossRef] [PubMed]

P. D. Gianino, J. L. Horner, “Additional Properties of the Phase-Only Correlation Filter,” Opt. Eng. 23, 695–697 (1984).
[CrossRef]

Horner, J. L.

P. D. Gianino, J. L. Horner, “Additional Properties of the Phase-Only Correlation Filter,” Opt. Eng. 23, 695–697 (1984).
[CrossRef]

J. L. Horner, P. D. Gianino, “Phase-Only Matched Filtering,” Appl. Opt. 23, 812–816 (1984).
[CrossRef] [PubMed]

Hsu, Y. N.

H. H. Arsenault, Y. N. Hsu, K. C. Macukow, “Rotation Invariant Pattern Recognition,” Opt. Eng. 23, 705–709 (1984).
[CrossRef]

Y. N. Hsu, H. H. Arsenault, “Optical Pattern Recognition Using Circular Harmonic Expansion,” Appl. Opt. 21, 4016–4019 (1982).
[CrossRef] [PubMed]

Y. N. Hsu, H. H. Arsenault, G. April, “Rotational-Invariant Digital Pattern Recognition Using Circular Harmonic Expansion,” Appl. Opt. 21, 4012–4015 (1982).
[CrossRef] [PubMed]

H. H. Arsenault, Y. N. Hsu, K. C. Macukow, Y. Yang, “Rotation Invariant Pattern Recognition,” Proc. Soc. Photo-Opt. Instrum. Eng. 359, 266–272 (1982).

Lim, J. S.

A. V. Oppenheim, J. S. Lim, “The Importance of Phase in Signals,” Proc. IEEE 69, 529–541 (1981).
[CrossRef]

Macukow, K. C.

H. H. Arsenault, Y. N. Hsu, K. C. Macukow, “Rotation Invariant Pattern Recognition,” Opt. Eng. 23, 705–709 (1984).
[CrossRef]

H. H. Arsenault, Y. N. Hsu, K. C. Macukow, Y. Yang, “Rotation Invariant Pattern Recognition,” Proc. Soc. Photo-Opt. Instrum. Eng. 359, 266–272 (1982).

Oppenheim, A. V.

A. V. Oppenheim, J. S. Lim, “The Importance of Phase in Signals,” Proc. IEEE 69, 529–541 (1981).
[CrossRef]

Sheng, Y.

Yang, Y.

H. H. Arsenault, Y. N. Hsu, K. C. Macukow, Y. Yang, “Rotation Invariant Pattern Recognition,” Proc. Soc. Photo-Opt. Instrum. Eng. 359, 266–272 (1982).

Appl. Opt. (3)

J. Opt. Soc. Am. A (1)

Opt. Eng. (2)

H. H. Arsenault, Y. N. Hsu, K. C. Macukow, “Rotation Invariant Pattern Recognition,” Opt. Eng. 23, 705–709 (1984).
[CrossRef]

P. D. Gianino, J. L. Horner, “Additional Properties of the Phase-Only Correlation Filter,” Opt. Eng. 23, 695–697 (1984).
[CrossRef]

Proc. IEEE (1)

A. V. Oppenheim, J. S. Lim, “The Importance of Phase in Signals,” Proc. IEEE 69, 529–541 (1981).
[CrossRef]

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

H. H. Arsenault, Y. N. Hsu, K. C. Macukow, Y. Yang, “Rotation Invariant Pattern Recognition,” Proc. Soc. Photo-Opt. Instrum. Eng. 359, 266–272 (1982).

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Figures (10)

Fig. 1
Fig. 1

Block diagram for the preparation of the filter function and recognition algorithm: fr(x,y), reference target; fr1(r,θ), first circular harmonic component of the reference target F r 1 * complex conjugate of the Fourier transform of fr1g(x,y) input pattern to be identified.

Fig. 2
Fig. 2

(a) Computer input consisting of four F characters in various orientations for recognition. The white spot in one of the F letters indicates the position of the proper center of the first circular harmonic component. (b) Recognition result of the input in Fig. 2(a) by the CH phase-only scheme as shown on the computer monitor. No thresholding was used. (c) Recognition result on the computer monitor of the input in Fig. 2(a) by the traditional CH filtering scheme. No thresholding.

Fig. 3
Fig. 3

(a) Computer input consisting of three F characters in various orientations for recognition. (b) Recognition result of the input in Fig. 3(a) by traditional CH filtering as shown on the computer monitor. No thresholding. (c) Recognition result on the computer monitor of the input in Fig. 3(a) by the CH phase-only filtering scheme. No thresholding.

Fig. 4
Fig. 4

Computer input consisting of three closely packed F characters in various orientations for recognition.

Fig. 5
Fig. 5

(a) Recognition result of the input in Fig. 4 by traditional CH filtering as shown on the computer monitor. No thresholding. (b), and (c) Experimental results similar to Fig. 5(a) but with higher and higher thresholding.

Fig. 6
Fig. 6

(a) Recognition result of the input in Fig. 4 by the CH phase-only scheme as shown on the computer monitor. No thresholding. (b) Experimental result similar to Fig. 6(a) but with thresholding.

Fig. 7
Fig. 7

Computer input consisting of three F, H, and E letters for recognition, (b) Recognition result of the input in (a) by traditional CH filtering as shown on the computer monitor. No thresholding. (c) Recognition result on the computer monitor of the input in (a) by the CH phase-only filtering scheme. No thresholding, (d) Experimental result similar to (c) but with thresholding, (e) Experimental result similar to (b) but with thresholding.

Fig. 8
Fig. 8

(a) Three-dimensional plot of Fig. 5(a). (b) Three-dimensional plot of Fig. 6(a).

Fig. 9
Fig. 9

(a) Three-dimensional plot of Fig. 7(b). (b) Two-dimensional view of Fig. 9(a) looking along the x-direction.

Fig. 10
Fig. 10

(a) Three-dimensional plot of Fig. 7(c). (b) Two-dimensional view of (a) looking along the x direction.

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